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A distribution with probability function P(x)=(x^(alpha-1)(1+x)^(-alpha-beta))/(B(alpha,beta)), where B is a beta function. The mode of a variate distributed as ...

Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...

Stable distributions are a class of probability distributions allowing skewness and heavy tails (Rimmer and Nolan 2005). They are described by an index of stability (also ...

The map-Airy distribution is a statistical distribution having probability density function and distribution function P(x) = 2e^(-2x^3/3)[xAi(x^2)-Ai^'(x^2)] (1) D(x) = (2) ...

The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and ...

Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. ...

Let S_n be the set of permutations of {1, 2, ..., n}, and let sigma_t be the continuous time random walk on S_n that results when randomly chosen transpositions are performed ...

The half-normal distribution is a normal distribution with mean 0 and parameter theta limited to the domain x in [0,infty). It has probability and distribution functions ...

Consider the sample standard deviation s=sqrt(1/Nsum_(i=1)^N(x_i-x^_)^2) (1) for n samples taken from a population with a normal distribution. The distribution of s is then ...

A function giving the distribution of the interpoint distances of a curve. It is defined by p(r)=1/Nsum_(ij)delta_(r_(ij)=r).