Polish Statistical Association

Central Statistical Office of Poland

**Subject:** Economics, Statistics & Probability

**ISSN:** 1234-7655

**eISSN:** 2450-0291

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**Keywords : **
Factorial moment generating function,
Skewness; Kurtosis,
Poisson distribution

**Citation Information : **
Statistics in Transition New Series. Volume 20,
Issue 3,
Pages 1-29,
DOI: https://doi.org/10.21307/stattrans-2019-022

**License : **
(CC BY-NC-ND 4.0)

**Received Date : **09-June-2018
/
**Published Online: ** 04-September-2019

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In this paper, we examined the characteristics of the sum of independent and non-identical set of binomial ranked set samples, where each set has different order depending success probability. The characterization is done by establishing the general recurrence relations for two different situations based on the number of cycle, which is initially pre-assumed as a constant integer and when it is a random variable. To extend the knowledge about the characteristics of sum in terms of their behaviour and pattern, ﬁrst four moments i.e., mean, variance, skewness and kurtosis are derive and compared with the sum of binomial simple random samples with same success probability. The proposed procedure has been illustrated through a reallife data on survivorship of children below one year in Empowered Action Groups (EAG) states of India.

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