CHARACTERIZATIONS OF THE PARETO DISTRIBUTION BY CONDITIONAL EXPECTATIONS OF RECORD VALUES

Title & Authors
CHARACTERIZATIONS OF THE PARETO DISTRIBUTION BY CONDITIONAL EXPECTATIONS OF RECORD VALUES
Lee, Min-Young;

Abstract
Let X$\small{_1}$, X$\small{_2}$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$\small{_j}$ is an upper record value of this sequence if X$\small{_j}$ > max {X$\small{_1}$,X$\small{_2}$,...,X$\small{_{j-1}}$}. We define u(n)=min{j$\small{\mid}$j> u(n-1), X$\small{_j}$ > X$\small{_{u(n-1)}}$, n $\small{\geq}$ 2} with u(1)=1. Then F(x) = 1-x$\small{^{\theta}}$, x > 1, $\small{{\theta}}$ < -1 if and only if ($\small{{\theta}}$+1)E[X$\small{_{u(n+1)}}$$\small{\mid}$X$\small{_{u(m)}}$=y] = ${\theta}E[X_{u(n)}$\small{\mid}$X_{u(m)}=y], (\theta+1)^2E[X_{u(n+2)}$\small{\mid}$X_{u(m)}=y] = \theta^2E[X_{u(n)}$\small{\mid}$X_{u(m)}=y], or (\theta+1)^3E[X_{u(n+3)}$\small{\mid}$X_{u(m)}=y] = \theta^3E[X_{u(n)}$\small{\mid}$X_{u(m)}=y], n $\small{\geq}$ M+1$.
Keywords
absolutely continuous distribution;characterization;conditional expectation;pareto distribution;record value;
Language
English
Cited by
1.
A NOTE ON THE CHARACTERIZATIONS OF PARETO DISTRIBUTION BY UPPER RECORD VALUES,Ahsanullah, Mohammad;Shakil, Mohammad;

대한수학회논문집, 2012. vol.27. 4, pp.835-842
2.
ON CHARACTERIZATIONS OF PARETO AND WEIBULL DISTRIBUTIONS BY CONSIDERING CONDITIONAL EXPECTATIONS OF UPPER RECORD VALUES,Jin, Hyun-Woo;Lee, Min-Young;

충청수학회지, 2014. vol.27. 2, pp.243-247
1.
ON CHARACTERIZATIONS OF PARETO AND WEIBULL DISTRIBUTIONS BY CONSIDERING CONDITIONAL EXPECTATIONS OF UPPER RECORD VALUES, Journal of the Chungcheong Mathematical Society, 2014, 27, 2, 243
2.
A NOTE ON THE CHARACTERIZATIONS OF PARETO DISTRIBUTION BY UPPER RECORD VALUES, Communications of the Korean Mathematical Society, 2012, 27, 4, 835
3.
Characterization of distributions by conditional expectation of record values, Journal of the Egyptian Mathematical Society, 2016, 24, 1, 83
4.
ON CHARACTERIZATIONS OF CONTINUOUS DISTRIBUTIONS BY CONDITIONAL EXPECTATIONS OF UPPER RECORD VALUES, Journal of the Chungcheong Mathematical Society, 2012, 25, 3, 501
References
1.
Inn. Inst. Stat. Math., 1978. vol.30. A, pp.429-433

2.
Nova Science publishers, 1995.

3.
Austral. J. Statist, 1977. vol.20. pp.70-73