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A continuous distribution defined on the range x in [0,2pi) with probability density function P(x)=(e^(bcos(x-a)))/(2piI_0(b)), (1) where I_0(x) is a modified Bessel function ...

If Y_i have normal independent distributions with mean 0 and variance 1, then chi^2=sum_(i=1)^rY_i^2 (1) is distributed as chi^2 with r degrees of freedom. This makes a chi^2 ...

For a bivariate normal distribution, the distribution of correlation coefficients is given by P(r) = (1) = (2) = (3) where rho is the population correlation coefficient, ...

Kurtosis is defined as a normalized form of the fourth central moment mu_4 of a distribution. There are several flavors of kurtosis, the most commonly encountered variety of ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

In most computer programs and computing environments, the precision of any calculation (even including addition) is limited by the word size of the computer, that is, by ...

Bayesian analysis is a statistical procedure which endeavors to estimate parameters of an underlying distribution based on the observed distribution. Begin with a "prior ...

The Bernoulli distribution is a discrete distribution having two possible outcomes labelled by n=0 and n=1 in which n=1 ("success") occurs with probability p and n=0 ...

If F(x) is a probability distribution with zero mean and rho=int_(-infty)^infty|x|^3dF(x)<infty, (1) where the above integral is a stieltjes integral, then for all x and n, ...

A general type of statistical distribution which is related to the gamma distribution. Beta distributions have two free parameters, which are labeled according to one of two ...