Abstract
The poblem of characterizing of discrete probability distributions is an important problem. Recently many new results are obtained in characterization of distributions using kth records. Based on the distributional properties of kth weak and ordinary records some characterizations of geometric and discrete pareto distributions are given.
Highlights
Let X1, X 2, 2 be a sequence of independent and identically distributed (i.i.d) random variables taking values 0, 1, with probability function = p j P= ( X1 j ) and q j = P ( X1 ≥ j ), j ≥ 0
The properties and characterizations for kth record values from continuous and discrete distribution have been widely studied in books as Ahsanullah (1995)
We refer the interested readers to the reference Ahsanullah and Hamedani (2012) for characterizations of continuous distributions via conditional survival function of generalized order statistics
Summary
Let X1, X 2, 2 be a sequence of independent and identically distributed (i.i.d) random variables taking values 0, 1, with probability function = p j P= ( X1 j ) and q j = P ( X1 ≥ j ), j ≥ 0 . Many characterization studies are based on kth record values and most of them are based on conditional expectation. The properties and characterizations for kth record values from continuous and discrete distribution have been widely studied in books as Ahsanullah (1995). Characterization studies based on kth record values of geometric distribution introduced by Danielak and Dembinska (2007), Dembinska and Lopez-Blazquez (2005a), Dembinska (2008).
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