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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.

MSC:
62E15 Exact distribution theory in statistics
62F10 Point estimation
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[1] DOI: 10.2307/1266418 · doi:10.2307/1266418
[2] Gupta R.C., Sankhya 36 pp 288– (1974)
[3] Gupta R.C., Communications in Statistics 5 pp 45– (1975) · Zbl 0326.60014 · doi:10.1080/03610927608827330
[4] Gupta R.C., Communications in Statistics 4 pp 689– (1975) · doi:10.1080/03610917508548427
[5] Gupta R.C., Scandinavian Journal of Statistics 3 pp 215– (1976)
[6] DOI: 10.1080/03610927908827786 · Zbl 0444.62017 · doi:10.1080/03610927908827786
[7] Gupta R.C., Mathematische Operations - forschung und statistics 15 pp 571– (1984)
[8] Gupta R.C., Encyclopedia of Statistical Sciences 5 pp 593– (1985)
[9] DOI: 10.1007/BF03013757 · Zbl 0267.60012 · doi:10.1007/BF03013757
[10] DOI: 10.1093/biomet/62.1.29 · Zbl 0297.92015 · doi:10.1093/biomet/62.1.29
[11] Patil G.P., Sankhya 38 pp 48– (1976)
[12] Patil G.P., In Applications of Statistics pp 383– (1977)
[13] DOI: 10.2307/2530008 · Zbl 0384.62014 · doi:10.2307/2530008
[14] Rao C.R., In Classical and Contagious Discrete Distributions pp 320– (1965)
[15] DOI: 10.2307/2682973 · doi:10.2307/2682973
[16] DOI: 10.2307/1267291 · Zbl 0238.62011 · doi:10.2307/1267291
[17] Simon R., American Journal of Epidemiology 11 pp 444– (1980)
[18] DOI: 10.1080/03610928508829014 · Zbl 0585.62044 · doi:10.1080/03610928508829014
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