• Title, Summary, Keyword: order statistics

### RELATIONS OF DAGUM DISTRIBUTION BASED ON DUAL GENERALIZED ORDER STATISTICS

• KUMAR, DEVENDRA
• 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.

### On Distribution of Order Statistics from Kumaraswamy Distribution

• Garg, Mridula
• 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.

### Moments of Order Statistics from Doubly Truncated Linear-Exponential Distribution

• Saran, Jagdish;Pushkarna, Narinder
• 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)

### Recurrence Relation and Characterization of The Rayleigh Distribution Using Order Statistics

• Lee, In-Suk;Kim, Sang-Moon
• 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.

### RECURRENCE RELATIONS FOR QUOTIENT MOMENTS OF GENERALIZED PARETO DISTRIBUTION BASED ON GENERALIZED ORDER STATISTICS AND CHARACTERIZATION

• Kumar, Devendra
• 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.

### Kullback-Leibler Information of Consecutive Order Statistics

• Kim, Ilmun;Park, Sangun
• 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.

### MOMENTS OF LOWER GENERALIZED ORDER STATISTICS FROM DOUBLY TRUNCATED CONTINUOUS DISTRIBUTIONS AND CHARACTERIZATIONS

• Kumar, Devendra
• 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.

### Recurrence Relations in the Fisher Information in Order Statistics

• Park, Sang-Un
• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.397-402
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• 1999
• We first derive the Fisher information identity in order statistics in terms of the hazard rate by considering the Fisher information identity in terms of the hazard rate (Efron and Johnstone, 1990). Then we use the identity and show an interesting and useful result that some identities and recurrence relations for the Fisher information in order statistics can be directly obtained from those between the c.d.f.s of order statistics.

### CHARACTERIZATIONS OF PARETO, WEIBULL AND POWER FUNCTION DISTRIBUTIONS BASED ON GENERALIZED ORDER STATISTICS

• Ahsanullah, Mohammad;Hamedani, G.G.
• 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.

### Stochastic Comparisons of Order Statistics under Non-standard Conditions

• Kim, S. H.
• 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.