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**A comparison between the ordinary and the length-biased modified power series distributions with applications.**
*(English)*
Zbl 0653.62014

Summary: The class of modified power series distributions (MPSD) is a very wide class which contains many well known distributions as special cases. In this article, a comparison is presented between the MPSD and its length- biased version in a unified manner. Specifically, the moments of the length-biased MPSD are expressed in terms of the moments of the original class, and the information contained in the random samples from the two classes of distributions are compared. These comparisons are studied for some members of the class.

A generalized geometric distribution is obtained as the length-biased version of a generalized log-series distribution recently presented by the authors [ibid. 14, 1779-1799 (1985; Zbl 0585.62044)]. An example is provided where the generalized geometric distribution gives a better fit than the corresponding generalized log-series distribution.

A generalized geometric distribution is obtained as the length-biased version of a generalized log-series distribution recently presented by the authors [ibid. 14, 1779-1799 (1985; Zbl 0585.62044)]. An example is provided where the generalized geometric distribution gives a better fit than the corresponding generalized log-series distribution.

### Keywords:

length-biased sampling; modified power series distributions; length- biased MPSD; moments; information; generalized geometric distribution; generalized log-series distribution### Citations:

Zbl 0585.62044
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\textit{R. C. Tripathi} and \textit{R. C. Gupta}, Commun. Stat., Theory Methods 16, 1195--1206 (1987; Zbl 0653.62014)

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### References:

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