Document Zbl 1486.62032

Power exponentiated family of distributions with application on two real-life datasets. (English) Zbl 1486.62032

Thail. Stat. 19, No. 3, 536-546 (2021).

MSC:

62E10	Characterization and structure theory of statistical distributions
62E15	Exact distribution theory in statistics
62F10	Point estimation
62G30	Order statistics; empirical distribution functions
62N05	Reliability and life testing

Keywords:

exponential distribution; moments; Renyi entropy; order statistics; maximum likelihood estimation

Cite Review PDF

Full Text: Link

References:

[1]	Alzaatreh A, Lee C, Famoye F. A new method for generating families of continuous distributions. Metron. 2013; 71(1): 63-79. · Zbl 1302.62026
[2]	Azzalini A. A class of distributions which includes the normal ones. Scand J Stat. 1985; 12: 171-178. · Zbl 0581.62014
[3]	Barreto-Souza WM, Cordeiro GM, Simas AB. Some results for beta Fréchet distribution. Commun Stat Theory Methods. 2011; 40: 798-811. · Zbl 1216.62018
[4]	Cooray K, Ananda MMA. Modeling actuarial data with a composite lognormal-Pareto model. Scand Actuar J. 2005; 5: 321-334. · Zbl 1143.91027
[5]	David HA. Order statistics. New York: John Wiley & Sons; 1981. · Zbl 0553.62046
[6]	Eugene N, Lee C, Famoye F. Beta-normal distribution and its applications. Commun Stat Theory Methods. 2002; 31: 497-512. · Zbl 1009.62516
[7]	Ferreira JT, Steel MF. A constructive representation of univariate skewed distributions. J Am Stat Assoc. 2006; 101: 823-829. · Zbl 1119.62311
[8]	Gradshteyn IS, Ryzhik IM. Table of integrals, series and products, San Diego: Academic Press; 2007. · Zbl 1208.65001
[9]	Marshall AW, Olkin I. A new method for adding a parameter to a family of distributions with application to the Exponential and Weibull families. Biometrika. 1997; 84:641-652. · Zbl 0888.62012
[10]	Maurya SK, Kaushik A, Singh RK et al. A new method of proposing distribution and its application to real data. Imp J Interdiscip Res. 2016; 2(6): 1331-1338.
[11]	Modi K, Gill V. Length-biased weighted Maxwell distribution. Pak J Stat Oper Res. 2015; 11(4): 465-472. · Zbl 1509.60053
[12]	Modi K, Joshi L. On the distribution of product and ratio of t and Rayleigh random variables. J Cal Math Soc. 2012; 8(1): 53-60.
[13]	Mudholkar GS, Srivastava DK. Exponentiated Weibull family analyzing bath-tub failure-rate data. IEEE Trans Reliab. 1993; 42: 299-302. · Zbl 0800.62609
[14]	Nichols MD, Padgett WJ. A bootstrap control chart for Weibull percentiles. Qual Reliab Eng Int. 2006; 22: 141-151.
[15]	Pappas V, Adamidis K, Loukas S. A family of lifetime distributions. Qual Reliab Eng Int. 2012; doi:10.1155/2012/760687. · Zbl 1264.62009 · doi:10.1155/2012/760687
[16]	Renyi A. On measures of information and entropy. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics; 1961. pp.547-561. · Zbl 0106.33001
[17]	Smith RL, Naylor JC. A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. J Appl Stat. 1987; 36: 358-369.

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.