scholarly journals Concomitants of dual generalized order statistics from bivariate burr II distribution

2015 ◽  
Vol 33 (2) ◽  
pp. 18
Author(s):  
Haseeb Athar ◽  
Nayabuddin ◽  
M. Almech Ali
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Order Statistics ◽  
Density Function ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Lower Record ◽  
Lower Record Values ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

Dual generalized order statistics is a common approach to enable descending ordered random variables like reverse order statistics and lower record values. In this paper probability density function of single concomitant and joint probability density function of two concomitants of dual generalized order statistics from bivariate Burr II distribution are obtained and expressions for moment generating function and cumulant generating function are derived. Also the expressions for mean, variance and covariance are given. Further, results are deduced for the reverse order statistics and lower record values.

scholarly journals Inferences for generalized Topp-Leone distribution under dual generalized order statistics with applications to Engineering and COVID-19 data

2021 ◽  
Vol 16 (2) ◽  
pp. 125-141
Author(s):  
Devendra Kumar ◽  
Mazen Nassar ◽  
Sanku Dey ◽  
Ahmed Elshahhat
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Lower Record ◽  
Lower Record Values ◽  
Dual Generalized Order Statistics ◽  
Lower Records ◽  
Highest Posterior Density ◽  
Generalized Order

This article accentuates the estimation of a two-parameter generalized Topp-Leone distribution using dual generalized order statistics (dgos). In the part of estimation, we obtain maximum likelihood (ML) estimates and approximate confidence intervals of the model parameters using dgos, in particular, based on order statistics and lower record values. The Bayes estimate is derived with respect to a squared error loss function using gamma priors. The highest posterior density credible interval is computed based on the MH algorithm. Furthermore, the explicit expressions for single and product moments of dgos from this distribution are also derived. Based on order statistics and lower records, a simulation study is carried out to check the efficiency of these estimators. Two real life data sets, one is for order statistics and another is for lower record values have been analyzed to demonstrate how the proposed methods may work in practice.

scholarly journals Dual Generalized Order Statistics from Gompertz-Verhulst Distribution and Characterization

2020 ◽  
Vol 8 (4) ◽  
pp. 801-809
Author(s):  
Izhar Khan
Keyword(s):  
Order Statistics ◽  
Conditional Expectation ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Characterization Result ◽  
Lower Record ◽  
Lower Record Values ◽  
Dual Generalized Order Statistics ◽  
Reversed Order ◽  
Generalized Order

The dual generalized order statistics is a unified scheme which contains the well known decreasingly ordered random variables such as (reversed) order statistics, lower record values and lower Pfeifer record values. In this article, characterization results on Gompertz-Verhulst distribution through the conditional expectation of dual generalized order statistics based on non-adjacent dual generalized order statistics are given. These relations are deduced for moments of reversed order statistics, order statistics and lower record values. Further a characterization result through the truncated moment is also derived.

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

2013 ◽  
Vol 44 (4) ◽  
pp. 445-452
Author(s):  
Imtiyaz A. Shah
Keyword(s):  
Order Statistics ◽  
Generalized Pareto Distribution ◽  
Generalized Order Statistics ◽  
Generalized Pareto ◽  
Record Statistics ◽  
Power Function Distribution ◽  
Lower Record ◽  
Upper Record ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

Generalized Erlang-truncated exponential distribtion ${F(x)=[1-e^{-\beta(1-e^{-\lambda})x}]}$ has been characterized through translation of two non-adjacent dual generalized order statistics (dgos) and then the characterizing results are obtained for generalized Pareto distribution through dilation of dual generalized order statistics (dgos) and generalized power function distribution through pcontraction of non-adjacent generalized order statistics (gos). Further, the results are deduced for order statistics, lower record statistics, upper record statistics and adjacent generalized order statistics and dual generalized order statistics.

scholarly journals Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 335
Author(s):  
Mohamed A. Abd Elgawad ◽  
Haroon M. Barakat ◽  
Shengwu Xiong ◽  
Salem A. Alyami
Keyword(s):  
Order Statistics ◽  
General Framework ◽  
Bivariate Distribution ◽  
Generalized Order Statistics ◽  
Information Measures ◽  
Progressive Type ◽  
Information Number ◽  
Fisher Information Number ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,⋯,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.

scholarly journals Nonparametric Prediction Intervals of generalized order statistics from two independent sequences

2016 ◽  
Vol 4 (1) ◽  
pp. 36 ◽  
Author(s):  
Mostafa Mohie El-Din ◽  
Walid Emam
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Prediction Intervals ◽  
Generalized Order Statistics ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
Nonparametric Prediction ◽  
Nonparametric Prediction Intervals ◽  
Generalized Order

<p>This paper, discusses the problem of predicting future a generalized order statistic of an iid sequence sample was drawn from an arbitrary unknown distribution, based on observed also generalized order statistics from the same population. The coverage probabilities of these prediction intervals are exact and free of the parent distribution F(). Prediction formulas of ordinary order statistics and upper record values are extracted as special cases from the productive results. Finally, numerical computations on several models of ordered random variables are given to illustrate the proposed procedures.</p>

Likelihood ratio comparisons and logconvexity properties of p-spacings from generalized order statistics

2021 ◽  
pp. 1-20
Author(s):  
Mahdi Alimohammadi ◽  
Maryam Esna-Ashari ◽  
Jorge Navarro
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Stochastic Comparisons ◽  
Sequential Order Statistics ◽  
Progressive Type ◽  
Likelihood Ratio Ordering ◽  
Generalized Order

Due to the importance of generalized order statistics (GOS) in many branches of Statistics, a wide interest has been shown in investigating stochastic comparisons of GOS. In this article, we study the likelihood ratio ordering of $p$ -spacings of GOS, establishing some flexible and applicable results. We also settle certain unresolved related problems by providing some useful lemmas. Since we do not impose restrictions on the model parameters (as previous studies did), our findings yield new results for comparison of various useful models of ordered random variables including order statistics, sequential order statistics, $k$ -record values, Pfeifer's record values, and progressive Type-II censored order statistics with arbitrary censoring plans. Some results on preservation of logconvexity properties among spacings are provided as well.

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