Central Limit TVarianceSampling DistributionsDegreesProbabilitiesComputeApproximationRegressionRandom variablesConfidence IntervalsStatistical distributionsMultivariateLeast squaresMaximum likelihoodUnivariate distributionsBinomial distributionsProbability densityVariancesNoncentral chi-squareStandard deviationParametersCumulative distribuPoisson distributionEstimatorsGoodnessSignificanceDescribes the probabilitySymmetricNull hypothesisStatisticFrequency DistributionsGeometricCorrelationEstimationInferenceAsymptoticMonte CarloNoncentrality parameterMathematicalExponentialHomogeneousHypothesis TestingDensityUniform distributionContingency tableParameterTriangularTutors

- The normal, or Gaussian, distribution is one of the most familiar in statistics, endeared to statisticians by its simplicity and by virtue of the Central Limit Theorem (which states that a sample mean will follow an approximately normal distribution, if sample size is large enough, even if the data themselves are not normally distributed). (gsu.edu)
- Test statistics that follow a chi-squared distribution arise from an assumption of independent normally distributed data, which is valid in many cases due to the central limit theorem . (wikipedia.org)
- For these hypothesis tests, as the sample size, n, increases, the sampling distribution of the test statistic approaches the normal distribution (central limit theorem). (wikipedia.org)
- In the early nineteenth century Pierre-Simon Laplace (1749 - 1827), when working on the central limit theorem , showed that the distribution of sample means tends to be normally distributed: The larger the number of samples, the closer is the fit to normality - a result that holds regardless of whatever the population distribution might be. (encyclopedia.com)

- Another example is the test statistic for testing equality of means of k independent normal distributions with homogeneous variance is also distributed as an F distribution. (scirp.org)
- In this paper, we consider the problem of testing equality of means of k independent normal distributions with homogeneous variance. (scirp.org)
- a distribution in which a variable is distributed like the sum of the the squares of any given independent random variable , each of which has a normal distribution with mean of zero and variance of one. (biology-online.org)
- Xv*Xv is Chi-square distributed with v degrees of freedom with mean = v and variance = 2*v . The importance of the Chi-square distribution stems from the fact that it describes the distribution of the Variance of a sample taken from a Normal distributed population. (uva.nl)
- The distribution of the underlying sample values X has mean = 0 and variance = 1 , i.e., is Standard Normal . (uva.nl)
- Okay, so I am interested if there is a way to derive the variance for a Chi-Square distribution using the property that it is the sum of independent unit normal distributions squared. (stackexchange.com)
- distribution is obtained from the values of the ratio of the sample variance and population variance multiplied by the degrees of freedom. (richland.edu)
- The mean and variance of the chi square distribution also increase as k increases and the mean = k and variance = 2 k . (symynet.com)
- The normal distribution has two parameters, one representing the mean of the variable and one representing the variance. (gsu.edu)
- The standard normal distribution, which constrains the mean to 0 and the variance to 1, is probably the most widely known statistical distribution. (gsu.edu)
- The mean of a chi-square distribution is equal to its degrees of freedom, and the variance is equal to twice the degrees of freedom. (gsu.edu)
- Understand the role and use of moment generating functions and be able to use them to compute the expectation and variance of standard distributions. (york.ac.uk)
- Chi-squared tests are often constructed from a sum of squared errors , or through the sample variance . (wikipedia.org)
- Many other statistical tests also use this distribution, such as Friedman's analysis of variance by ranks. (wikipedia.org)
- Chi-squared test of independence in contingency tables Chi-squared test of goodness of fit of observed data to hypothetical distributions Likelihood-ratio test for nested models Log-rank test in survival analysis Cochran-Mantel-Haenszel test for stratified contingency tables It is also a component of the definition of the t-distribution and the F-distribution used in t-tests, analysis of variance, and regression analysis. (wikipedia.org)
- where exp is the exponential function, μ the mean of the distribution, σ the standard deviation , and σ 2 the variance . (encyclopedia.com)

- Sampling Distributions. (routledge.com)
- 102 . . . . . . . . . . . . . . 5 Sampling Distributions 95 5. (scribd.com)

- This new approximation exhibits remarkable accuracy even when the degrees of freedom of the F distribution are small. (scirp.org)
- distribution, where r is the degrees of freedom, which is the difference in the number of unconstrained parameters being estimated and the number of constrained parameters being estimated. (scirp.org)
- Table 5 provides the chi-square for the corresponding value of alpha and the number of degrees of freedom. (oreilly.com)
- Students compare the chi-square distribution to the standard normal distribution and determine how the Chi-Square distribution changes as they increase the degrees of freedom. (ti.com)
- As the degrees of freedom increase the distribution becomes less skewed and more symmetric. (ti.com)
- The chi-square distribution has one parameter k , the degrees of freedom. (symynet.com)
- If we wish to reject H o at the .05 level, we will determine if our value of chi square is greater than the critical value of chi square that cuts off the upper 5% of the distribution at our particular degrees of freedom value. (symynet.com)
- Degrees of freedom of the non-central chi-square distribution. (scilab.org)
- The degrees of freedom of the resulting chi-square distribution are equal to the number of variables that are summed. (gsu.edu)
- That is, a chi-square-distributed variable with d1 degrees of freedom can be added to one with d2 degrees of freedom to yield a chi-square-distributed variable with d1 + d2 degrees of freedom, as long as the two added variables are independent. (gsu.edu)
- Generate sample data of size 1000 from a noncentral chi-square distribution with degrees of freedom 8 and noncentrality parameter 3. (mathworks.com)
- Explain how the degrees of freedom affect a Chi-Square Distribution. (foxessays.com)
- Visualize how changes in degrees of freedom affect the shape of the chi square distribution. (rdrr.io)
- and the conditional distribution of Z given J = i is chi-squared with k + 2 i degrees of freedom. (wikipedia.org)
- Chi square distribution explains a variable with k degrees of liberty, dispersed like the amount of the squares of n independent random variables each which have a typical distribution with mean of absolutely no and variation of 1. (academicpaperwriter.com)
- You can quickly depend on our Chi-Square Distributions composing Help as we offer the very best services and these services are supplied to the students by our professionals who all hold master and specialized degrees or more. (academicpaperwriter.com)
- Pearson dealt first with the case in which the expected numbers m i are large enough known numbers in all cells assuming every x i may be taken as normally distributed , and reached the result that, in the limit as n becomes large, X 2 follows the χ 2 distribution with k − 1 degrees of freedom. (wikipedia.org)
- In probability theory and statistics, the chi-squared distribution (also chi-square or χ2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. (wikipedia.org)
- Zk are independent, standard normal random variables, then the sum of their squares, Q = ∑ i = 1 k Z i 2 , {\displaystyle Q\ =\sum _{i=1}^{k}Z_{i}^{2},} is distributed according to the chi-squared distribution with k degrees of freedom. (wikipedia.org)
- The chi-squared distribution has one parameter: k - a positive integer that specifies the number of degrees of freedom (i. e. the number of Zi's). (wikipedia.org)
- We can use a chi square test with 12-1=11 degrees of freedom to compare the observed data against our null hypothesis. (ucla.edu)
- Using the SOCR Chi-Square Distribution Calculator, at 11 degrees of freedom, a chi square value of 8.8 gives us a p-value of 0.36. (ucla.edu)

- This page provides a table of Chi-square distribution probabilities with degress of freedom 1-45. (causeweb.org)
- This page provides a table of F distribution probabilities for alpha = 0.10, 0.05, 0.025, and 0.01. (causeweb.org)
- these two values and two probabilities make up the probability distribution of the single coin flipping event. (mcgill.ca)
- The applet also displays the probabilities associated with the distribution. (causeweb.org)
- Use this calculator to compute F-distribution probabilities. (mathcracker.com)
- If you need to compute normal distribution probabilities, please go to our normal distribution curve calculator , where you'll find an online tool that will help with the calculation and it will graph the corresponding area. (mathcracker.com)

- Formula 26.4.25 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to compute the cumulative distribution function. (scilab.org)
- The functions in this section compute various probability distributions. (delorie.com)
- Compute the 99% confidence interval for the distribution parameters. (mathworks.com)
- Now, that is all great, but how do you compute any normal probability using the standard normal distribution? (mathcracker.com)

- In this paper, a simple chi-square approximation for the cumulative distribution of the F -distribution is obtained via an adjusted log-likelihood ratio statistic. (scirp.org)
- As a result, a normal approximation for the cdf of the F distribution is obtained. (scirp.org)
- approximation for the cdf of the F distribution is obtained. (scirp.org)
- A gaussian approximation to the distribution of a definite quadratic form. (springer.com)
- Note on an approximation to the distribution of non-central χ 2 . (springer.com)
- This applet demonstrates the Normal approximation to the Poisson Distribution. (causeweb.org)
- The basis for his statistical mathematics came from a long tradition of work on the method of least squares approximation , worked out early in the 19th century in order to estimate quantities from repeated astronomical and geodetic measures using probability theory . (britannica.com)
- For this reason, it is preferable to use the t distribution rather than the normal approximation or the chi-squared approximation for small sample size. (wikipedia.org)
- The proposed low complexity technique is analyzed in an oversampled OFDM system and a simple distribution approximation of the oversampled and linearly filtered OFDM signals is also proposed. (scirp.org)

- For example, it is used for testing: equality of variances of two independent normal distributions, equality of means in the one-way ANOVA setting, overall significance of a normal linear regression model, and so on. (scirp.org)
- Understand the theoretical framework of linear regression models: standard model assumptions, Least Squares estimators for the model parameters and their properties, inference techniques for the model parameters. (york.ac.uk)

- Distribution for random variables constrained to be equal to or greater than 0 and which (unlike normal distribution) traces an asymmetric curve. (businessdictionary.com)
- Browse other questions tagged probability statistics probability-distributions random-variables covariance or ask your own question . (stackexchange.com)
- Probability Distributions An example will make clear the relationship between random variables and probability distributions. (slideplayer.com)
- This help page describes the probability distributions provided in the Statistics package, how to construct random variables using these distributions and the functions that are typically used in conjunction with these distributions. (maplesoft.com)
- The concept of the probability distribution and the random variables which they describe underlies the mathematical discipline of probability theory , and the science of statistics . (mcgill.ca)
- Probability and Statistical Inference 1 (Autumn) will give students a theoretical and mathematically formal framework for joint and conditional distributions of random variables and for studying the asymptotic behaviour of sequences of random variables. (york.ac.uk)
- Be able to apply various limit theorems to prove convergence in probability or in distribution of a sequence of random variables. (york.ac.uk)

- The intervals next to the parameter estimates are the 95% confidence intervals for the distribution parameters. (mathworks.com)
- The chi-square distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, e. g., in hypothesis testing or in construction of confidence intervals. (wikipedia.org)

- Much of the distributional theory that underlies SEM today is built upon a handful of continuous statistical distributions--some well known, and some less so. (gsu.edu)
- The normal distribution also lies at the root of many other continuous statistical distributions. (gsu.edu)
- Monte Carlo and Statistical Distributions. (routledge.com)

- Note that the multivariate normal distribution is not a mere composite of univariate normal distributions. (gsu.edu)
- Even if every variable in a set is normally distributed, it is still possible that the combined distribution is NOT multivariate normal. (gsu.edu)
- This distribution arises in multivariate statistics as a derivative of the multivariate normal distribution . (wikipedia.org)
- Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test. (eudml.org)
- θk)T, on the basis of a sample from non-truncated or truncated multivariate Modified Power Series Distributions. (eudml.org)
- We have applied the properties of MVUE's and the results from the theory of MVU estimation to construct a goodness-of-fit chi-squared test for multivariate modified power series distributions. (eudml.org)
- BAN estimator}, language = {eng}, number = {3}, pages = {301-326}, title = {Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test. (eudml.org)
- 2011. On the distribution of sample measure of multivariate kurtosis. (springer.com)

- Surveys basic statistical methods used in the genetics and epidemiology literature, including maximum likelihood and least squares. (wiley.com)
- Gauss also derived the statistical method of least squares from the assumption that errors were normally distributed. (encyclopedia.com)

- Be able to estimate parameters of standard distributions following the Maximum Likelihood approach. (york.ac.uk)

- Continuous univariate distributions , vol. 2 of Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics . (springer.com)

- In the early eighteenth century Abraham de Moivre (1667 - 1754) showed that certain binomial distributions could be approximated by the same general curve. (encyclopedia.com)

- Discrete distributions are defined by their probability function rather than by their probability density function in order to avoid singularities. (maplesoft.com)

- For example, the test statistic for testing equality of variances of two independently distributed normal distributions is distributed as an F distribution. (scirp.org)
- On the other hand, considering testing equality of variances of two independent normal distributions, Wong derives the modified signed log-likelihood ratio statistic. (scirp.org)
- In classical statistics, there are three distributions often used in hypothesis testing: F and Chi-square distributions used in comparing variances and t distributions in comparing means. (thefreedictionary.com)

- We derive Laguerre expansions for the density and distribution functions of a sum of positive weighted noncentral chi-square variables. (springer.com)
- On the computation of noncentral chi-square distribution function. (springer.com)
- Some alternative expansions for the distribution function of a noncentral chi-square random variable. (springer.com)
- has a noncentral chi-square distribution then the distribution of X = [square root of [X. (thefreedictionary.com)
- In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. (ed.gov)
- Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the noncentral chi-square distribution is justified by statistical theory. (ed.gov)
- Actually, when the null hypothesis is not trivially violated, the noncentral chi-square distribution cannot describe the LR statistic well even when data are normally distributed and the sample size is large. (ed.gov)
- Examples with real data illustrate the difference between the noncentral chi-square distribution and the normal distribution. (ed.gov)
- Monte Carlo results compare the strength of the normal distribution against that of the noncentral chi-square distribution. (ed.gov)
- The aim is to provide the least technical material for quantitative graduate students in social science to understand the condition and limitation of the noncentral chi-square distribution. (ed.gov)
- Estimate the parameters of the noncentral chi-square distribution from the sample data. (mathworks.com)

- If we're given a sample mean, sample standard deviation,…sample size, and alpha,…what we can do is use the sampling distribution of the mean…to find the one minus alpha confidence interval. (lynda.com)
- The standard error of the mean equals…the sample standard deviation divided by…the square root of the sample size,…which is 30 divided by the square root of 100,…or 30 divided by 10, which is three. (lynda.com)
- The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. (wikipedia.org)
- It is also used in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. (ucla.edu)
- This corresponds to the case of a normal distribution with mean equal to \(\mu\) = 0, and standard deviation equal to \(\sigma\) = 1. (mathcracker.com)

- From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. (scilab.org)
- On the bad side, normal distributions increase the likelihood that the parameters of statistical models will not be identified , because there will be relatively few pieces of distinct information--fewer "knowns"--available for this purpose ( Bekker, Merckens and Wansbeek, 1994 ). (gsu.edu)
- Be able to derive a confidence interval, exact and/or approximate, for parameters of probability distributions. (york.ac.uk)
- The arguments to the algebraic functions are the value of the random variable first, then whatever other parameters define the distribution. (delorie.com)
- Returns the cumulative distribution function, its inverse, or one of its parameters, of the beta distribution. (php.net)

- Johnson and Kotz give a comprehensive review on the approximations to the cumulative distribution function (cdf) of the F distribution. (scirp.org)
- Define a custom probability density and cumulative distribution function. (mathworks.com)
- A probability distribution is called discrete if its cumulative distribution function only increases in jumps. (mcgill.ca)

- The Poisson distribution is shown in blue, and the Normal distribution is shown in red. (causeweb.org)
- 2. Significance: suppose you hypothesized that your obervations (a.k.a. sample or data) have a Poisson distribution (as in 'customer arrival' data which is usually assumed to be Poisson). (physicsforums.com)

- Bentler's EQS package includes estimators specifically designed to be appropriate for elliptical distributions. (gsu.edu)

- The Chi-Square distribution is used in the chi-square tests for goodness of fit of an observed distribution to a theoretical one and the independence of two criteria of classification of qualitative data. (ucla.edu)
- Chi Square Test for Goodness of Fit: There are 60 people in a statistics class, and we have data on the month of their birth. (ucla.edu)
- This page will calculate the value of chi-square for a one- dimensional "goodness of fit" test, for up to 8 mutually exclusive categories labeled A through H. To enter an observed cell frequency, click the cursor into the appropriate cell, then type in the value. (causeweb.org)

- Chi-Square Distributions has fantastic significance in stats. (academicpaperwriter.com)
- At the .05 significance level is there a difference in the two distributions? (scribd.com)
- I am currently using the chi-square method to determine the probability that my data is not randomly distributed, but would like have a stronger significance measurement. (physicsforums.com)
- 3. Simulate several experiments and see if the significance for the test of a uniform distribution is always significant. (onlinestatbook.com)

- A smooth function that describes the probability of landing anywhere on the dartboard is the probability distribution of the dart throwing event. (mcgill.ca)

- Chi-square is non-symmetric. (richland.edu)
- Since the chi-square distribution isn't symmetric, the method for looking up left-tail values is different from the method for looking up right tail values. (richland.edu)
- The chi squared distribution becomes more symmetric as k increases. (symynet.com)
- The distribution is unimodal and symmetric about the mean. (gsu.edu)
- Elliptical distributions are symmetric and unimodal, but are not constrained regarding kurtosis. (gsu.edu)
- While the normal distribution is symmetric, the chi-square distribution is skewed to the right, and has a minimum of 0. (gsu.edu)
- A symmetric distribution, such as normal distribution, might not be a good fit. (mathworks.com)

- Using the one-dimensional case, this article provides the details showing that the LR statistic asymptotically follows a normal distribution, which also leads to an asymptotically correct confidence interval for the discrepancy between the null hypothesis/model and the population. (ed.gov)
- A Chi-square test is a statistical hypothesis test where tasting distribution of the test data is specified as a chi square distribution while either the null hypothesis holds true or it is asymptotically real. (academicpaperwriter.com)
- Simply puts chi-square test is a test with test fact that has a chi-square distribution when the null hypothesis holds true, or any where the likelihood distribution of the test figure (presuming the null hypothesis holds true) can be made to approximate a chi-square distribution as carefully as preferred by making the sample size huge enough. (academicpaperwriter.com)
- If there is substantial distinction from the null hypothesis or weather the outcomes support the null hypothesis, Chi square table is made use of in Chi square test to examine. (academicpaperwriter.com)
- A chi-squared test , also written as χ 2 test , is any statistical hypothesis test where the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. (wikipedia.org)
- A chi-squared test can be used to attempt rejection of the null hypothesis that the data are independent. (wikipedia.org)
- Also considered a chi-squared test is a test in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chi-squared distribution as closely as desired by making the sample size large enough. (wikipedia.org)
- Pearson proposed that, under the circumstance of the null hypothesis being correct, as n → ∞ the limiting distribution of the quantity given below is the χ 2 distribution. (wikipedia.org)
- If so, then the null hypothesis that the numbers were sampled from a uniform distribution could be rejected. (onlinestatbook.com)

- is based on the asymptotic distribution of the log-likelihood ratio statistic. (scirp.org)
- The chi-square test is a statistical test based on comparison of a test statistic to a chi-square distribution . (biology-online.org)
- Chi-square Test Statistic. (routledge.com)
- Because the test statistic (such as t) is asymptotically normally distributed, provided the sample size is sufficiently large, the distribution used for hypothesis testing may be approximated by a normal distribution. (wikipedia.org)
- Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution, and the distribution of the square of the test statistic approaches a chi-squared distribution. (wikipedia.org)
- the Chi-square test statistic, your sample statistic. (coursera.org)

- Frequency Distributions. (routledge.com)

- Random variate generator for the geometric distribution, computing the number of failures before success. (haskell.org)
- Random variate generator for geometric distribution for number of trials. (haskell.org)

- The general sampling distribution of multiple correlation coefficient. (springer.com)
- This page generates a graph of the sampling distribution of r, the Pearson correlation coefficient. (causeweb.org)

- Thus, elliptical distributions themselves can be thought of as an intermediate point between the normal distribution and the general continuous distribution described in Browne's (1982) work on asymptotically distribution-free (ADF) estimation. (gsu.edu)
- Using the general theory of estimation and the results of Patil (1965) and Patel (1978) we give the tables of MVUE's for functions of parameter θ of trinomial, multinomial, negative-multinomial and left-truncated modified power series distributions. (eudml.org)
- In between there are full chapters on parametric probability distributions, sampling, Chi-Square distributions, point estimation, and tests of parametric statistical hypotheses. (maa.org)

- although both have an asymptotic chi-square distribution). (ethz.ch)

- In our example, the p-values based on the nominal chi-square distribution were often similar to those based on the Monte Carlo simulations. (thefreedictionary.com)
- Toward the bottom of the page is an option for estimating the relevant probability via Monte Carlo simulation of the multinomial sampling distribution. (causeweb.org)

- The resulting noncentral distributions are characterized by one additional parameter--a noncentrality parameter. (gsu.edu)

- As a result, the distribution mean is identical to the two alternative measures of central tendency , namely, the mode (the most frequent value of X ) and the median (the middle value of X ). Second, the mathematical function provides the basis for specifying the number of observations that should fall within select portions of the curve. (encyclopedia.com)
- In the first decade of the nineteenth century the mathematicians Adrien-Marie Legendre (1752 - 1833) and Carl Friedrich Gauss (1777 - 1855) worked out the precise mathematical formula, and Gauss demonstrated that this curve provided a close fit to the empirical distribution of observational errors. (encyclopedia.com)
- However, the normal distribution also appeared in other mathematical contexts. (encyclopedia.com)

- Unlike more widely known distributions such as the normal distribution and the exponential distribution, the chi-squared distribution is not as often applied in the direct modeling of natural phenomena. (wikipedia.org)

- The distribution of homogeneous and non-homogeneous quadratic functions of normal variables. (springer.com)

- The chi-squared distribution is used primarily in hypothesis testing. (wikipedia.org)
- The primary reason that the chi-squared distribution is used extensively in hypothesis testing is its relationship to the normal distribution. (wikipedia.org)

- Propability density function ( chi-square distribution). (blogspot.com)
- A normal distribution variable can take random values on the whole real line, and the probability that the variable belongs to any certain interval is obtained by using its density function . (mathcracker.com)

- This probability distribution is called the uniform distribution. (slideplayer.com)
- Uniform Distribution. (slideplayer.com)
- Thus, we have a uniform distribution. (slideplayer.com)
- The observed data do not show evidence of a non-uniform distribution of birth months. (ucla.edu)
- 1. Non-randomness: chi-sq. is a test of 'randomness' in the sense that if your observations are not uniformly distributed then they probably have an underlying probability distribution which is different from the uniform distribution. (physicsforums.com)
- In this simulation, 100 numbers are either sampled from a normal distribution or a uniform distribution. (onlinestatbook.com)
- The expected frequencies based on both a normal distribution (on the left) or a uniform distribution (on the right) are shown just to the left of the observed frequencies. (onlinestatbook.com)
- 2. Compare the observed frequencies from the "From a Uniform Distribution" section to the expected frequencies. (onlinestatbook.com)
- 4. Make the actual distribution a uniform distribution and do more simulated experiments. (onlinestatbook.com)
- This simulation samples 100 values from a normal or uniform distribution and calulates the the Chi Square value. (onlinestatbook.com)

- So, we construct a contingency table that shows the distribution of one variable at each level of the other variable. (symynet.com)

- Calculates any one parameter of the non-central chi-square distribution given values for the others. (scilab.org)
- Create a probability distribution object using specified parameter values. (mathworks.com)
- stats_cdf_beta - Calculates any one parameter of the beta distribution given values for the others. (php.net)

- This applet demonstrates the Binomial distribution by simulating Galton's Board, dropping balls through a triangular array of nails. (causeweb.org)

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