• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.477-493
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• 2017

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random variables like order statistics and lower record values. With this definition we give simple expressions for single and product moments of dual generalized order statistics from Dagum distribution. The results for order statistics and lower records are deduced from the relations derived and some computational works are also carried out. Further, a characterizing result of this distribution on using the conditional moment of the dual generalized order statistics is discussed. These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, skewness and kurtosis of order statistics and record values of the Dagum distribution.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.279-296
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• 1999

In this paper we establish some recurrence relations for both single and product moments of order statistics from a doubly truncated linear- exponential distribution with increasing hazard rate. These recurrence relations would enable one to compute all the higher order moments of order statistics for all sample sizes from those of the lower order in a simple recursive way. In addition, percentage points of order statistics are also discussed. These generalize the corresponding results for the linear- exponential distribution with increasing hazard rate derived by Balakrishnan and Malik(1986)

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.411-417
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• 2008

In the present paper we derive the distribution of single order statistics, joint distribution of two order statistics and the distribution of product and quotient of two order statistics when the independent random variables are from continuous Kumaraswamy distribution. In particular the distribution of product and quotient of extreme order statistics and consecutive order statistics have also been obtained. The method used is based on Mellin transform and its inverse.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.299-311
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• 1999

In this paper the single and product moments of order statistics of the doubly truncated Rayleigh distribution are studied. Some recurrence relations of order statistics are derived. Using order statistics, also characterization of the Rayleigh distribution are derived.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.347-361
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• 2014

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto or Lomax distribution. In this paper, we established exact expressions and recurrence relations satised by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.487-494
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• 2015

A calculation of the Kullback-Leibler information of consecutive order statistics is complicated because it depends on a multi-dimensional integral. Park (2014) discussed a representation of the Kullback-Leibler information of the first r order statistics in terms of the hazard function and simplified the r-fold integral to a single integral. In this paper, we first express the Kullback-Leibler information in terms of the reversed hazard function. Then we establish a generalized result of Park (2014) to an arbitrary consecutive order statistics. We derive a single integral form of the Kullback-Leibler information of an arbitrary block of order statistics; in addition, its relation to the Fisher information of order statistics is discussed with numerical examples provided.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.441-451
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• 2013

In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.385-396
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• 2016

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.187-195
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• 1996

This paper deals with the stochastic comparisons of order statistics from independent but nonidentically distributed (i.n.i.d) variates. And we consider order statistics under positive dependence, negative dependence, and exchangeability.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.184-197
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• 1995

An objective and one-step detection procedure of multiple outliers is suggested by using the gaps of the order statistics. The detection procedure can be used as a routine outlier detection method of a statistical analysis computer program. The procedure is applied to some examples including the data selected by Kitagawa.