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On a Generalization of Gompertz Distribution and its Applications

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Abstract

Gompertz distribution was proposed by Gompertz in 1825 and he showed that age specific mortality rates increase exponentially with age over much of adult life span. In this paper, we introduce a new generalization of Gompertz distribution and study its properties. Characterizations of the new distribution are obtained. The expressions for moments, quantile function and distribution of order statistics are derived and limiting behaviour of sample minima is studied. The stochastic ordering property of the new distribution is established. The unknown parameters of the distribution are estimated using maximum likelihood method, method of least squares, weighted least squares, and Cramer-von-Mises method. Simulation study is carried out to assess the performance of estimates. Autoregressive time series model with the generalized Gompertz distribution as marginal is developed. The proposed model is fitted to two real data sets to show the flexibility of the model.

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Acknowledgements

The second author wishes to thank the University Grants Commission, New Delhi for the financial assistance in the form of Junior Research Fellowship.

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Authors and Affiliations

  1. Department of Statistics, University of Calicut, Malappuram, Kerala, 673 635, India

    K. Jayakumar & A. Mohammed Shabeer

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  1. K. Jayakumar
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  2. A. Mohammed Shabeer
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Correspondence to K. Jayakumar.

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Jayakumar, K., Shabeer, A.M. On a Generalization of Gompertz Distribution and its Applications. J Indian Soc Probab Stat 23, 241–265 (2022). https://doi.org/10.1007/s41096-022-00125-6

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