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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 11 > No. 1


Alpha Power Modified Weibull Distribution: Actuarial Measures and Applications to Failure Data

PP: 13-34
Irene Dekomwine Angbing, Abdul Ghaniyyu Abubakari, Suleman Nasiru,
In this study, a new modified Weibull distribution, called the alpha power modified Weibull distribution, is proposed and studied. The new distribution is a generalization of several well known distributions. The shapes of the density and hazard rate functions are obtained. The density function shows several shapes including skewed, approximately symmetric and decreasing shapes. The hazard rate function also shows shapes including decreasing, increasing, bathtub and modified bathtub shapes. Several properties of the distribution including moments, moment generating function, inequality measures, order statistics and stochastic ordering are derived. Also, several actuarial measures are derived. The numerical studies of the actuarial measures of the developed distribution are compared with other distributions. Various estimation methods are used to estimate the parameters of the distribution and a simulation study is conducted to ascertain the performance of the estimators. A bivariate extension of the distribution is also derived in the study. The distribution is used to model two real failure data sets to ascertain its usefulness. The results show that the new distribution can serve as an alternative to modeling failure data sets.

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