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Husseiny IA, Alawady MA, Alyami SA, Abd Elgawad MA. Measures of Extropy Based on Concomitants of Generalized Order Statistics under a General Framework from Iterated Morgenstern Family. MATHEMATICS 2023; 11:1377. [DOI: 10.3390/math11061377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
In this work, we reveal some distributional characteristics of concomitants of generalized order statistics (GOS) with parameters that are pairwise different, arising from iterated Farlie–Gumbel–Morgenstern (IFGM) family of bivariate distributions. Additionally, the joint distribution and product moments of concomitants of GOS for this family are discussed. Moreover, some well-known information measures, i.e., extropy, cumulative residual extropy (CRJ), and negative cumulative extropy (NCJ), are derived. Applications of these results are given for order statistics, record values, and progressive type-II censored order statistics with uniform marginals distributions. Additionally, the issue of estimating the CRJ and NCJ is looked into, utilizing the empirical technique and the concomitant of GOS. Finally, bivariate real-world data sets have been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory.
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Affiliation(s)
- Islam A. Husseiny
- Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
| | - Metwally A. Alawady
- Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
| | - Salem A. Alyami
- Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
| | - Mohamed A. Abd Elgawad
- Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
- Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
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Berred A, Stepanov A. Asymptotic properties of lower exponential spacings under Type-II progressive censoring. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1824276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Alexandre Berred
- UFR des Sciences et Techniques, Université du Havre Normandie, Le Havre Cedex, France
| | - Alexei Stepanov
- Institute of Physics, Mathematics and Information Technology, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
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Abd Elgawad MA, Alawady MA. On concomitants of generalized order statistics from generalized FGM family under a general setting. MATHEMATICA SLOVACA 2022; 72:507-526. [DOI: 10.1515/ms-2022-0033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
AbstractIn this work, we study the distributional and moment properties of concomitants of dual generalized order statistics and consequently generalized order statistics. When the parameters are assumed to be pairwise different from Bairamov-Kotz-Becki Farlie-Gumbel-Morgenstern (BKB-FGM) family. Furthermore, an example of progressive type-II censored order statistics of BKB-FGM family under uniform distribution is obtained. Moreover, the joint distribution of dual generalized order statistics and record values of concomitants for this family are discussed. Finally, an application is given for some well-known distributions such as exponential, Pareto, and power function distributions.
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Affiliation(s)
| | - Metwally A. Alawady
- Department of Mathematics , Faculty of Science Zagazig University , Zagazig , 44519 , Egypt
- School of Computer Science and Technology , Wuhan University of Technology , Wuhan , 430070 , China
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Abd Elgawad MA, Barakat HM, Xiong S, Alyami SA. Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution. ENTROPY 2021; 23:e23030335. [PMID: 33809021 PMCID: PMC8001131 DOI: 10.3390/e23030335] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Revised: 03/06/2021] [Accepted: 03/09/2021] [Indexed: 11/25/2022]
Abstract
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.
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Affiliation(s)
- Mohamed A. Abd Elgawad
- School of Computer Science and Technology, Wuhan University of Technology, Wuhan 430070, China;
- Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
- Correspondence:
| | - Haroon M. Barakat
- Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt;
| | - Shengwu Xiong
- School of Computer Science and Technology, Wuhan University of Technology, Wuhan 430070, China;
| | - Salem A. Alyami
- Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia;
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Berred A, Stepanov A. Asymptotic results for lower exponential spacings. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2019.1565781] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Alexandre Berred
- UFR des Sciences et Techniques, Université du Havre Normandie, Le Havre Cedex, France
| | - Alexei Stepanov
- Institute of Physics, Mathematics and Information Technology, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
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Berred A, Stepanov A. Asymptotic properties of the number of near minimum-concomitant observations in the case of progressive type-II censoring. METRIKA 2014. [DOI: 10.1007/s00184-014-0502-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Ateya SF. Estimation under modified Weibull distribution based on right censored generalized order statistics. J Appl Stat 2013. [DOI: 10.1080/02664763.2013.825705] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Parsi S, Ganjali M, Farsipour NS. Conditional Maximum Likelihood and Interval Estimation for Two Weibull Populations under Joint Type-II Progressive Censoring. COMMUN STAT-THEOR M 2011. [DOI: 10.1080/03610921003764175] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Parsi S, Ganjali M, Farsipour NS. Simultaneous Confidence Intervals for the Parameters of Pareto Distribution under Progressive Censoring. COMMUN STAT-THEOR M 2010. [DOI: 10.1080/03610920802687785] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Maturi TA, Coolen-Schrijner P, Coolen FP. Nonparametric predictive comparison of lifetime data under progressive censoring. J Stat Plan Inference 2010. [DOI: 10.1016/j.jspi.2009.07.027] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Some nonparametric precedence-type tests based on progressively censored samples and evaluation of power. J Stat Plan Inference 2010. [DOI: 10.1016/j.jspi.2009.08.003] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Parsi S, Bairamov I. Expected values of the number of failures for two populations under joint Type-II progressive censoring. Comput Stat Data Anal 2009. [DOI: 10.1016/j.csda.2009.03.023] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Bairamov I, Eryilmaz S. JOINT BEHAVIOUR OF PRECEDENCES AND EXCEEDANCES IN RANDOM THRESHOLD MODELS. AUST NZ J STAT 2008. [DOI: 10.1111/j.1467-842x.2008.00512.x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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On the joint distribution of placement statistics under progressive censoring and applications to precedence test. J Stat Plan Inference 2008. [DOI: 10.1016/j.jspi.2007.06.018] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Balakrishnan N, Stepanov A. Asymptotic properties of numbers of near minimum observations under progressive Type-II censoring. J Stat Plan Inference 2008. [DOI: 10.1016/j.jspi.2007.05.029] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Beg M, Ahsanullah M. Concomitants of generalized order statistics from Farlie–Gumbel–Morgenstern distributions. ACTA ACUST UNITED AC 2008. [DOI: 10.1016/j.stamet.2007.04.001] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Kuş C, Kaya MF. Estimation for the Parameters of the Pareto Distribution Under Progressive Censoring. COMMUN STAT-THEOR M 2007. [DOI: 10.1080/03610920601077089] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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