The Marshall–Olkin exponential Weibull distribution

Year 2015, Volume: 44 Issue: 6, 1579 - 1594, 01.12.2015

Tibor K. Pogány Abdus Saboor Serge Provost

Abstract

A new four-parameter model called the Marshall–Olkin exponential–Weibull probability distribution is being introduced in this paper, generalizing a number of known lifetime distributions. This model turns
out to be quite flexible for analyzing positive data. The hazard rate
functions of the new model can be increasing and bathtub shaped.
Our main objectives are to obtain representations of certain associated
statistical functions, to estimate the parameters of the proposed distribution and to discuss its modality. As an application, the probability
density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as
measured by the Anderson–Darling and Cramér–von Mises goodness–
of–fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling
positive data arising in various fields of scientific investigation such as
reliability theory, hydrology, medicine, meteorology, survival analysis
and engineering. 

Keywords

Marshall–Olkin exponential–Weibull distribution, goodness–of–fit statistics, moments, median, mode, unimodal distribution, quantile function, Fox– Wright pΨq function, Goyal–Laddha generalized Hurwitz–Lerch zeta function

References

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