The Marshall-Olkin extended Weibull family of distributions. (English) Zbl 1338.60041
Summary: We introduce a new class of models called the Marshall-Olkin extended Weibull family of distributions based on the work by A. W. Marshall and I. Olkin [Biometrika 84, No. 3, 641–652 (1997; Zbl 0888.62012)]. The proposed family includes as special cases several models studied in the literature such as the Marshall-Olkin Weibull, Marshall-Olkin Lomax, Marshal-Olkin Fréchet and Marshall-Olkin Burr XII distributions, among others. It defines at least twenty-one special models and thirteen of them are new ones. We study some of its structural properties including moments, generating function, mean deviations and entropy. We obtain the density function of the order statistics and their moments. Special distributions are investigated in some details. We derive two classes of entropy and one class of divergence measures which can be interpreted as new goodness-of-fit quantities. The method of maximum likelihood for estimating the model parameters is discussed for uncensored and multi-censored data. We perform a simulation study using Markov Chain Monte Carlo method in order to establish the accuracy of these estimators. The usefulness of the new family is illustrated by means of two real data sets.
MSC:
| 60E05 | Probability distributions: general theory |
| 62F03 | Parametric hypothesis testing |
| 62F10 | Point estimation |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
extended Weibull distribution; hazard rate function; Marshall-Olkin distribution; maximum likelihood estimation; survival functionCitations:
Zbl 0888.62012References:
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