A Novel Parsimonious Gamma Mixture with Applications to Reliability Data
Aderoju, S.A.
Adesina, S.B.
Olasupo, A.O.
Sanni, B.I.
Kalu, U.
Olaboye, D.F.
Yussuf, T.A.
Abstract
Lifetime distributions are salient statistical tools to model the different characteristics of lifetime datasets. The statistical literature contains very modern distributions to analyze these kinds of datasets. Nonetheless, these distributions have many parameters, which cause a problem in the estimation step. To offer fresh possibilities in modeling these kinds of datasets, we propose a Parsimonious Gamma Mixture (PGM) distribution using a finite mixture of Gamma distributions with parameter-dependent mixing weights. The proposed distribution has only one parameter and simple mathematical forms. The mathematical properties of the distributions, including moments, reliability functions and order statistics, are studied in detail. The unknown model parameter is estimated by using the maximum likelihood. The extensive simulation study is used to study the performance of parameter estimation. To convince the readers in favour of the proposed distribution, three real datasets from engineering and materials science are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other similar existing distributions. Its consistent achievement of the lowest AIC and BIC values across all datasets confirms its enhanced ability to capture diverse data patterns with remarkable parameter parsimony, making it a highly effective tool for modelling reliability and survival data.
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