Abstract
In this paper, a new distribution namely, The Marshall–OlkinGeneralized Inverse Weibull Distribution is illustrated and studied. The new distribution is very flexible and contains sub-models such asinverse exponential, inverse Rayleigh, Weibull, inverse Weibull, Marshall–Olkininverse Weibull and Fréchetdistributions. Also, the hazard function of the new distribution can produce variety of forms:an increase, a decrease and an upside-down bathtub. Some properties such as hazard function, quintile function, entropy, moment generating function and order statistics are obtained. Different estimation approaches namely, maximum likelihood estimators, interval estimators, least square estimators, fisher information matrix and asymptotic confidence intervals are described. To illustrate the superior performance of the proposed distribution, a simulation study and a real data analysis are investigated against other models.
Highlights
Many authors have been interested in the Weibull distribution which is extensively used over the past decades for reliability studies and is adequate for modeling monotone data
This study aims at providing a new extension of weibull distribution namely, The Marshall–Olkin Generalized Inverse Weibull (MOGIW for short) distribution
The well-known inverse Weibull distribution, is extended by introducing one extra shape parameters, defining the Marshal Olikin Generalized Inverse Weibull (MOGIW) distribution having a broader class of hazard rate and density functions
Summary
Many authors have been interested in the Weibull distribution which is extensively used over the past decades for reliability studies and is adequate for modeling monotone data. (Felipe et al 2011) discussed the properties of the GIW distribution including hazard function, survival function, central and non-central moments and moment generating function They provided maximum likelihood estimators, asymptotic confidence intervals and fisher information matrix as well. This study aims at providing a new extension of weibull distribution namely, The Marshall–Olkin Generalized Inverse Weibull (MOGIW for short) distribution It contains more significant fits than some distributions such as Marshall–Olkin extended inverse Weibull, inverse Weibull, Fréchet, inverse Rayleigh and inverse exponential being sub-models from the proposed distribution. The motivations to introduce the MOGIW distribution are: (i) some known distributions are sub-models from it; (ii) in case the hazard function is non-monotone or unimodal, the MOGIW distribution is a superior fit to other common lifetime distributions; (iii) the MOGIW distribution can use in different areas such as breast cancer and wear-out periods in medical and physical fields respectively; (iv) to illustrate the applicability of the MOGIW distribution by conducting study of a numerical and an actual data. The survival function R x and the hazard rate function h x of the MOGIW distribution respectively are ( ) ( ) R
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