Original Research

Parameter-rich unconditional distributions with a stochastic parameter in the conditional gamma distribution

A. Bekker, J. J. J. Roux
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 10, No 4 | a506 | DOI: https://doi.org/10.4102/satnt.v10i4.506 | © 1991 A. Bekker, J. J. J. Roux | This work is licensed under CC Attribution 4.0
Submitted: 08 July 1991 | Published: 08 July 1991

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A. Bekker,, South Africa
J. J. J. Roux,, South Africa

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Abstract

Suppose that the scale parameter in the two-parameter gamma distribution (as conditional distribution) is a function of a variate. This stochastic scale parameter is determined by the form which the regression curve can assume. Parameter-rich unconditional distributions with the two-parameter gamma distribution as a mixed distribution are derived for the regres­sion functions ay and a/y. A generalized distribution is used as a mixed distribution to derive a wide class of unconditional distributions with enrichment induced by regression parameters.

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