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###### Normaldistribution
... and Distributions modeled as normal - the normal distribution being the distribution with maximum entropy for a given mean and ... The conjugate prior of the mean of a normal distribution is another normal distribution. Specifically, if x1, …, xn are iid N(μ ... Measurement errors in physical experiments are often modeled by a normal distribution. This use of a normal distribution does ... The generalized normal distribution, also known as the exponential power distribution, allows for distribution tails with ...
###### Folded normaldistribution
The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed ... the distribution of Y is a half-normal distribution. The random variable (Y/σ)2 has a noncentral chi-squared distribution with ... "The Folded Normal Distribution". J Qual Technol. 12 (4): 236-238. Elandt RC (1961). "The folded normal distribution: two ... "On multivariate folded normal distribution". Sankhya B. 75 (1): 1-15. Virtual Laboratories: The Folded Normal Distribution. ...
###### Half-normaldistribution
... follows a half-normal distribution. Thus, the half-normal distribution is a fold at the mean of an ordinary normal distribution ... see truncated normal distribution) If Y has a half-normal distribution, then (Y/σ)2 has a chi square distribution with 1 degree ... The entropy of the half-normal distribution is exactly one bit less the entropy of a zero-mean normal distribution with the ... In probability theory and statistics, the half-normal distribution is a special case of the folded normal distribution. Let X ...
###### Logit-normaldistribution
... a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If Y is a ... The logistic normal distribution is a generalization of the logit-normal distribution to D-dimensional probability vectors by ... The logistic normal distribution is a more flexible alternative to the Dirichlet distribution in that it can capture ... Beta distribution and Kumaraswamy distribution, other two-parameter distributions on a bounded interval with similar shapes ...
###### Complex normaldistribution
Distribution of the mean Normal distribution Multivariate normal distribution (a complex normal distribution is a bivariate ... The modulus of a complex normal random variable follows a Hoyt distribution. The 'circularly-symmetric normal distribution ... normal distribution) Generalized chi-squared distribution Wishart distribution Complex random variable Goodman (1963) ... has the complex normal distribution. This distribution can be described with 3 parameters: μ = E ⁡ [ Z ] , Γ = E ⁡ [ ( Z − μ ...
###### Matrix normaldistribution
... the matrix normal distribution is a probability distribution that is a generalization of the multivariate normal distribution ... Multivariate normal distribution. A K Gupta; D K Nagar (22 October 1999). "Chapter 2: MATRIX VARIATE NORMAL DISTRIBUTION". ... Dawid (1981) provides a discussion of the relation of the matrix-valued normal distribution to other distributions, including ... from the matrix normal distribution is a special case of the sampling procedure for the multivariate normal distribution. Let X ...
###### Skew normaldistribution
... the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non ... skew multivariate t distribution and others. The distribution is a particular case of a general class of distributions with ... Then the probability density function (pdf) of the skew-normal distribution with parameter α {\displaystyle \alpha } is given ... One can verify that the normal distribution is recovered when α = 0 {\displaystyle \alpha =0} , and that the absolute value of ...
###### Wrapped normaldistribution
... a wrapped normal distribution is a wrapped probability distribution that results from the "wrapping" of the normal distribution ... the circular moments of the wrapped normal distribution are the characteristic function of the normal distribution evaluated at ... e iθn drawn from a wrapped normal distribution may be used to estimate certain parameters of the distribution. The average of ... which is a useful measure of dispersion for the wrapped normal distribution and its close relative, the von Mises distribution ...
###### Split normaldistribution
The split normal distribution results from merging two halves of normal distributions. In a general case the 'parent' normal ... In probability theory and statistics, the split normal distribution also known as the two-piece normal distribution results ... of normal distributions in their common mode. The PDF of the split normal distribution is given by f ( x ; μ , σ 1 , σ 2 ) = A ... the split normal distribution reduces to normal distribution with variance σ ∗ 2 {\displaystyle \sigma _{*}^{2}} . When σ2≠σ1 ...
###### Log-normaldistribution
Likewise, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A ... The log-normal distribution also has been associated with other names, such as McAlister, Gibrat and Cobb-Douglas. A log-normal ... The log-normal distribution is the maximum entropy probability distribution for a random variate X for which the mean and ... In fact, there is a whole family of distributions with the same moments as the log-normal distribution.[citation needed] The ...
###### Normal-gamma distribution
Here λ, α and β are parameters of the joint distribution. Then (X,T) has a normal-gamma distribution, and this is denoted by ( ... In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four- ... The normal-inverse-gamma distribution is essentially the same distribution parameterized by variance rather than precision The ... parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean ...
###### Normal-Wishart distribution
The multivariate normal distribution and Wishart distribution are the component distributions out of which this distribution is ... In probability theory and statistics, the normal-Wishart distribution (or Gaussian-Wishart distribution) is a multivariate four ... is a multivariate normal distribution. The marginal distribution over μ {\displaystyle {\boldsymbol {\mu }}} is a multivariate ... The normal-inverse Wishart distribution is essentially the same distribution parameterized by variance rather than precision. ...
###### Normal-exponential-gamma distribution
As for the Laplace distribution, the pdf of the NEG distribution can be expressed as a mixture of normal distributions, f ( x ... In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a ... the distribution-names should be interpreted as meaning the density functions of those distributions. The distribution has ... of the normal-exponential-gamma distribution is proportional to f ( x ; μ , k , θ ) ∝ exp ⁡ ( ( x − μ ) 2 4 θ 2 ) D − 2 k − 1 ...
###### Normal-inverse-gamma distribution
See the articles on normal-gamma distribution and conjugate prior. See the articles on normal-gamma distribution and conjugate ... In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four- ... The normal-gamma distribution is the same distribution parameterized by precision rather than variance A generalization of this ... has an inverse gamma distribution. Then ( x , σ 2 ) {\displaystyle (x,\sigma ^{2})} has a normal-inverse-gamma distribution, ...
###### Normal-inverse-Wishart distribution
The multivariate normal distribution and inverse Wishart distribution are the component distributions out of which this ... In probability theory and statistics, the normal-inverse-Wishart distribution (or Gaussian-inverse-Wishart distribution) is a ... The normal-Wishart distribution is essentially the same distribution parameterized by precision rather than variance. If ( μ , ... is a multivariate t-distribution. Suppose the sampling density is a multivariate normal distribution y i , μ , Σ ∼ N p ( μ , Σ ...
###### Normal-inverse Gaussian distribution
The normal-inverse Gaussian distribution (NIG) is a continuous probability distribution that is defined as the normal variance- ... The normal-inverse Gaussian distribution can also be seen as the marginal distribution of the normal-inverse Gaussian process ... Hyperbolic Distributions and Distributions on Hyperbolae, Scandinavian Journal of Statistics 1978 O. Barndorff-Nielsen, Normal ... The class of normal-inverse Gaussian distributions is closed under convolution in the following sense: if X 1 {\displaystyle X ...
###### Statistics education
Binomial Distribution; Poisson Distributions; Continuous Probability Distributions; The Normal Distribution; Estimation; ... The coverage of "Further Statistics" includes: Continuous Probability Distributions; Estimation; Hypothesis Testing; One Sample ... "variability is normal" and how "coincidences… are not uncommon because there are so many possibilities." Gal (2002) suggests ... approach of reasoning under the null and the restrictions of normal theory, they use comparative box plots and bootstrap to ...
###### Normality test
The normal distribution has the highest entropy of any distribution for a given standard deviation. There are a number of ... The empirical distribution of the data (the histogram) should be bell-shaped and resemble the normal distribution. This might ... measures how well the data are modeled by a normal distribution. For normal data the points plotted in the QQ plot should fall ... of the standardized data against the standard normal distribution. Here the correlation between the sample data and normal ...
###### Student's t-distribution
This distribution results from compounding a Gaussian distribution (normal distribution) with mean μ {\displaystyle \mu } and ... Chi-squared distribution F-distribution Gamma distribution Folded-t and half-t distributions Hotelling's T-squared distribution ... t-distribution arises as the marginal distribution of the unknown mean of a normal distribution, when the dependence on an ... a t-distribution with infinitely many degrees of freedom is a normal distribution. (See Related distributions above). The first ...
###### Gaussian function
... s appear as the density function of the normal distribution, which is a limiting probability distribution of ... Also see multivariate normal distribution. A more general formulation of a Gaussian function with a flat-top and Gaussian fall- ... Normal distribution Lorentzian function Radial basis function kernel Using the logarithmic identity log ⁡ x = − log ⁡ ( 1 x ... Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian ...
###### Rachev ratio
"Beyond the Normal Distribution" (PDF). Frankfurter Allgemeine Zeitung. Retrieved 16 March 2006. Cheridito, P.; Kromer, E. (2013 ... Since the performance levels in the Rachev ratio are quantiles of the active return distribution, they are relative levels as ... In quantitative finance, non-Gaussian return distributions are common. The Rachev ratio, as a risk-adjusted performance ... they adjust according to the distribution. For example, if the scale is small, then the two performance levels will be closer ...