Applications of Mathematics, Vol. 62, No. 3, pp. 269-296, 2017

A new weighted Gompertz distribution with applications to reliability data

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

Received October 4, 2016.   First published April 28, 2017.

Hassan S. Bakouch, Ahmed M. T. Abd El-Bar, Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt, e-mail:,

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.

Keywords: continuous distribution; distributional properties; weight function; estimation; estimated survival function

Classification (MSC 2010): 60E05, 60E99, 62E15

DOI: 10.21136/AM.2017.0277-16

Full text available as PDF.

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