scholarly journals Measures of Extropy for Concomitants of Generalized Order Statistics in Morgenstern Family

2022 ◽  
Author(s):  
Zahra Almaspoor ◽  
Ali Akbar Jafari ◽  
Saeid Tahmasebi
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Empirical Method ◽  
Generalized Order Statistics ◽  
Concomitants Of Order Statistics ◽  
Cumulative Residual ◽  
Generalized Order

AbstractIn this paper, a measure of extropy is obtained for concomitants of m-generalized order statistics in the Morgenstern family. The cumulative residual extropy (CREX) and negative cumulative extropy (NCEX) are presented for the rth concomitant of m-generalized order statistics. In addition, the problem of estimating the CREX and NCEX is studied utilizing the empirical method in concomitants of m-generalized order statistics. Some applications of these results are given for the concomitants of order statistics and record values.

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.

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.

NONNEGATIVITY OF COVARIANCES BETWEEN FUNCTIONS OF ORDERED RANDOM VARIABLES

2007 ◽  
Vol 21 (4) ◽  
pp. 557-577 ◽  
Author(s):  
Taizhong Hu ◽  
Junchao Yao ◽  
Qingshu Lu
Keyword(s):  
Order Statistics ◽  
Random Variables ◽  
Random Variable ◽  
Record Values ◽  
Poisson Processes ◽  
Generalized Order Statistics ◽  
Geometric Processes ◽  
Unified Method ◽  
Generalized Order

In this article we investigate conditions by a unified method under which the covariances of functions of two adjacent ordered random variables are nonnegative. The main structural results are applied to several kinds of ordered random variable, such as delayed record values, continuous and discrete ℓ∞⩽-spherical order statistics, epoch times of mixed Poisson processes, generalized order statistics, discrete weak record values, and epoch times of modified geometric processes. These applications extend the main results for ordinary order statistics in Qi [28] and for usual record values in Nagaraja and Nevzorov [25].

scholarly journals Inference for generalized exponential distribution based on generalized order statistics

2015 ◽  
Vol 4 (2) ◽  
pp. 370
Author(s):  
Eldesoky Afify
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Survival Function ◽  
Simulated Data ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Generalized Exponential Distribution ◽  
Upper Record Values ◽  
Upper Record ◽  
Generalized Order

<p>Estimation of a parameter of generalized exponential distribution (gexp) is obtained based on generalized order statistics. The maximum likelihood and Bayes methods are used for this purpose. Survival function and hazard rate are also computed. Estimation based on upper record values from generalized exponential distribution is obtained as a special case and compared by simulated data.</p>

ON STOCHASTIC AND AGING PROPERTIES OF GENERALIZED ORDER STATISTICS

2011 ◽  
Vol 25 (2) ◽  
pp. 187-204 ◽  
Author(s):  
Mahdi Tavangar ◽  
Majid Asadi
Keyword(s):  
Order Statistics ◽  
Stochastic Ordering ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Type Ii ◽  
Random Data ◽  
Aging Properties ◽  
Right Censored Order Statistics ◽  
Censoring Scheme ◽  
Generalized Order

The generalized order statistics (GOS) model is a unified model that contains the well-known ordered random data such as order statistics and record values. In the present article, we investigate some stochastic ordering results and aging properties of the conditional GOS. The results of the article subsume some of the existing results, which recently are obtained in the literature, on conditional GOS. In particular, our results hold for the model of progressively type II right censored order statistics without any restriction on the censoring scheme.

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.

STOCHASTIC COMPARISONS OF GENERALIZED ORDER STATISTICS

2005 ◽  
Vol 19 (1) ◽  
pp. 99-120 ◽  
Author(s):  
Félix Belzunce ◽  
José-Angel Mercader ◽  
José-María Ruiz
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Stochastic Comparisons ◽  
Imperfect Repair ◽  
Generalized Order

In this article, we give several results on (multivariate and univariate) stochastic comparisons of generalized order statistics. We give conditions on the underlying distributions and the parameters on which the generalized order statistics are based, to obtain stochastic comparisons in the stochastic, dispersive, hazard rate, and likelihood ratio orders. Our results generalize some recent results for order statistics, record values, and generalized order statistics and provide some new results for other models such ask-record values and order statistics under multivariate imperfect repair.

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