Geodesic
A new family of compound lifetime distributions
Kybernetika, Tome 50 (2014) no. 1, pp. 142-169

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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.
DOI : 10.14736/kyb-2014-1-0142
Classification : 60E05, 62E15, 62E20, 62N05
Keywords: estimation; failure rate shapes; moments; Poisson–Lindley distribution 
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     title = {A new family of compound lifetime distributions},
     journal = {Kybernetika},
     pages = {142--169},
     publisher = {mathdoc},
     volume = {50},
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     year = {2014},
     doi = {10.14736/kyb-2014-1-0142},
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     zbl = {1291.62040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-1-0142/}
}
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Asgharzadeh, A.; Bakouch, Hassan S.; Nadarajah, Saralees; Esmaeili, L. A new family of compound lifetime distributions. Kybernetika, Tome 50 (2014) no. 1, pp. 142-169. doi: 10.14736/kyb-2014-1-0142

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