Probability Content of Regions Under Spherical Normal Distributions, I

An asymptotic expansion for a class of multivariate normal integrals

“…[5]). Consider the probability-mass in that portion of the cone (an infinitesimal "slab") demarcated by two adjoining (n -l)-flats orthogonal to the axis of the cone and distant x and x + dx from the vertex of the cone.…”

“…The if-functions are closely related to Godwin's G-function [1], [2] introduced in connection with the distribution of the absolute mean deviation in normal samples, and some further statistical applications of the functions have been discussed in [4] and [5]. Clearly, Kjf(x) is bounded by 1.…”

The Random-Effects Model in Discriminant Analysis

“…W iere h j s ^ ( 3 .1 .9 ) Ruben (1960) proves that fo r any B > 0 the series (3,1.7) is unformly convergent In any bounded y -in te rva l o f y > 0> and uniformly convergent fo r f l l y > 0 i f 6 is chosen so that .max |1 -g /a j <1, He also j =l i» » »*r suggests that the value:…”

Mathematical Models of Target Coverage and Missile Allocation

“…Furthermore, little if any attention is given to that part of the literature which deals with the mathematical properties of variou6 probability density functions useful in coverage problems. The reader interested in these details is referred to Ruben (1960). Part of the material in this chapter is discussed in two excellent review articles on coverage problems by Guenther and Terrag-no (1964) and Guenther (1966).…”