Cubic Transformation of Exponential Weibull and its Statistical Properties

Main Article Content

Haiyue Wang
Zhenhua Bao

Abstract

In this paper, a cubic transformation exponential Weibull distribution is proposed by using the family of cubic transformation distributions introduced by Rahman et al.The reasoning process of the proposed cubic transformation exponential Weibull distribution is discussed in detail, and its statistical properties and parameter estimation are also discussed.Using real data, the maximum likelihood estimation is used to simulate. Through the comparison of fitting results, it is concluded that the cubic transformation exponential Weibull distribution proposed in this paper has stronger applicability.

Keywords:
Cubic transformation, maximum likelihood estimation, moment, reliability analysis, exponential Weibull.

Article Details

How to Cite
Wang, H., & Bao, Z. (2020). Cubic Transformation of Exponential Weibull and its Statistical Properties. Journal of Scientific Research and Reports, 26(11), 39-50. https://doi.org/10.9734/jsrr/2020/v26i1130334
Section
Original Research Article

References

Weibull WA. statistical distribution function of wide applicability. J Appl Mech. 1951;18: 293–297.

Mudholkar GS, Srirastava DK, Kollia GD. A generalization of the Weibull distribution with application to analysis of survival data. J Am Stat Assoc.1996;91:1575–1583.

Pham H, Lai C-D. On recent generalizations of the Weibull distribution. IEEE Trans Reliab. 2007;56:454–458.

Xie M, Tang Y, Goh TN. A modifified Weibull extension with bathtub shaped failure rate function. Reliab Eng Syst Saf. 2002;76:279–285.

Lai CD, Xie M, Murthy DNP. A modifified Weibull distribution. IEEE Trans Reliab. 2003;52:33–37.

Nassar MM, Eissa FH. On the exponentiated Weibull distribution. Commun Stat Theory Methods. 2003;32:1317–1336.

Pal M, Ali MM, Woo J. Exponentiated weibull distribution. statistica. 2006;66:139–147.

Jiang R, Murthy DNP. Models involving two inverse Weibull distributions. Reliab Eng Syst Saf. 2001;73:73–81.

Shaw WT, Buckley IRC. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Papers. 2009.

Aryal GR, Tsokos CP. Transmuted Weibull distribution: A generalization of the Weibull probability distribution. Eur J Pure Appl Math. 2001;4:89–102.

Granzotto DCT, Louzada F, Balakrishnan N. Cubic rank transmuted distributions: Inferential issues and applications. J Stat Comput Simul. 2017;87:2760–2778.

Al-Kadim KA, Mohammed MH. The cubic transmuted Weibull distribution. J Univ Babylon. 2017;3:862–876.

Rahman MM, Al-Zahrani B, Shahbaz MQ. A general transmuted family of distributions. Pak J Stat Oper Res. 2018;14:451–469.

Rahman M, Al-Zahrani B, Shahbaz MQ. Cubic transmuted Weibull distribution: Properties and applications[J]. Annals of Data Science. 2019;6(1):1-20.

Gradshteyn IS, Ryzhik IM. Table of integrals, series, and products. Mathematics of Computation. 2007;20(96):1157–1160.

Jong PD, Heller GZ. Generalized Linear Models for Insurance Data. Cambridge University Press; 2008.