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Approximations to noncentral distributions
Author(s) -
Cox David R.,
Reid Nancy
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315199
Subject(s) - cumulant , mathematics , random variable , noncentral chi squared distribution , distribution (mathematics) , gamma distribution , asymptotic expansion , edgeworth series , generalized gamma distribution , mathematical analysis , ratio distribution , asymptotic distribution , statistics , estimator
Two methods for approximating the distribution of a noncentral random variable by a central distribution in the same family are presented. The first consists of relating a stochastic expansion of a random variable to a corresponding asymptotic expansion for its distribution function. The second approximates the cumulant generating function and is used to provide central χ 2 and gamma approximations to the noncentral χ 2 and gamma distributions.