Geodesic
A new weighted Gompertz distribution with applications to reliability data
Applications of Mathematics, Tome 62 (2017) no. 3, pp. 269-296 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A new weighted version of the Gompertz distribution is introduced. It is noted that the model represents a mixture of classical Gompertz and second upper record value of Gompertz densities, and using a certain transformation it gives a new version of the two-parameter Lindley distribution. The model can be also regarded as a dual member of the log-Lindley-$X$ family. Various properties of the model are obtained, including hazard rate function, moments, moment generating function, quantile function, skewness, kurtosis, conditional moments, mean deviations, some types of entropy, mean residual lifetime and stochastic orderings. Estimation of the model parameters is justified by the method of maximum likelihood. Two real data sets are used to assess the performance of the model among some classical and recent distributions based on some evaluation goodness-of-fit statistics. As a result, the variance-covariance matrix and the confidence interval of the parameters, and some theoretical measures have been calculated for such data for the proposed model with discussions.
A new weighted version of the Gompertz distribution is introduced. It is noted that the model represents a mixture of classical Gompertz and second upper record value of Gompertz densities, and using a certain transformation it gives a new version of the two-parameter Lindley distribution. The model can be also regarded as a dual member of the log-Lindley-$X$ family. Various properties of the model are obtained, including hazard rate function, moments, moment generating function, quantile function, skewness, kurtosis, conditional moments, mean deviations, some types of entropy, mean residual lifetime and stochastic orderings. Estimation of the model parameters is justified by the method of maximum likelihood. Two real data sets are used to assess the performance of the model among some classical and recent distributions based on some evaluation goodness-of-fit statistics. As a result, the variance-covariance matrix and the confidence interval of the parameters, and some theoretical measures have been calculated for such data for the proposed model with discussions.
DOI : 10.21136/AM.2017.0277-16
Classification : 60E05, 60E99, 62E15
Keywords: continuous distribution; distributional properties; weight function; estimation; estimated survival function 
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     author = {Bakouch, Hassan S. and Abd El-Bar, Ahmed M. T.},
     title = {A new weighted {Gompertz} distribution with applications to reliability data},
     journal = {Applications of Mathematics},
     pages = {269--296},
     year = {2017},
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     doi = {10.21136/AM.2017.0277-16},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0277-16/}
}
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Bakouch, Hassan S.; Abd El-Bar, Ahmed M. T. A new weighted Gompertz distribution with applications to reliability data. Applications of Mathematics, Tome 62 (2017) no. 3, pp. 269-296. doi: 10.21136/AM.2017.0277-16

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