Distributional Properties of Order Statistics and Record Statistics

Abstract

Distributional properties of the order statistics, upper and lower record statistics have been utilized to characterize distributions of interest. Further, one sided random dilation and contraction are utilized to obtain the distribution of non-adjacent ordered statistics and also their important deductions are discussed.

Characterization through distributional properties of dual generalized order statistics

“…where X sÀrÀj:nÀr is independent of X r:n if and only if X 1 $ Par(a), as obtained by Castan˜o-Martı´nez et al [5] and Khan and Shah Imtiyaz [7].…”

“…where Y sÀrÀj:sÀ1 is the (s À r À j) th order statistic from a sample of size (s À 1) drawn from exp(a) distribution and is independent of X L(s) if and only if X 1 $ Gum(a), as obtained by Khan and Shah [7].…”

“…Khan and Shah [7] have characterized distributions using distributional properties of non-adjacent lower records, upper records and order statistics. In this paper, distributional properties of the dgos have been used to characterize a general form of distributions for non-adjacent dgos under random translation, dilation and contraction, thus generalizing the results of Ahsanullah [1].…”

On a characterization of generalized Erlang-truncated exponential distribution through distributional properties of dual generalized order statistics

“…where Y j :s−1 is the j th order statistic from a sample of size (s − 1) drawn from exp(β) distribution and is independent of X L(s) if and only if X 1 ∼ Gum(β), as obtained by Khan and Shah [7].…”

Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

“…Record values appeared naturally in many real-life applications such as data relating to sport, weather, and lifetesting studies. Many authors studied record values and the associated statistics such as [1][2][3][4][5][6]. Furthermore, there are several studies which discussed some inferential methods based on record values for the Rayleigh [7,8], Weibull [9], inverse Weibull [10,11], exponentiated Family [12,13], Lomax [14,15], power Lindley model [16], exponentiated Weibull [17,18], and normal distribution [19].…”