Parameter Estimation for the Exponentiated Kumaraswamy-Power Function Distribution Based on Order Statistics with Application

被引：0

作者：

Kumar D. ^{[1
]}

Jain N. ^{[2
]}

Nassar M. ^{[3
,4
]}

Abo-Kasem O.E. ^{[4
]}

机构：

[1] Department of Statistics, Central University of Haryana, Adalpur

[2] Department of Statistics, University of Delhi, New Delhi

[3] Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah

[4] Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig

来源：

Annals of Data Science | 2021年 / 8卷 / 04期

关键词：

Estimations; Exponentiated Kumaraswamy-power function; Moments and moment generating function; Monte Carlo simulation; Order statistics;

D O I：

10.1007/s40745-019-00233-4

中图分类号：

学科分类号：

摘要：

Exponentiated Kumaraswamy-power function (EKPF) distribution has been proposed recently by Bursa and Ozel (Hacet J Math Stat 46:277–292, 2017) as a quite flexible in terms of probability density and hazard rate functions than power function distribution. In this paper, we obtain the explicit expressions for the single, double (product), triple and quadruple moments and moment generating function for single, double, triple and quadruple of order statistics of the EKPF distribution. By using these relations, we have tabulated the means and variances of order statistics from samples of sizes up to 10 for various values of the parameters. We use five frequentist estimation methods to estimate the unknown parameters and a simulation study is used to compare the performance of the different estimators. Finally, we analyse a real data set for illustrative purpose. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

引用

页码：785 / 811

页数：26

共 31 条

[1]

Arnold B.C., Balakrishnan N., Nagaraja H.N., A first course in order statistics, (1992)

[2]

Balakrishnan N., Malik H.J., Order statistics from the linear—exponential distribution, Part II

[3]

Increasing hazard rate case, Commun Stat Theory Methods, 15, pp. 179-203, (1986)

[4]

Balakrishnan N., Malik H.J., Ahmad S.E., Recurrence relations and identities for moments of order statistics, II: Specific continuous distributions, Commun Stat Theory Methods, 17, pp. 2657-2694, (1988)

[5]

Balakrishnan N., Zhu X., Al-Zaharani B., Recursive computation of the single and product moments of order statistics for the complementary exponential-geometric distribution, J Stat Comput Simul, 85, pp. 2187-2201, (2015)

[6]

Bebbington M., Lai C.D., Zitikis R., A flexible weibull extension, Reliab Eng Syst Saf, 92, pp. 719-726, (2007)

[7]

Bursa N., Ozelz G., The exponentiated Kumaraswamy-power function distribution, Hacet J Math Stat, 46, pp. 277-292, (2017)

[8]

Cheng R.C.H., Amin N.A.K., Estimating parameters in continuous univariate distributions with a shifted origin, J R Stat Soc Ser B, 3, pp. 394-403, (1983)

[9]

Cordeiro G.M., Edwin M.M.O., Nadarajah S., The Kumaraswamy Weibull distribution with application to failure data, J Frankl Inst, 347, pp. 1399-1429, (2010)

[10]

David H.A., Order statistics, (1981)

← 1 2 3 4 →