###### Binomial Distribution

###### Poisson Distribution

###### Models, Statistical

## Association of NAD(P)H:quinone oxidoreductase (NQO1) null with numbers of basal cell carcinomas: use of a multivariate model to rank the relative importance of this polymorphism and those at other relevant loci. (1/133)

Glutathione S-transferase GSTM1 B and GSTT1 null, and cytochrome P450 CYP2D6 EM have been associated with cutaneous basal cell carcinoma (BCC) numbers, although their quantitative effects show that predisposition to many BCC is determined by an unknown number of further loci. We speculate that other loci that determine response to oxidative stress, such as NAD(H):quinone oxidoreductase (NQO1) are candidates. Accordingly, we assessed the association between NQO1 null and BCC numbers primarily to rank NQO1 null in a model that included genotypes already associated with BCC numbers. We found that only 14 out of 457 cases (3.1%) were NQO1 null. This frequency did not increase in cases with characteristics linked with BCC numbers including gender, skin type, a truncal lesion or more than one new BCC at any presentation (MPP). However, the mean number of BCC in NQO1*0 homozygotes was greater than in wild-type allele homozygotes and heterozygotes, although the difference was not quite significant (P = 0.06). These data reflect the link between NQO1 null and BCC numbers in the 42 MPP cases rather than the whole case group. We identified an interaction between NQO1 null and GSTT1 null that was associated with more BCC (P = 0.04), although only four cases had this combination. The relative influence of NQO1 null was studied in a multivariate model that included: (i) 241 patients in whom GSTM1 B, GSTT1 null and CYP2D6 EM genotype data were available, and (ii) 101 patients in whom these genotypes, as well as data on GSTM3, CYP1A1 and melanocyte-stimulating hormone receptor (MC1R) genotypes were available. NQO1 null (P = 0.001) and MC1R asp294/asp294 (P = 0.03) were linked with BCC numbers, and the association with CYP2D6 EM approached significance (P = 0.08). In a stepwise regression model only these genotypes were significantly associated with BCC numbers with NQO1 null being the most powerful predictor. (+info)## A likelihood-based method of identifying contaminated lots of blood product. (2/133)

BACKGROUND: In 1994 a small cluster of hepatitis-C cases in Rhesus-negative women in Ireland prompted a nationwide screening programme for hepatitis-C antibodies in all anti-D recipients. A total of 55 386 women presented for screening and a history of exposure to anti-D was sought from all those testing positive and a sample of those testing negative. The resulting data comprised 620 antibody-positive and 1708 antibody-negative women with known exposure history, and interest was focused on using these data to estimate the infectivity of anti-D in the period 1970-1993. METHODS: Any exposure to anti-D provides an opportunity for infection, but the infection status at each exposure time is not observed. Instead, the available data from antibody testing only indicate whether at least one of the exposures resulted in infection. Using a simple Bernoulli model to describe the risk of infection in each year, the absence of information regarding which exposure(s) led to infection fits neatly into the framework of 'incomplete data'. Hence the expectation-maximization (EM) algorithm provides estimates of the infectiousness of anti-D in each of the 24 years studied. RESULTS: The analysis highlighted the 1977 anti-D as a source of infection, a fact which was confirmed by laboratory investigation. Other suspect batches were also identified, helping to direct the efforts of laboratory investigators. CONCLUSIONS: We have presented a method to estimate the risk of infection at each exposure time from multiple exposure data. The method can also be used to estimate transmission rates and the risk associated with different sources of infection in a range of infectious disease applications. (+info)## A priori estimation of accuracy and of the number of wells to be employed in limiting dilution assays. (3/133)

The use of limiting dilution assay (LDA) for assessing the frequency of responders in a cell population is a method extensively used by immunologists. A series of studies addressing the statistical method of choice in an LDA have been published. However, none of these studies has addressed the point of how many wells should be employed in a given assay. The objective of this study was to demonstrate how a researcher can predict the number of wells that should be employed in order to obtain results with a given accuracy, and, therefore, to help in choosing a better experimental design to fulfill one's expectations. We present the rationale underlying the expected relative error computation based on simple binomial distributions. A series of simulated in machina experiments were performed to test the validity of the a priori computation of expected errors, thus confirming the predictions. The step-by-step procedure of the relative error estimation is given. We also discuss the constraints under which an LDA must be performed. (+info)## Hepatitis C virus (HCV) infection and liver-related mortality: a population-based cohort study in southern Italy. The Association for the Study of Liver Disease in Puglia. (4/133)

BACKGROUND: Hepatitis C virus (HCV) is a common cause of chronic liver diseases but the degree to which these diseases contribute to liver-related mortality is not well established. The aim of this study was to estimate the absolute and relative effects of HCV infection on liver-related mortality. METHODS: A population random sample of 2472 subjects aged > or = 30 years was enrolled and followed up from 1985 to 1996. At enrollment, a structured interview and a clinical evaluation were performed. Serum samples were tested using HCV ELISA and RIBA HCV. Outcomes were overall and liver-related mortality and tracing procedures included review of office and hospital records, death certificates, and interviews with general practitioners, attending hospital and next of kin. Statistical analysis was performed using Poisson and binomial prospective data regression. RESULTS: Crude overall and liver-related mortality rates were 7.66 (95% CI : 6.68-8.79) and 0.9 (95% CI : 0.3-2.2) per 10(3) person-years, respectively. For HCV infection effect, incidence rate ratio and difference (per 10(3) person-year), risk ratio and difference were 27.5 (95% CI : 6.5-115.6), 4 (95% CI : 3-7), 33.1 (95% CI : 7.8- 139.3) and 0.06 (95% CI : 0.04-0.08), respectively; all measures were adjusted for age at death, sex and daily alcohol intake. CONCLUSIONS: The results show a strong relative but weak absolute effect of HCV infection on liver-related mortality in the 10-year period considered. Poisson and binomial models are virtually equivalent, but the choice of the summarizing measure of effect may have a different impact on health policy. (+info)## Molecular genetic maps in wild emmer wheat, Triticum dicoccoides: genome-wide coverage, massive negative interference, and putative quasi-linkage. (5/133)

The main objectives of the study reported here were to construct a molecular map of wild emmer wheat, Triticum dicoccoides, to characterize the marker-related anatomy of the genome, and to evaluate segregation and recombination patterns upon crossing T. dicoccoides with its domesticated descendant Triticum durum (cultivar Langdon). The total map length exceeded 3000 cM and possibly covered the entire tetraploid genome (AABB). Clusters of molecular markers were observed on most of the 14 chromosomes. AFLP (amplified fragment length polymorphism) markers manifested a random distribution among homologous groups, but not among genomes and chromosomes. Genetic differentiation between T. dicoccoides and T. durum was attributed mainly to the B genome as revealed by AFLP markers. The segregation-distorted markers were mainly clustered on 4A, 5A, and 5B chromosomes. Homeoalleles, differentially conferring the vigor of gametes, might be responsible for the distortion on 5A and 5B chromosomes. Quasilinkage, deviation from free recombination between markers of nonhomologous chromosomes, was discovered. Massive negative interference was observed in most of the chromosomes (an excess of double crossovers in adjacent intervals relative to the expected rates on the assumption of no interference). The general pattern of distribution of islands of negative interference included near-centromeric location, spanning the centromere, and median/subterminal location. [An appendix describing the molecular marker loci is available as an online supplement at http://www.genome.org.] (+info)## The targeting of somatic hypermutation closely resembles that of meiotic mutation. (6/133)

We have compared the microsequence specificity of mutations introduced during somatic hypermutation (SH) and those introduced meiotically during neutral evolution. We have minimized the effects of selection by studying nonproductive (hence unselected) Ig V region genes for somatic mutations and processed pseudogenes for meiotic mutations. We find that the two sets of patterns are very similar: the mutabilities of nucleotide triplets are positively correlated between the somatic and meiotic sets. The major differences that do exist fall into three distinct categories: 1) The mutability is sharply higher at CG dinucleotides under meiotic but not somatic mutation. 2) The complementary triplets AGC and GCT are much more mutable under somatic than under meiotic mutation. 3) Triplets of the form WAN (W = T or A) are uniformly more mutable under somatic than under meiotic mutation. Nevertheless, the relative mutabilities both within this set and within the SAN (S = G or C) triplets are highly correlated with those under meiotic mutation. We also find that the somatic triplet specificity is strongly symmetric under strand exchange for A/T triplets as well as for G/C triplets in spite of the strong predominance of A over T mutations. Thus, we suggest that somatic mutation has at least two distinct components: one that specifically targets AGC/GCT triplets and another that acts as true catalysis of meiotic mutation. (+info)## Allelic imbalance on chromosomes 13 and 17 and mutation analysis of BRCA1 and BRCA2 genes in monozygotic twins concordant for breast cancer. (7/133)

To study genetic changes associated with the development of breast cancer and the extent of its hereditary predisposition, paraffin-embedded tissue samples were obtained from monozygotic twin pairs concordant for breast cancer through the linked Swedish Twin and Cancer Registries. DNA samples extracted from the matched tumour and normal tissues of nine twin pairs were analysed for allelic imbalance using a series of microsatellite markers on chromosomes 13 and 17, containing loci with known tumour suppressor genes. Multiple losses of constitutional heterozygosity (LOH), consistent with a loss of large genomic region, the whole chromosome or chromosome arm, was found in at least three pairs of twins. One double mitotic crossover was identified in one tumour sample in a pair concordant for LOH at multiple loci on both chromosomes. Recombination breakpoints were mapped to regions delineated by D13S218 and D13S263, and D13S155 and D13S279, respectively. In general, no genetic effect of losing the same allele within a twin pair was found. However, for one marker at chromosome 13 (D13S328, between the BRCA2 and the RB-1 loci) and two markers on chromosome 17 (D17S786, distal to the p53 locus, and D17S855, an intragenic BRCA1 marker) the proportion of twin pairs with the same LOH was significantly higher than expected. These regions may reflect hereditary genomic changes in our sample set. In addition, tumour DNA samples from a subset of 12 twin pairs were analysed for BRCA1 and BRCA2 mutations using exon-by-exon single-strand conformation polymorphism analysis. Two unclassified BRCA2 variants, with a putative pathogenic effect, were identified, but no pathogenic alterations were found in the BRCA1 gene. (+info)## Incidence, aetiology, and outcome of non-traumatic coma: a population based study. (8/133)

AIM: To determine the incidence, presentation, aetiology, and outcome of non-traumatic coma in children aged between 1 month and 16 years. METHODS: In this prospective, population based, epidemiological study in the former Northern NHS region of the UK, cases were notified following any hospital admission or community death associated with non-traumatic coma. Coma was defined as a Glasgow Coma Score below 12 for more than six hours. RESULTS: The incidence of non-traumatic coma was 30.8 per 100 000 children under 16 per year (6.0 per 100 000 general population per year). The age specific incidence was notably higher in the first year of life (160 per 100 000 children per year). CNS specific presentations became commoner with increasing age. In infants, nearly two thirds of presentations were with non-specific, systemic signs. Infection was the commonest overall aetiology. Aetiology remained unknown in 14% despite extensive investigation and/or autopsy. Mortality was highly dependent on aetiology, with aetiology specific mortality rates varying from 3% to 84%. With follow up to approximately 12 months, overall series mortality was 46%. (+info)**Binomial** **distribution**

... the

**binomial****distribution**is a Bernoulli**distribution**. The**binomial****distribution**is the basis for the popular**binomial**test of ... The**binomial****distribution**is a special case of the Poisson**binomial****distribution**, which is the**distribution**of a sum of n ... portal Logistic regression Multinomial**distribution**Negative**binomial****distribution**Beta-**binomial****distribution****Binomial**measure ... Interactive graphic: Univariate**Distribution**Relationships**Binomial****distribution**formula calculator Difference of two**binomial**...###### Poisson **binomial** **distribution**

The ordinary

**binomial****distribution**is a special case of the Poisson**binomial****distribution**, when all success probabilities are ... Harremoës, P. (2001). "**Binomial**and Poisson**distributions**as maximum entropy**distributions**" (PDF). IEEE Transactions on ... In probability theory and statistics, the Poisson**binomial****distribution**is the discrete probability**distribution**of a sum of ... Hong, Yili (March 2013). "On computing the**distribution**function for the Poisson**binomial****distribution**". Computational ...###### Beta-**binomial** **distribution**

The beta-

**binomial****distribution**is the**binomial****distribution**in which the probability of success at each of n trials is not ... The beta-**binomial**is a one-dimensional version of the Dirichlet-multinomial**distribution**as the**binomial**and beta**distributions**... The Beta**distribution**is a conjugate**distribution**of the**binomial****distribution**. This fact leads to an analytically tractable ... Interactive graphic: Univariate**Distribution**Relationships Beta-**binomial**functions in VGAM R package Beta-**binomial****distribution**...###### Negative **binomial** **distribution**

... negative

**binomial****distribution**Extended negative**binomial****distribution**Negative multinomial**distribution****Binomial****distribution**... The negative**binomial****distribution**is infinitely divisible, i.e., if Y has a negative**binomial****distribution**, then for any ... "Mathworks: Negative**Binomial****Distribution**". Cook, John D. "Notes on the Negative**Binomial****Distribution**" (PDF). Saha, Abhishek ... "Negative**Binomial****Distribution**". mathworld.wolfram.com. SAS Institute, "Negative**Binomial****Distribution**", SAS(R) 9.4 Functions ...###### Extended negative **binomial** **distribution**

... the extended negative

**binomial****distribution**is a discrete probability**distribution**extending the negative**binomial****distribution**... It is a truncated version of the negative**binomial****distribution**for which estimation methods have been studied. In the context ... Gerber, Hans U. (1992). "From the generalized gamma to the generalized negative**binomial****distribution**". Insurance: Mathematics ... by Willmot and put into a parametrized family with the logarithmic**distribution**and the negative**binomial****distribution**by H.U. ...###### Beta negative **binomial** **distribution**

Univariate

**Distribution**Relationships (Discrete**distributions**, Compound probability**distributions**, Factorial and**binomial**... The beta geometric**distribution**is an important special case of the beta negative**binomial****distribution**occurring for r = 1 {\ ... The beta negative**binomial****distribution**contains the beta geometric**distribution**as a special case when either r = 1 {\ ... In probability theory, a beta negative**binomial****distribution**is the probability**distribution**of a discrete random variable X {\ ...###### Conway-Maxwell-**binomial** **distribution**

...

**distribution**is a three parameter discrete probability**distribution**that generalises the**binomial****distribution**in an analogous ... Poisson**binomial****distribution**in a way analogous to the CMP and CMB generalisations of the Poisson and**binomial****distributions**. ... The**distribution**was introduced by Shumeli et al. (2005), and the name Conway-Maxwell-**binomial****distribution**was introduced ... The case ν = 1 {\displaystyle \nu =1} is the usual Poisson**binomial****distribution**and the case p 1 = ⋯ = p n = p {\displaystyle ...**Binomial** sum variance inequality

If Z has a

**binomial****distribution**with parameters n and p, then the expected value of Z is given by E[Z] = np and the variance ... If success probabilities differ, the probability**distribution**of the sum is not**binomial**. The lack of uniformity in success ... Butler, Ken; Stephens, Michael (1993). "The**distribution**of a sum of**binomial**random variables" (PDF). Technical Report No. 467 ... Drezner, Zvi; Farnum, Nicholas (1993). "A generalized**binomial****distribution**". Communications in Statistics - Theory and Methods ...**Binomial** proportion confidence interval

... but all of them rely on the assumption of a

**binomial****distribution**. In general, a**binomial****distribution**applies when an ... interval since it is based directly on the**binomial****distribution**rather than any approximation to the**binomial****distribution**. ... Because the**binomial****distribution**is a discrete probability**distribution**(i.e., not continuous) and difficult to calculate for ... instead of repeated draws of a**binomial****distribution**. In this case, the underlying**distribution**would be the hypergeometric ...**Binomial** options pricing model

The

**binomial**model assumes that movements in the price follow a**binomial****distribution**; for many trials, this**binomial**... The**Binomial**Model for Pricing Options, Prof. Thayer Watkins**Binomial**Option Pricing (PDF), Prof. Robert M. Conroy**Binomial**... Implied**binomial**tree Edgeworth**binomial**tree William F. Sharpe, Biographical, nobelprize.org Cox, J. C.; Ross, S. A.; ...**Binomial**Value, Exercise Value). For a Bermudan option, the value at nodes where early exercise is allowed is: Max (**Binomial**...###### Statistics education

Discrete Probability

**Distributions**;**Binomial****Distribution**; Poisson**Distributions**; Continuous Probability**Distributions**; The ... The coverage of "Further Statistics" includes: Continuous Probability**Distributions**; Estimation; Hypothesis Testing; One Sample ... Normal**Distribution**; Estimation; Hypothesis Testing; Chi-Squared; Correlation and Regression. ...###### Nonparametric skew

... σ where σ is the standard deviation of the

**binomial****distribution**. Burr**distribution**: Birnbaum-Saunders**distribution**: S = 2 β 2 ... examples of such**distributions**include the gamma**distribution**, inverse-chi-squared**distribution**, the inverse-gamma**distribution**... A simple example illustrating these relationships is the**binomial****distribution**with n = 10 and p = 0.09. This**distribution**when ... beta and gamma**distributions**. This rule does not hold for the unimodal Weibull**distribution**. For a unimodal**distribution**the ...**Binomial** test

... the

**binomial****distribution**is well approximated by convenient continuous**distributions**, and these are used as the basis for ... To find an answer to this question using the**binomial**test, we use the**binomial****distribution**B ( N = 235 , p = 1 / 6 ) {\ ... Calculating a p {\displaystyle p} -value for a two-tailed test is slightly more complicated, since a**binomial****distribution**... "The**binomial**test". www.graphpad.com.**Binomial**Probability Calculator (Articles needing additional references from November ...###### Ronald Fisher bibliography

doi:10.1111/j.1469-1809.1941.tb02281.x. Fisher, R. A. (1941). "The Negative

**Binomial****Distribution**". Annals of Eugenics. 11: 182 ... "The**Distribution**of Gene Ratios for Rare Mutations". Proceedings of the Royal Society of Edinburgh. 50: 205-220. 1930. (with J ... "On a**Distribution**Yielding the Error Functions of Several Well Known Statistics". Proceedings of the International Congress of ... "The**Distribution**of the Partial Correlation Coefficient". Metron. 3: 329-332. 1924. Fisher, R. A. (1924). "Studies in crop ...###### Geometric **distribution**

Hypergeometric

**distribution**Coupon collector's problem Compound Poisson**distribution**Negative**binomial****distribution**A modern ... The geometric**distribution**Y is a special case of the negative**binomial****distribution**, with r = 1. More generally, if Y1, ..., ... unlike the**binomial****distribution**which has a set number of trials. The**distribution**gives the probability that there are zero ... follows a negative**binomial****distribution**with parameters r and p. The geometric**distribution**is a special case of discrete ...###### Negative hypergeometric **distribution**

In contrast, negative-

**binomial****distribution**(like the**binomial****distribution**) deals with draws with replacement, so that the ... The negative hypergeometric**distribution**is a special case of the beta-**binomial****distribution**with parameters α = r {\ ... The negative hypergeometric**distribution**, N H G N , K , r ( k ) {\displaystyle NHG_{N,K,r}(k)} is the discrete**distribution**of ... Negative-hypergeometric**distribution**(like the hypergeometric**distribution**) deals with draws without replacement, so that the ...###### Quantitative genetics

The entire

**Binomial****Distribution**is examined here. [There is no further benefit to be had from an abbreviated example.] Earlier ... An example based upon s = 5 is likely to be biased, however, when compared to an appropriate entire**binomial****distribution**based ... which is the variance of the whole**binomial****distribution**.: 382-395 : 49-63 Furthermore, the "Wahlund equations" show that the ... provided it is unbiased with respect to the full**binomial****distribution**. ...###### Stein's method

Ehm, W. (1991). "

**Binomial**approximation to the Poisson**binomial****distribution**". Statistics & Probability Letters. 11 (1): 7-16. ... the**binomial****distribution**by Ehm (1991), Poisson processes by Barbour and Brown (1992), the Gamma**distribution**by Luk (1994), ... the standard normal**distribution**). We assume now that the**distribution**Q {\displaystyle Q} is a fixed**distribution**; in what ... However, it seems that for many**distributions**there is a particular good one, like (2.3) for the normal**distribution**. There are ...###### Tilde

... for a

**binomial****distribution**). A tilde can also be used to represent geometric similarity (e.g. ∆ABC ~ ∆DEF, meaning triangle ...###### Turn (angle)

Harremoës, Peter (2017). "Bounds on tail probabilities for negative

**binomial****distributions**". Kybernetika. 52 (6): 943-966. ...###### Tau-leaping

Chatterjee, Abhijit; Vlachos, Dionisios G.; Katsoulakis, Markos A. (2005-01-08). "

**Binomial****distribution**based τ-leap ...###### Statistical significance

2010). "Developing fundamentals of hypothesis testing using the

**binomial****distribution**". Research design and statistical ... of the sampling**distribution**. These 5% can be allocated to one side of the sampling**distribution**, as in a one-tailed test, or ... 2010). "The t**distribution**and its applications". Research Design and Statistical Analysis (3rd ed.). New York, NY: Routledge. ... of a normal**distribution**, with significance thresholds set at a much stricter level (e.g. 5σ). For instance, the certainty of ...###### Bernoulli **distribution**

"

**Binomial****distribution**", Encyclopedia of Mathematics, EMS Press, 2001 [1994]. Weisstein, Eric W. "Bernoulli**Distribution**". ... The Beta**distribution**is the conjugate prior of the Bernoulli**distribution**. The geometric**distribution**models the number of ... The Bernoulli**distribution**is a special case of the**binomial****distribution**where a single trial is conducted (so n would be 1 ... The Bernoulli**distribution**is a special case of the**binomial****distribution**with n = 1. {\displaystyle n=1.} The kurtosis goes to ...###### Andrzej Kajetan Wróblewski

Mystery of the negative

**binomial****distribution**(with co-authors; 1987), Constraints on multiplicity**distribution**of quark pairs ... New AMY and DELPHI multiplicity data and the log-normal**distribution**(with co-authors; 1990), Genesis of the lognormal ... multiplicity**distribution**in the e² e²- collisions and other stochastic processes (with co-authors; 1990), ...###### Galton board

... the

**binomial****distribution**approximates the normal**distribution**provided that the number of rows and the number of balls are ... This is the probability mass function of a**binomial****distribution**. The number of rows correspond to the size of a**binomial**... in particular that with sufficient sample size the**binomial****distribution**approximates a normal**distribution**. Among its ...**distribution**in number of trials, while the probability p of each pin is the**binomial's**p. According to the central limit ...###### Multinomial **distribution**

When k = 2, the multinomial

**distribution**is the**binomial****distribution**. Categorical**distribution**, the**distribution**of each trial ... the multinomial**distribution**is the Bernoulli**distribution**. When k is 2 and n is bigger than 1, it is the**binomial****distribution**... Discrete**distributions**, Multivariate discrete**distributions**, Factorial and**binomial**topics, Exponential family**distributions**). ... Dirichlet-multinomial**distribution**. Beta-**binomial**model. Negative multinomial**distribution**Hardy-Weinberg principle (it is a ...###### Discrete phase-type **distribution**

Negative

**binomial****distribution**- 2 or more identical phases in sequence. Mixed Geometric**distribution**- 2 or more non-identical ... Chapter 2: PH**Distributions**; ASA SIAM, 1999. (Discrete**distributions**, Types of probability**distributions**, Markov models). ... Just as the continuous time**distribution**is a generalisation of the exponential**distribution**, the discrete time**distribution**is ... Degenerate**distribution**, point mass at zero or the empty phase-type**distribution**- 0 phases. Geometric**distribution**- 1 phase. ...###### Probability **distribution** fitting

This duality is the reason that the

**binomial****distribution**is applicable. With the**binomial****distribution**one can obtain a ... the Gumbel**distribution**, the exponential**distribution**, the Pareto**distribution**, the Weibull**distribution**, the Burr**distribution**... Gumbel**distribution**, the Dagum**distribution**(mirrored Burr**distribution**), or the Gompertz**distribution**, which is bounded to the ... Probability**distribution**fitting or simply**distribution**fitting is the fitting of a probability**distribution**to a series of ...###### Latent variable model

Their conditional

**distributions**are assumed to be**binomial**or multinomial. Because the**distribution**of a continuous latent ... their conditional**distribution**given the latent variables is assumed to be normal. In latent trait analysis and latent class ... and in latent profile analysis and latent class analysis as from a multinomial**distribution**. The manifest variables in factor ... variable can be approximated by a discrete**distribution**, the distinction between continuous and discrete variables turns out ...###### Super-Poissonian **distribution**

An example of super-Poissonian

**distribution**is negative**binomial****distribution**. The Poisson**distribution**is a result of a ... In probability theory it is common to say a**distribution**, D, is a sub-**distribution**of another**distribution**E if D 's moment- ... a super-Poissonian**distribution**is a probability**distribution**that has a larger variance than a Poisson**distribution**with the ... A**distribution**is strictly sub- if C ≤ 1. From this definition a**distribution**, D, is sub-Poissonian if E X ∼ D [ exp ( t X ...###### Length of stay

Carter & Potts (2014) instead recommend use of negative

**binomial**regression. Length of stay is commonly used as a quality ... gamma and log-normal**distributions**". Value in Health. 12 (2): 309-314. doi:10.1111/j.1524-4733.2008.00421.x. PMID 20667062. ...###### Latua

241-242), as the generic element in the

**binomial**Latua venenosa. The current**binomial**, Latua pubiflora, juxtaposing Grisebach's ... The range of**distribution**of the species thus corresponds roughly to the Los Lagos Region ( Lakes Region ), the plant occurring ... The**binomial**Latua pubiflora in its entirety may thus be translated as the deadly poisonous plant with hairy flowers. The ... The plant first entered the scientific record in the mid 19th century with the publication of the Linnaean**binomial**...###### Taxonomy of lemurs

Early

**distribution**of lemur species among genera differed in a number of ways from current taxonomy. For example, the fork- ... the founder of modern**binomial**nomenclature, created the genus Lemur to include three species: Lemur tardigradus (the red ... However, the species diversity and**distribution**are now known to be significantly more complex. Revisions throughout the 1990s ...###### Short-eared owl

See a map of the short-eared owl's

**distribution**across the New World.) Sexual maturity is attained at one year. Breeding season ... The short-eared owl was formally described in 1763 by the Lutheran bishop Erik Pontoppidan under the**binomial**name Strix ... thus it has one of the most widespread**distributions**of any bird. A. flammeus breeds in Europe, Asia, North and South America, ...###### White wagtail

Information on the plumage differences and

**distribution**of the subspecies of the white wagtail is shown below. The British ... Taxobox**binomials**not recognized by IUCN). ... "Historical change of the geographical**distribution**of two ...###### Hyacinthoides non-scripta

Despite the wide

**distribution**of H. non-scripta, it reaches its greatest densities in the British Isles, where "bluebell woods ... See**binomial**nomenclature for more details of the naming rules used for plant scientific names. See Wiktionary's entry on ... "Hyacinthoides non-scripta (British bluebell) >**Distribution**and ecology". Species of the day. Natural History Museum. Retrieved ... Evidence from**distributions**and co-occurrence in Scotland" (PDF). Biological Conservation. 142 (1): 61-74. doi:10.1016/j.biocon ...###### Leptomantis gauni

ISBN 978-1-907807-42-8. Leong, T. M. & Heok., H. T. (2002). "Geographic

**distribution**: Rhacophorus gauni" (PDF). Herpetological ... Taxobox**binomials**not recognized by IUCN, Amphibians of Borneo). ...###### Willet

He placed it in the genus Scolopax and coined the

**binomial**name Scolopax semipalmata. Gmelin based his description on the " ... It has been suggested that the two subspecies be treated as separate species as there are clear differences in**distribution**, ...###### Snow petrel

... treated the larger form as a separate species and introduced the

**binomial**name Pagodroma confusa. The two forms are now usually ... forms hybridise extensively and this has led to uncertainty about the taxonomic status and the precise geographic**distribution**... the snow petrel in the genus Procellaria that had been erected for the petrels by Carl Linnaeus in 1758 and coined the**binomial**...###### Snow bunting

Despite the wide

**distribution**of this species there are only very small differences between different phenotypes. Four ... He placed it with the buntings in the genus Emberiza and coined the**binomial**name Emberiza nivalis. He specified the locality ...###### Thue-Morse sequence

This follows directly from the expansion given by the

**binomial**theorem applied to the**binomial**representing the nth element of ... An example showed how a divorcing couple might reach a fair settlement in the**distribution**of jointly-owned items. The parties ... Bugeaud, Yann (2012).**Distribution**modulo one and Diophantine approximation. Cambridge Tracts in Mathematics. Vol. 193. ...###### Relativistic mechanics

The Lorentz factor γ(v) can be expanded into a Taylor series or

**binomial**series for (v/c)2 < 1, obtaining: γ = 1 1 − ( v / c ) ... so for an extended object one sums or integrates over the**distribution**of mass. The work-energy theorem says the change in ... or integrates the density of angular momentum over the extent of a continuous mass**distribution**. Each of the six components ...###### Cryptoblepharus

There are a large number of species, with a

**distribution**range across many continents; they are the most widespread genus of ... A**binomial**authority in parentheses indicates that the species was originally described in a genus other than Cryptoblepharus. ...###### Austrogomphus praeruptus

**Distributions**and Habitats of Australian Odonata. Melbourne: CSIRO. p. 278. ISBN 0643051368. (CS1 French-language sources (fr ... Taxobox

**binomials**not recognized by IUCN). ...

###### Barrow's goldeneye

Bourget, D. (2007). "

**Distribution**, diet and dive behavior of Barrow's and common goldeneyes during spring and autumn in the St ... He placed it with the ducks, geese and swans in the genus Anas and coined the**binomial**name Anas islandica. Gmelin based his ...###### Erdős-Rényi model

The

**distribution**of the degree of any particular vertex is**binomial**: P ( deg ( v ) = k ) = ( n − 1 k ) p k ( 1 − p ) n − 1 − ... Edge-dual graphs of Erdos-Renyi graphs are graphs with nearly the same degree**distribution**, but with degree correlations and a ... Exponential random graph models describe a general probability**distribution**of graphs on "n" nodes given a set of network ... E. J.; Strogatz, S. H.; Watts, D. J. (2001). "Random graphs with arbitrary degree**distributions**and their applications". ...###### Reed-Frost model

This is an example of a "chain

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Ogilvie & Rose (2002) 94 Kloskowski, Janusz (2001). "Temporal patterns of parental resource

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Gauto, Irene; Spichiger, Rodolphe E.; Stauffer, Fred W. (2011). "Diversity,

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It has a very narrow

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The tanagers: Natural history,

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**Binomial** Probability **Distribution**

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**binomial****distribution**for 0 , s , n, and 0 , p , 1 ... the frequecies (densities) of the**binomial****distribution**for 0 , ... the probability density function of the F-**distribution**. finv(p, df1, df2). returns the critical value of the F-**distribution**,. a ... the probability density function of the t-**distribution**. tinv(p, df). returns the critical t of Students t-**distribution**,. a ... the density function of the exponential**distribution**. expinv(p, lamda). the inverse of the cumulative exponential**distribution**...###### Pig genome functional annotation enhances the biological interpretation of complex traits and human disease | Nature...

0.05 for both the

**binomial**and the hypergeometric**distribution**-based tests.. The motifs of tissue-specific EnhAs were ... By examining the**distribution**of chromatin states among all 14 tissues, we found that enhancer activity was the most variable ... The**distribution**of individual epigenetic marks and chromatin accessibility with respect to genomic features (e.g., 5UTRs and ... 16b, c). Overall, we found that the densities of chromatin states and gene elements followed a similar U-shaped**distribution**( ...###### S04 | Graduate Certificate in Theoretical Statistics & Probability

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Specific discrete probability

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Chapter 10: Discrete Probability

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###### Approximation3

- Normal Approximation Method of the Binomial Confidence Interval. (netlify.app)
- The equation for the Normal Approximation for the Binomial CI is shown below. (netlify.app)
- The standardised 'Wald' confidence interval employs the Normal approximation to the Binomial distribution sketched in Figure 1. (netlify.app)

###### Poisson Distributions2

- Both the binomial and the Poisson distributions can arise in two ways: from the terms of a discrete mathematical series, and by repeated random samples of a binary variable. (influentialpoints.com)
- Poor, HV 1991, ' The maximum difference between the binomial and Poisson distributions ', Statistics and Probability Letters , vol. 11, no. 2, pp. 103-106. (princeton.edu)

###### Parameters13

- The binomial distribution is an integer valued distribution with * two parameters, @c t and @c p. (boost.org)
- c t and @c p * are the parameters of the distribution. (boost.org)
- Construct an @c binomial_distribution object from the * parameters. (boost.org)
- Returns a random variate distributed according to the * binomial distribution with parameters specified by @c param. (boost.org)
- Returns the parameters of the distribution. (boost.org)
- Sets parameters of the distribution. (boost.org)
- Let n and p be the distribution parameters, and k1 resp. (hpmuseum.org)
- Binomial Distribution is a probability distribution that describes a likelihood of a value which would take place of either of the two independent values under a given set of parameters. (acadgild.com)
- Explicit expressions are given for the maximum error between the binomial distribution with parameters n and p and its Poisson approximants, for sufficiently small values of np. (princeton.edu)
- Calculate the parameters of the binomial distribution. (philoid.com)
- The mean and variance of binomial variate with parameters n and p are 16 and 8 respectively. (philoid.com)
- Here in my binomial calculator, I need to add in parameters of my distribution. (aspiremountainacademy.com)
- Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. (nih.gov)

###### Variance15

- begingroup$ Wouldn't it be the variance of the binomial distribution? (stackexchange.com)
- The negative binomial distribution was also small in the sense of variance. (thematlabprojects.com)
- Determine the binomial distribution whose mean is 9 and variance 9/4. (philoid.com)
- Can the mean of a binomial distribution be less than its variance? (philoid.com)
- If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution. (philoid.com)
- Find the binomial distribution when the sum of its mean and variance for 5 trials is 4.8. (philoid.com)
- In a binomial distribution, the sum and product of the mean and the variance are 25/3 and 50/3 respectively. (philoid.com)
- Find the binomial distribution whose mean is 5 and variance 10/3. (philoid.com)
- If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P(X ≤ 5). (philoid.com)
- The mean and variance of a binomial distribution are 4/3 and 8/9 respectively. (philoid.com)
- If the sum of the mean and variance of a binomial distribution for 6 trials is 10/3, find the distribution. (philoid.com)
- Also, find the mean and variance of the distribution. (philoid.com)
- Hence, find the mean and variance of the distribution. (philoid.com)
- The variance of a quasi-Poisson model is a linear function of the mean while the variance of a negative binomial model is a quadratic function of the mean. (nih.gov)
- Because the variance is a function of the mean, large and small counts get weighted differently in quasi-Poisson and negative binomial regression. (nih.gov)

###### Probabilities3

- In such a situation it is difficult and tedious to estimate expected probabilities from the binomial distribution. (influentialpoints.com)
- For example, a binomial distribution is the set of various possible outcomes and probabilities, for the number of heads observed when a coin is flipped ten times. (netlify.app)
- You can use the Binomial Distribution Calculator to automatically calculate binomial probabilities for any values for n , k , and p . (statology.org)

###### Discrete3

- The actual distribution, shown by the columns, is assumed to be a discrete Binomial distribution, but to obtain the interval we first approximate it to a continuous Normal curve, shown by the line. (netlify.app)
- 17. Nonlinear mixed-effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero-inflated discrete Weibull distribution. (nih.gov)
- 20. A robust Bayesian mixed effects approach for zero inflated and highly skewed longitudinal count data emanating from the zero inflated discrete Weibull distribution. (nih.gov)

###### Bernoulli3

- The Bernoulli distribution is a special case of the binomial, which has the same parameter, same interpretation. (stackexchange.com)
- A special case of the binomial distribution is Bernoulli distribution which is the sum of a series of multiple independent and identically distributed trials. (acadgild.com)
- The Bernoulli distribution is a special case of binomial distribution. (nih.gov)

###### Successes6

- For example if the two states of the binary variable are success and failure, their probability functions describe the average distribution of a simple statistic, the sum or frequency of the number of successes in that sample, when it is calculated from many identical random samples of an infinite population. (influentialpoints.com)
- The binomial distribution gives the number of 'successes' in a series of independent trials or random samples where the probability of success remains constant from one sample to the other - and where random selection is the only source of variation. (influentialpoints.com)
- The distribution is unimodal, in this case with a mode at 2-3 successes for a sample size of 8, as would be expected for P=0.333. (influentialpoints.com)
- P (X) provides probability of successes in n binomial trials. (acadgild.com)
- The binomial distribution in statistics describes the probability of obtaining k successes in n trials when the probability of success in a single experiment is p . (statology.org)
- If getting a doublet is considered a success, find the probability distribution of a number of successes and hence find its mean. (philoid.com)

###### IntType1

- 1 */ explicit param_type(IntType t_arg = 1, RealType p_arg = RealType (0.5)) : _t(t_arg), _p(p_arg) {} /** Returns the @c t parameter of the distribution. (boost.org)

###### Calculator4

- As with the exact binomial confidence interval method used in Chapter 4, exact methods tend to be An online Fisher exact test calculator is available at Available online 19 September 2006 and symmetry on the confidence limits for the probability of success, the parameter in a binomial distribution. (netlify.app)
- Binomial Test Calculator · Chi-Square Calculator A Single Sample Confidence Interval Calculator (T Statistic) Calculator · A Normal Distribution Generator The endpoints for the confidence interval can be determined by considering that the sample mean from a normally distributed sample is normally distributed, 16 Jan 2013 The distribution of X is entirely determined by P(X = 1) = p, since. (netlify.app)
- Return to Binomial Confidence Interval Calculator. (netlify.app)
- And to do that, we're going to use the binomial distribution calculator in StatCrunch. (aspiremountainacademy.com)

###### Mutually exclusive outcomes1

- When you receive two mutually exclusive outcomes you call it frequency distribution. (studentsassignments.com)

###### Parameter5

- Returns the @c p parameter of the distribution. (boost.org)
- A five-parameter model, called the Burr XII negative binomial distribution, is defined and studied. (ccsenet.org)
- Since P and n are combined, λ is the only parameter of the Poisson distribution. (influentialpoints.com)
- Within the interval, in this case from 0.44 to 0.64, which kind of probability distribution is it assumed for the true parameter? (netlify.app)
- Available online 19 September 2006 and symmetry on the confidence limits for the probability of success, the parameter in a binomial distribution. (netlify.app)

###### Outcomes1

- The binomial distribution states the probability that a number of positive outcomes occurs given the expected percentage of positive outcomes and the total number of observations taken. (cdc.gov)

###### Straightforward2

- One important advantage of using the Poisson formulae is that the calculations tend to be rather more straightforward than those of the binomial. (influentialpoints.com)
- To paraphrase Milton Friedman: "A good good place to start is with a simple, straightforward and inexpensive zero binomial see page 2. (thematlabprojects.com)

###### Assumption3

- Since the assumption of independence of events applies for the Poisson distribution, just as it does for the binomial, one of the commonest use of the Poisson distribution is as a test of randomness in space or time. (influentialpoints.com)
- This interval is equivariant under X → n − X and p → 1 − p, has approximately equal probability tails, is approximately unbiased, has Crow's property of minimizing the sum of the n + 1 possible lengths, and each of its ends is increasing in X and Binomial confidence interval calculation rely on the assumption of binomial distribution. (netlify.app)
- Binomial confidence interval calculation rely on the assumption of binomial distribution. (netlify.app)

###### Positives2

- This answer may give you the answer to getting to the bottom of the question with these binomial distributions, but I wanted to take time out to answer some questions I frequently hear about positive and negative binomials and about good positives. (thematlabprojects.com)
- The graph below il ustrates a possible distribution plot of the observed negatives (green bars) and positives (red bars) of these values. (nih.gov)

###### Graph1

- After that, I will choose a good positive or negative binomial: We'll start by going through the nLSY graph, which for non-linear weights is the maximum number of times a positive or negative binomial is used to estimate the probability that at a particular point in Visit Website you will generate your positive or negative binomial distribution in the first place. (thematlabprojects.com)

###### Approximate1

- When the Normal Distribution may be used to approximate a binomial distribution. (ck12.org)

###### Assignment2

- Various theories, equations that are important for completion of binomial distribution assignment help are not that easy to handle. (studentsassignments.com)
- Need binomial distribution assignment help? (studentsassignments.com)

###### Proportion4

- Select Population Binomial (Proportion vs Std) . (cdc.gov)
- 2. How does the Binomial distribution change as the sample size (n) and proportion value (p) changes? (geogebra.org)
- Interval estimation of one binomial proportion is one of the most basic problems in statistics. (netlify.app)
- confint like function which computes confidence intervals for a binomial proportion. (netlify.app)

###### Negative17

- 5 Examples Of Geometric And Negative Binomial Distributions To Inspire You To Use Meta-Analysis To Reduce Risks To Your Risk. (thematlabprojects.com)
- In fact, its authors suggest ignoring the more general negative binomial distribution and instead focusing on the negative binomial distribution itself. (thematlabprojects.com)
- What about positive and negative binomials? (thematlabprojects.com)
- A negative binomial is a linear one, with the negative binomial acting the same as a positive binomial. (thematlabprojects.com)
- However, if you have an arbitrarily small number of negative numbers and you're looking for a less than optimal binomial distribution, you'll usually want to use another bad binomial as the key. (thematlabprojects.com)
- My response is that I'm going to use 'good positive binomial distribution' to assess the effects of positive and negative binomials. (thematlabprojects.com)
- The positive net marginal distribution did not have to be exactly negative. (thematlabprojects.com)
- This implies that the overall effect size for positive and negative binomials is 1. (thematlabprojects.com)
- I've calculated its coefficient: The negative net marginal distribution is about 1. (thematlabprojects.com)
- 2. What about the "good number" of negative and good binomials? (thematlabprojects.com)
- I've seen negative binomials ranging from 0.000001% to 0. (thematlabprojects.com)
- Quasi-Poisson vs. negative binomial regression: how should we model overdispersed count data? (nih.gov)
- We present results on a data set that showed a dramatic difference on estimating abundance of harbor seals when using quasi-Poisson vs. negative binomial regression. (nih.gov)
- Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models. (nih.gov)
- 8. A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives. (nih.gov)
- 13. Two-part zero-inflated negative binomial regression model for quantitative trait loci mapping with count trait. (nih.gov)
- 16. The utility of the zero-inflated Poisson and zero-inflated negative binomial models: a case study of cross-sectional and longitudinal DMF data examining the effect of socio-economic status. (nih.gov)

###### Evaluate1

- Today we're going to learn how to use a binomial distribution to evaluate toy manufacturing quality control. (aspiremountainacademy.com)

###### Trials1

- When there is the presence of a large number of trials but the probability of the success is small, the use of binomial probability becomes redundant. (acadgild.com)

###### Cumulative2

- The binomial tables are cumulative, so we only directly look up values of \[P(X \le x)\] for particular values of \[n, \: p\] . (astarmathsandphysics.com)
- Both the error in the cumulative distribution function and that in the probability mass function are given for Poisson approximants having means λ = np and λ = -n log(1 - p). (princeton.edu)

###### Statistics1

- Students who study probability theory and statistics must be very friendly with the concept of binomial distribution. (studentsassignments.com)

###### Weibull1

- The new model contains as special cases some important lifetime distributions discussed in the literature, such as the log-logistic, Weibull, Pareto type II and Burr XII distributions, among several others. (ccsenet.org)

###### Random2

###### Theories1

- A problem that is always associated with the study with binomial theories is proper understanding of complex practical problems. (studentsassignments.com)

###### Model2

- Although it is often used differently, the Poisson model is merely a special case of the binomial one - and makes very much the same assumptions. (influentialpoints.com)
- 9. Distribution-free model selection for longitudinal zero-inflated count data with missing responses and covariates. (nih.gov)

###### Data3

- An application to real data demonstrates that the new distribution can provide a better fit than other classical lifetime models. (ccsenet.org)
- To identify the patterns in the data and statistical inferences - a data scientist should be well versed with probability distribution of data. (acadgild.com)
- 4. Distribution-free Inference of Zero-inated Binomial Data for Longitudinal Studies. (nih.gov)

###### Page1

- For X with Binomial (n, p) distribution, Section 1 gives a one-page table of .95 and .99 confidence intervals for p, for n = 1, 2, …, 30. (netlify.app)

###### Marginal1

- Using the platform, we can see that all sorts of things can be manipulated to reach our positive net marginal distribution. (thematlabprojects.com)

###### Success1

- The assumptions related to the binomial distribution is that it has only one outcome for each trial which are mutually exclusive and has same probability of success. (acadgild.com)

###### Models3

- Matsumoto, K & Hashimoto, K 1999, ' Degradation detection for telecommunication networks using time varying binomial distribution models ', Proceedings of the IEEE International Conference on Systems, Man and Cybernetics , vol. 1, pp. (elsevierpure.com)
- 1. Variable selection for distribution-free models for longitudinal zero-inflated count responses. (nih.gov)
- 2. On performance of parametric and distribution-free models for zero-inflated and over-dispersed count responses. (nih.gov)

###### Variable2

- Sometimes, when sampling a binomial variable, the probability of observing the event is very small (that is P tends to zero) and the sample size is large (that is n tends to infinity). (influentialpoints.com)
- Is x a binomial variable? (mywordsolution.com)

###### Sample size1

- Sample size of the binomial distribution. (netlify.app)

###### Values2

###### Standard3

- Find the mean and standard deviation of this binomial distribution. (mywordsolution.com)
- The mean of a binomial distribution is 20, and the standard deviation 4. (philoid.com)
- If the probability of a defective bolt is 0.1, find the (i) mean and (ii) standard deviation for the distribution of bolts in a total of 400 bolts. (philoid.com)