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The third singular value k_3, corresponding to K^'(k_3)=sqrt(3)K(k_3), (1) is given by k_3=sin(pi/(12))=1/4(sqrt(6)-sqrt(2)). (2) As shown by Legendre, ...

The log-series distribution, also sometimes called the logarithmic distribution (although this work reserves that term for a distinct distribution), is the distribution of ...

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) = ...

When the elliptic modulus k has a singular value, the complete elliptic integrals may be computed in analytic form in terms of gamma functions. Abel (quoted in Whittaker and ...

The tabulation of raw data obtained by dividing it into classes of some size and computing the number of data elements (or their fraction out of the total) falling within ...

The distribution of a product of two normally distributed variates X and Y with zero means and variances sigma_x^2 and sigma_y^2 is given by P_(XY)(u) = ...

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 ...

Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is ...

The distribution of the product X_1X_2...X_n of n uniform variates on the interval [0,1] can be found directly as P_(X_1...X_n)(u) = ...

The ratio X/Y of independent normally distributed variates with zero mean is distributed with a Cauchy distribution. This can be seen as follows. Let X and Y both have mean 0 ...