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Maximum-likelihood estimation of the parameters of a four-parameter class of probability distributions

Published online by Cambridge University Press:  20 January 2009

Siegfried H. Lehnigk
Siegfried H. Lehnigk
Affiliation:
Micom, Amsmi-rd-re-op, Redstone Arsenal, AL 35898-5248, USA
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We shall concern ourselves with the class of continuous, four-parameter, one-sided probability distributions which can be characterized by the probability density function (pdf) class

It depends on the four parameters: shift c ∈ R, scale b > 0, initial shape p < 1, and terminal shape β > 0. For p ≦ 0, the definition of f(x) can be completed by setting f(c) = β/bΓ(β−1)>0 if p = 0, and f(c) = 0 if p < 0. For 0 < p < 1, f(x) remains undefined at x = c; f(x)↑ + ∞ as x↓c.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 271 - 283
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

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