Concept of Sub-Independence and Characterizations of 2SQLindley and 2DQLindley Distributions

G.G. Hamedani^1,

¹Department of Mathematical and Statistical Sciences, Marquette University, Milwaukee, WI 53201-1881

Cite this paper:
G.G. Hamedani. Concept of Sub-Independence and Characterizations of 2SQLindley and 2DQLindley Distributions. American Journal of Applied Mathematics and Statistics. 2022; 10(2):39-43. doi: 10.12691/ajams-10-2-1

Abstract

Amer et al. [1] considered the distributions of the sum and the difference of two independent and identically distributed random variables with the common Quasi Lindley distribution. They derived, very nicely, the above mentioned distributions and provided certain important mathematical and statistical properties as well as simulations and applications of the new distributions. Wang and Ma [2] considered the sum of the gamma random variables under the assumption of independence of the summands and presented very interesting results. In this short note, we like to show that the assumption of "independence" can be replaced with a much weaker assumption of "sub-independence" in both papers. Then we present certain characterizations of the distributions derived by Amer et al. [1], called 2SQLindley and 2DQLindley distributions.

Keywords:
quasi lindley distribution gamma distribution sub-independence identically distributed random variables characterizations of distributions

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