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SOME SIMPLE APPROXIMATIONS FOR THE DOUBLY NONCENTRAL z DISTRIBUTION
Author(s) -
SENGUPTA SUKALYAN
Publication year - 1991
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1991.tb00425.x
Subject(s) - noncentral chi squared distribution , mathematics , simple (philosophy) , distribution (mathematics) , f distribution , series (stratigraphy) , cumulative distribution function , mathematical analysis , statistics , probability distribution , ratio distribution , probability density function , asymptotic distribution , philosophy , paleontology , epistemology , estimator , biology
Summary We give two simple approximations for evaluating the cumulative probabilities of the doubly noncentral z distribution. These can easily be used for evaluating the cumulative probabilities of the doubly noncentral F distribution as well. We compare our results with those obtained by Tiku (1965) using series expansion. An industrial situation where a quality characteristic of interest follows the doubly noncentral z distribution is also cited. However, in this case the exact probabilities could be calculated using results on the ratio of two normal variables.