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The noncentral chi-squared distribution with noncentrality parameter lambda is given by P_r(x) = ...

A correction to a discrete binomial distribution to approximate a continuous distribution. P(a<=X<=b) approx P((a-1/2-np)/(sqrt(np(1-p)))<=z<=(b+1/2-np)/(sqrt(np(1-p)))), ...

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at ...

The "kurtosis excess" (Kenney and Keeping 1951, p. 27) is defined in terms of the usual kurtosis by gamma_2 = beta_2-3 (1) = (mu_4)/(mu_2^2)-3. (2) It is commonly denoted ...

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 ...

A multinomial series is generalization of the binomial series discovered by Johann Bernoulli and Leibniz. The multinomial series arises in a generalization of the binomial ...

The converse of Fisher's theorem.

The number of multisets of length k on n symbols is sometimes termed "n multichoose k," denoted ((n; k)) by analogy with the binomial coefficient (n; k). n multichoose k is ...

The number of staircase walks on a grid with m horizontal lines and n vertical lines is given by (m+n; m)=((m+n)!)/(m!n!) (Vilenkin 1971, Mohanty 1979, Narayana 1979, Finch ...

Probability and Statistics