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Journal Article

A Note on Characterisations of the Weibull Distribution

Dilip Roy and S. P. Mukherjee
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 48, No. 2 (Jun., 1986), pp. 250-253
Stable URL: http://www.jstor.org/stable/25050594
Page Count: 4

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Topics: Entropy, Random variables, Mathematical theorems
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A Note on Characterisations of the Weibull Distribution
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Abstract

Four different characterisations of the two-parameter Weibull law have been proposed. The first is in terms of a functional relation to be satisfied by the hazard function that need not hold for all values of the variables involved. According to the second result, failure rate follows Weibull law if and only if the parent (non-negative) random variable has an increasing failure rate Weibull distribution. Minimum Fisherian information in a somewhat restricted class of distributions provides the third characterization. The fourth states that the Weibull law has maximum entropy within the class of distributions (for non-negative random variables) with a given geometric mean and a given raw moment of an arbitrary order.

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