Characterization of the sum of binomial random variables under ranked set sampling

Vivek Verma; Dilip C. Nath

doi:10.21307/stattrans-2019-022

Characterization of the sum of binomial random variables under ranked set sampling

Vivek Verma Department of Neurology, All India Institute of Medical Sciences, New Delhi, 110029, India , Dilip C. Nath Assam University, Silchar, 788011, Assam, India Statistics in Transition new series, vol. 20, 2019, 3, pages: 1-29 Published online: 30 August 2019 DOI 10.21307/stattrans-2019-022

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ABSTRACT

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.

KEYWORDS

Factorial moment generating function, Skewness; Kurtosis, Poisson distribution

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