TABLES AND GRAPHS OF THE STABLE PROBABILITY DENSITY FUNCTIONS.

Abstract

Four-decimal-place tables are presented of the probability density function p(x; alpha , beta ) of the stable distribution for alpha equals 0. 25(. 25)2. 00, beta equals minus 1. 00(. 25)1. 00, and nonnegative x in steps varying by factors of 10 from 0. 001 to 100 such that interpolation is possible, the tabulation being terminated where p(x; alpha , beta ) falls to 0. 0001. The largest such value of x is 338, for alpha equals 0. 25, beta equals minus 1. 00. Graphs of p(x; alpha , beta ) are also provided for essentially the above values of alpha and beta . The methods of calculation (from the characteristic function), checking, and interpolation with respect to x, beta , and (to some extent) alpha are described. The most important properties of stable distributions are summarized. Some applications are cited. A selected bibliography with 91 items is included.