A New Extension of Chen Distribution with Applications to Lifetime Data

Abstract

In this paper, we introduce a new lifetime distribution with increasing, decreasing and bathtub-shaped hazard rate function which is constructed by compounding of the Weibull and Chen distributions and is called Weibull–Chen (W–C) distribution. The new distribution is more flexible to model the bathtub-shaped hazard rate data, and its hazard rate function is simple. We study its statistical properties including quantiles, moments, order statistics and Renyi entropy. The estimation of parameters by maximum likelihood method is discussed, and a Monte Carlo simulation study is conducted to investigate the performance of the maximum likelihood estimators. Finally, it is shown that the proposed distribution fits two real lifetime data better than other distributions.

Keywords

Chen distribution / Weibull distribution / Maximum likelihood estimation / Lifetime data analysis

References

[1] Aarset MV. How to identify bathtub hazard rate. IEEE Trans. Reliab.. 1987, 36 106-8

[2] Almalki SJ, Nadarajah S. Modifications of the Weibull distribution: a review. Reliab. Eng. Syst. Saf.. 2014, 124 32-55

[3] Carrasco M, Ortega EM, Cordeiro GM. A generalized modified Weibull distribution for lifetime modeling. Comput. Stat. Data Anal.. 2008, 53 450-462

[4] Chaubey YP, Zhang R. An extension of chens family of survival distributions with bathtub shape or increasing hazard rate function. Commun. Stat. Theory Methods. 2015, 44 4049-4064

[5] Chen Z. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Stat. Probab. Lett.. 2000, 49 155-161

[6] Cordeiro GM, Ortega EM, Silva GO. The Kumaraswamy modified Weibull distribution: theory and applications. J. Stat. Comput. Simul.. 2014, 84 1387-1411

[7] Cordeiro GM, Alizadeh M, Silva RB, Ramires TG. A new wider family of continuous models: the extended Cordeiro and de Castro family. Hacettepe J. Math. Stat.. 2018, 47 937-951

[8] Nelson W. Accelerated Life Testing: Statistical Models, Data Analysis and Test Plans. 1990 New York: Wiley

[9] Pappas V, Adamidis K, Loukas S. A family of lifetime distributions. Int. J. Qual. Stat. Reliab.. 2012, 2012 1-6

[10] Renyi A. On measures of entropy and information. Berkeley Symp. Math. Stat. Probab.. 1960, 1 547-561

[11] Sarhan AM, Apaloo J. Exponentiated modified Weibull extension distribution. Reliab. Eng. Syst. Saf.. 2013, 112 137-144

[12] Silva GO, Ortega EM, Cordeiro GM. The beta modified Weibull distribution. Lifetime Data Anal.. 2010, 16 409-430

[13] Sylwia KB. Makeham’s generalised distribution. Comput. Methods Sci. Technol.. 2007, 13 113-120

[14] Xie M, Lai CD. Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliab. Eng. Syst. Saf.. 1995, 52 87-93

[15] Xie M, Tang Y, Goh TN. A modified Weibull extension with bathtub-shaped failure rate function. Reliab. Eng. Syst. Saf.. 2002, 76 279-285