zbMATH — the first resource for mathematics

A new family of compound lifetime distributions. (English) Zbl 1291.62040
Summary: In this paper, we introduce a general family of continuous lifetime distributions by compounding any continuous distribution and the Poisson-Lindley distribution. It is more flexible than several recently introduced lifetime distributions. The failure rate functions of our family can be increasing, decreasing, bathtub shaped and unimodal shaped. Several properties of this family are investigated including shape characteristics of the probability density, moments, order statistics, (reversed) residual lifetime moments, conditional moments and Rényi entropy. The parameters are estimated by the maximum likelihood method and the Fisher’s information matrix is determined. Several special cases of this family are studied in some detail. An application to a real data set illustrates the performance of the family of distributions.

62E15 Exact distribution theory in statistics
62E20 Asymptotic distribution theory in statistics
Full Text: Link
[1] Adamidis, K., Loukas, S.: A lifetime distribution with decreasing failure rate. Statist. Probab. Lett. 39 (1998), 35-42. · Zbl 0908.62096
[2] Bakouch, H. S., Ristic, M. M., Asgharzadeh, A., Esmaily, L., Al-Zahrani, B. M.: An exponentiated exponential binomial distribution with application. Statist. Probab. Lett. 82 (2012), 1067-1081. · Zbl 1238.62011
[3] Barreto-Souza, W., Bakouch, H. S.: A new lifetime model with decreasing failure rate. Statistics 47 (2013), 465-476. · Zbl 1440.62357
[4] Barreto-Souza, W., Morais, A. L. de, Cordeiro, G. M.: The Weibull-geometric distribution. J. Statist. Comput. Simul. 81 (2011), 645-657. · Zbl 1348.60014
[5] Chahkandi, M., Ganjali, M.: On some lifetime distributions with decreasing failure rate. Comput. Statist. Data Anal. 53 (2009), 4433-4440. · Zbl 1298.62175
[6] Ghitany, M. E., Al-Mutairi, D. K., Nadarajah, S.: Zero-truncated Poisson-Lindley distribution and its application. Math. Comput. Simul. 79 (2008), 279-287. · Zbl 1153.62308
[7] Gupta, P. L., Gupta, R. C.: On the moments of residual life in reliability and some characterization results. Comm. Statist.-Theory and Methods 12 (1983), 449-461. · Zbl 0513.62017
[8] Hosking, J. R. M.: L-moments: Analysis and estimation of distributions using linear combinations of order statistics. J. Royal Statist. Soc. B 52 (1990), 105-124. · Zbl 0703.62018
[9] Kus, C.: A new lifetime distribution. Comp. Statist. Data Anal. 51 (2007), 4497-4509. · Zbl 1162.62309
[10] Lu, W., Shi, D.: A new compounding life distribution: The Weibull-Poisson distribution. J. Appl. Statist. 39 (2012), 21-38.
[11] McNeil, A. J.: Estimating the tails of loss severity distributions using extreme value theory. Astin Bull. 27 (1997), 117-137.
[12] Morais, A. L., Barreto-Souza, W.: A compound class of Weibull and power series distributions. Comput. Statist. Data Anal. 55 (2011), 1410-1425. · Zbl 1328.62032
[13] Mudholkar, G. S., Srivastava, D. K.: Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans. Reliability 42 (1993), 299-302. · Zbl 0800.62609
[14] Rényi, A.: On measures of entropy and information. Proc. Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. I (1961), University of California Press, Berkeley, pp. 547-561. · Zbl 0106.33001
[15] Tahmasbi, R., Rezaei, S.: A two-parameter lifetime distribution with decreasing failure rate. Comput. Statist. Data Anal. 52 (2008), 3889-3901. · Zbl 1245.62128
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.