Moments of Generalized Record Values from Kumaraswamy-log-logistic Distribution and Related Inferences
Keywords:
Order statistics, generalized upper record values, record values, Kumaraswamy-Fisk or Kumaraswamy-log-logistic distribution, single moments, product moments, recurrence relations, truncated moment, characterizationAbstract
In this paper, explicit expression for single moments and some recurrence relations satisfied by single and product moments of generalized upper record statistics or k-th upper record values from the Kumaraswamy-Fisk or Kumaraswamy-log-logistic distribution are derived. These relations can be used to obtain the higher order moments from those of the lower order. The results obtained are deduced for moments of upper record statistics. Further, conditional expectation, recurrence relations for the single as well as product moments and truncated moment are used to characterize this distribution.
References
Ahsanullah M. Record statistics. New York: Nova Science Publishers; 1995.
Ahsanullah M, Nevzorov VB. Record via probability theory. Paris: Atlantis Press; 2015.
Ahsanullah M, Shakil M, Golam Kibria BM. Characterization of continuous distribution by truncated moment. J Mod Appl Stat Methods. 2016; 15: 316-331.
Arnold BC, Balakrishnan N, Nagaraja HN. Records. New York: John Wiley; 1998.
Balakrishnan N, Cohen AC. Order statistics and inference: estimation methods. San Diego: Academic Press; 1991.
Chandler KN. The distribution and frequency of record values. J Roy Stat Soc Ser B. 1952; 14: 220-228.
Danielak K, Raqab MZ. Sharp bounds for expectations of k-th record increments. Aust NZ J Stat. 2004; 46: 665-673.
Dziubdziela W, Kopociński B. Limiting properties of the k-th record value. Appl Math (Warsaw). 1976; 15: 187-190.
Gradshteyn IS, Ryzhik IM. Tables of integrals, series of products. New York: Academic Press; 2007.
Grudzień Z. Characterization of distribution of time limits in record statistics as well as distributions and moments of linear record statistics from the sample of random numbers. Lublin: Praca Doktorska, UMCS; 1982.
Grudzień Z, Szynal D. On the expected values of k-th record values and association characterizations of distributions. Prob Stat Decision Theory A. 1983; 119-127.
Grudzień Z, Szynal D. Characterization of continuous distributions via moments of k-th record values with random indices. J Appl Stat Sci. 1997; 5: 259-266.
Huang S, Oluyede BO. Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data. J Stat Dist Appl. 2014; 18: 1-20.
Hwang JS, Lin GD. On a generalized moments problem II. Proc Amer Math Soc. 1984; 91: 577-580.
Kamps U. A concept of generalized order statistics. Germany: B.G. Teubner Stuttgart; 1995.
Khan RU, Khan MA. Moment properties of generalized order statistics from exponential-Weibull lifetime distribution. J Adv Stat. 2016; 1: 146-155.
Khan RU, Kulshrestha A, Khan MA. Relations for moments of -th record values from exponential-Weibull lifetime distribution and a characterization. J. Egyptian Math. Soc. 2015; 23: 558-562.
Khan RU, Khan MA, Khan MAR. Relations for moments of generalized record values from additive Weibull distribution and associated inference. Stat Optim Inf Comput. 2017; 5: 127-136.
Minimol S, Thomos PY. On some properties of Makeham distribution using generalized record values and its characterization. Braz J Probab Stat. 2013; 27: 487-501.
Minimol S, Thomos PY. On characterization of Gompertz distribution by properties of generalized record values. J Stat Theory Appl. 2014; 13: 38-45.
Pawlas P, Szynal D. Relations for single and product moments of k-th record values from exponential and Gumble distributions. J Appl Stat Sci. 1998; 7: 53-62.
Pawlas P, Szynal D. Recurrence relations for single and product moments of k-th record values from Pareto, generalized Pareto and Burr distributions. Comm Statist Theory Methods. 1999; 28: 1699-1709.
Pawlas P, Szynal D. Recurrence relations for single and product moments of k-th record values from Weibull distribution and a characterization. J Appl Stat Sci. 2000; 1: 17-25.
Ahsanullah M, Nevzorov VB. Record via probability theory. Paris: Atlantis Press; 2015.
Ahsanullah M, Shakil M, Golam Kibria BM. Characterization of continuous distribution by truncated moment. J Mod Appl Stat Methods. 2016; 15: 316-331.
Arnold BC, Balakrishnan N, Nagaraja HN. Records. New York: John Wiley; 1998.
Balakrishnan N, Cohen AC. Order statistics and inference: estimation methods. San Diego: Academic Press; 1991.
Chandler KN. The distribution and frequency of record values. J Roy Stat Soc Ser B. 1952; 14: 220-228.
Danielak K, Raqab MZ. Sharp bounds for expectations of k-th record increments. Aust NZ J Stat. 2004; 46: 665-673.
Dziubdziela W, Kopociński B. Limiting properties of the k-th record value. Appl Math (Warsaw). 1976; 15: 187-190.
Gradshteyn IS, Ryzhik IM. Tables of integrals, series of products. New York: Academic Press; 2007.
Grudzień Z. Characterization of distribution of time limits in record statistics as well as distributions and moments of linear record statistics from the sample of random numbers. Lublin: Praca Doktorska, UMCS; 1982.
Grudzień Z, Szynal D. On the expected values of k-th record values and association characterizations of distributions. Prob Stat Decision Theory A. 1983; 119-127.
Grudzień Z, Szynal D. Characterization of continuous distributions via moments of k-th record values with random indices. J Appl Stat Sci. 1997; 5: 259-266.
Huang S, Oluyede BO. Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data. J Stat Dist Appl. 2014; 18: 1-20.
Hwang JS, Lin GD. On a generalized moments problem II. Proc Amer Math Soc. 1984; 91: 577-580.
Kamps U. A concept of generalized order statistics. Germany: B.G. Teubner Stuttgart; 1995.
Khan RU, Khan MA. Moment properties of generalized order statistics from exponential-Weibull lifetime distribution. J Adv Stat. 2016; 1: 146-155.
Khan RU, Kulshrestha A, Khan MA. Relations for moments of -th record values from exponential-Weibull lifetime distribution and a characterization. J. Egyptian Math. Soc. 2015; 23: 558-562.
Khan RU, Khan MA, Khan MAR. Relations for moments of generalized record values from additive Weibull distribution and associated inference. Stat Optim Inf Comput. 2017; 5: 127-136.
Minimol S, Thomos PY. On some properties of Makeham distribution using generalized record values and its characterization. Braz J Probab Stat. 2013; 27: 487-501.
Minimol S, Thomos PY. On characterization of Gompertz distribution by properties of generalized record values. J Stat Theory Appl. 2014; 13: 38-45.
Pawlas P, Szynal D. Relations for single and product moments of k-th record values from exponential and Gumble distributions. J Appl Stat Sci. 1998; 7: 53-62.
Pawlas P, Szynal D. Recurrence relations for single and product moments of k-th record values from Pareto, generalized Pareto and Burr distributions. Comm Statist Theory Methods. 1999; 28: 1699-1709.
Pawlas P, Szynal D. Recurrence relations for single and product moments of k-th record values from Weibull distribution and a characterization. J Appl Stat Sci. 2000; 1: 17-25.
Downloads
Published
2018-12-27
How to Cite
Singh, B., Khan, R., & Khan, M. A. (2018). Moments of Generalized Record Values from Kumaraswamy-log-logistic Distribution and Related Inferences. Thailand Statistician, 17(1), 93–103. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/163214
Issue
Section
Articles
