Laplace transformed properties of the extended power-Gompertz model: Simulation and applications

Abstract

In this paper, a new four-parameter lifetime model tilted the exponentiated power Gompertz (EXPGO) model is proposed. The explicit expressions of the density, distribution and quantile functions of the EXPGO are provided. Its density function can be expressed as a linear mixture of the generalized Gompertz densities, and can be unimodal and left skewed. The failure rate of the new model can be concave decreasing and reversed J-shaped. Likewise, the structural properties of the new model like the moments, moments generating function, probability weighted moments and entropies expressed in Laplace transform are provided. The maximum likelihood estimator for the new model is discussed and the performance of the estimator evaluated using Monte Carlo simulations. Three real-data applications indicate that the EXPGO model provides a better fit and can be utilized in fitting skewed datasets with unimodal features and concave decreasing failure rates.

Keywords

• Exponential-G family
• Entropy
• Gompertz model
• Maximum likelihood estimation
• Laplace transform
• Simulation