The Alpha Power Gompertz Distribution: Characterization, Properties, and Applications

Joseph Thomas Eghwerido (), Lawrence Chukwudumebi Nzei and Friday Ikechukwu Agu
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Joseph Thomas Eghwerido: Federal University of Petroleum Resources
Lawrence Chukwudumebi Nzei: University of Benin
Friday Ikechukwu Agu: University of Calabar

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 19, 449-475

Abstract: Abstract A new three-parameter model called the Alpha power Gompertz is derived, studied and proposed for modeling lifetime Poisson processes. The advantage of the new model is that, it has left skew, decreasing, unimodal density with a bathtub shaped hazard rate function. The statistical structural properties of the proposed model such as probability weighted moments, moments, order statistics, entropies, hazard rate, survival, quantile, odd, reversed hazard, moment generating and cumulative functions are investigated. The new proposed model is expressed as a linear mixture of Gompertz densities. The parameters of the proposed model were obtained using maximum likelihood method. The behaviour of the new density is examined through simulation. The proposed model was applied to two real-life data sets to demonstrate its flexibility. The new density proposes provides a better fit when compared with other existing models and can serve as an alternative model in the literature.

Keywords: Alpha power distribution; Gompertz distribution; Gompertz failure rate; Moment generating function of Gompertz; Moment of Gompertz; 62E10; 62E15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13171-020-00198-0

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