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A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance. Let chi_m^2 and chi_n^2 be independent variates ...

Fischer's z-distribution is the general distribution defined by g(z)=(2n_1^(n_1/2)n_2^(n_2/2))/(B((n_1)/2,(n_2)/2))(e^(n_1z))/((n_1e^(2z)+n_2)^((n_1+n_2)/2)) (1) (Kenney and ...

The logarithmic distribution is a continuous distribution for a variate X in [a,b] with probability function P(x)=(lnx)/(b(lnb-1)-a(lna-1)) (1) and distribution function ...

If a random variable X has a chi-squared distribution with m degrees of freedom (chi_m^2) and a random variable Y has a chi-squared distribution with n degrees of freedom ...

P(Z)=Z/(sigma^2)exp(-(Z^2+|V|^2)/(2sigma^2))I_0((Z|V|)/(sigma^2)), where I_0(z) is a modified Bessel function of the first kind and Z>0. For a derivation, see Papoulis ...

The doubly noncentral F-distribution describes the distribution (X/n_1)/(Y/n_2) for two independently distributed noncentral chi-squared variables X:chi_(n_1)^2(lambda_1) and ...

The ratio X_1/X_2 of uniform variates X_1 and X_2 on the interval [0,1] can be found directly as P_(X_1/X_2)(u) = int_0^1int_0^1delta((x_1)/(x_2)-u)dx_1dx_2 (1) = ...

A discrete distribution of a random variable such that every possible value can be represented in the form a+bn, where a,b!=0 and n is an integer.

The binomial distribution gives the discrete probability distribution P_p(n|N) of obtaining exactly n successes out of N Bernoulli trials (where the result of each Bernoulli ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...