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Keywords:
estimation; failure rate shapes; moments; Poisson–Lindley distribution
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.
References:
[1] Adamidis, K., Loukas, S.: A lifetime distribution with decreasing failure rate. Statist. Probab. Lett. 39 (1998), 35-42. DOI 10.1016/S0167-7152(98)00012-1 | MR 1649319 | 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. DOI 10.1016/j.spl.2012.03.004 | MR 2915071 | Zbl 1238.62011
[3] Barreto-Souza, W., Bakouch, H. S.: A new lifetime model with decreasing failure rate. Statistics 47 (2013), 465-476. DOI 10.1080/02331888.2011.595489 | MR 3043713
[4] Barreto-Souza, W., Morais, A. L. de, Cordeiro, G. M.: The Weibull-geometric distribution. J. Statist. Comput. Simul. 81 (2011), 645-657. DOI 10.1080/00949650903436554 | MR 2788571
[5] Chahkandi, M., Ganjali, M.: On some lifetime distributions with decreasing failure rate. Comput. Statist. Data Anal. 53 (2009), 4433-4440. DOI 10.1016/j.csda.2009.06.016 | MR 2744336
[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. DOI 10.1016/j.matcom.2007.11.021 | MR 2477530 | 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. DOI 10.1080/03610928308828471 | MR 0697631 | 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. MR 1049304 | Zbl 0703.62018
[9] Kus, C.: A new lifetime distribution. Comp. Statist. Data Anal. 51 (2007), 4497-4509. DOI 10.1016/j.csda.2006.07.017 | MR 2364461 | Zbl 1162.62309
[10] Lu, W., Shi, D.: A new compounding life distribution: The Weibull-Poisson distribution. J. Appl. Statist. 39 (2012), 21-38. DOI 10.1080/02664763.2011.575126 | MR 2872325
[11] McNeil, A. J.: Estimating the tails of loss severity distributions using extreme value theory. Astin Bull. 27 (1997), 117-137. DOI 10.2143/AST.27.1.563210
[12] Morais, A. L., Barreto-Souza, W.: A compound class of Weibull and power series distributions. Comput. Statist. Data Anal. 55 (2011), 1410-1425. DOI 10.1016/j.csda.2010.09.030 | MR 2741424
[13] Mudholkar, G. S., Srivastava, D. K.: Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans. Reliability 42 (1993), 299-302. DOI 10.1109/24.229504 | Zbl 0800.62609
[14] Rényi, A.: On measures of entropy and information. In: Proc. Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. I (1961), University of California Press, Berkeley, pp. 547-561. MR 0132570 | 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. DOI 10.1016/j.csda.2007.12.002 | MR 2432214 | Zbl 1245.62128
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