Properties and Applications of the Gompertz Distribution

  • J. A. Adewara Distance Learning Institute, University of Lagos.
  • J. S. Adeyeye Department of Mathematics, University of Lagos.
  • C. P. Thron Department of Science and Mathematics, Texas A & M University-Central Texas.
Keywords: Gompertz distribution;, Skewed data, Maximum likelihood, Parameters, Reliability, Survival function, Hazard function, Quantile function

Abstract

The importance of statistical distributions in describing and predicting real world events cannot be over-emphasized. The Gompertz distribution is one example of a widely-used distribution, with many applications to survival analysis. In this paper, several properties of the Gompertz distribution are studied. The two-parameter Gompertz distribution is shown to be identical to the three-parameter Gompertz exponential distribution. Functions used in reliability analysis related to the Gompertz distribution are reviewed. Properties of maximum likelihood estimate (MLE) parameter estimates for the Gompertz distribution are studied: the bias and root mean squared error of parameter estimates are expressed as a function of sample size and parameter values. When the Gompertz shape parameter is large, MLE parameter estimates may fail to exist because of parameter degeneracy, as the two-parameter Gompertz distribution approaches a 1-parameter exponential distribution. The distribution is fitted to real life data sets from both industrial and biological applications. Compared to several 3-parameter distributions, the Gompertz distribution provides significantly better fits to the industrial data sets chosen, but the 3-parameter generalized Gompertz distribution gives a better fit to guinea pig lifetime data.

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Published
2019-05-13
How to Cite
Adewara, J. A., Adeyeye, J. S., & Thron, C. P. (2019). Properties and Applications of the Gompertz Distribution. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2019(1), 443 - 454. Retrieved from http://ijmso.unilag.edu.ng/article/view/346
Section
Articles