A new weighted Gompertz distribution with applications to reliability data

Hassan S. Bakouch; Ahmed M. T. Abd El-Bar

Applications of Mathematics (2017)

  • Volume: 62, Issue: 3, page 269-296
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Bakouch, Hassan S., and Abd El-Bar, Ahmed M. T.. "A new weighted Gompertz distribution with applications to reliability data." Applications of Mathematics 62.3 (2017): 269-296. <http://eudml.org/doc/288176>.

@article{Bakouch2017,
abstract = {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.},
author = {Bakouch, Hassan S., Abd El-Bar, Ahmed M. T.},
journal = {Applications of Mathematics},
keywords = {continuous distribution; distributional properties; weight function; estimation; estimated survival function},
language = {eng},
number = {3},
pages = {269-296},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new weighted Gompertz distribution with applications to reliability data},
url = {http://eudml.org/doc/288176},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Bakouch, Hassan S.
AU - Abd El-Bar, Ahmed M. T.
TI - A new weighted Gompertz distribution with applications to reliability data
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 3
SP - 269
EP - 296
AB - 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.
LA - eng
KW - continuous distribution; distributional properties; weight function; estimation; estimated survival function
UR - http://eudml.org/doc/288176
ER -

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