• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.785-804
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• 2021

The proposal of new families has been worked out by many authors over recent years. Many ways to generate new families have been developed as the methods of addition, linear combination, composition and, one of the newer, the T-X family of distributions. Using this latter method, Korkmaz et al. (2018) proposed a new class called Weibull Marshall-Olkin-G (WMO-G) family. In the present work, we propose a new distribution, based on the WMO-G family, using the Lomax distribution as baseline, called Weibull Marshall-Olkin Lomax (WMOL) distribution. The hazard rate function of this distribution can be increasing, decreasing, bathtub-shaped, decreasing-increasing-decreasing and unimodal. Some properties of the proposed model are developed. Besides that, we consider method of maximum likelihood for estimating the unknown parameters of the WMOL distribution. We provide a simulation study in order to verify the asymptotic properties of the maximum likelihood estimates. The applicability of the new distribution to modeling real life data is proved by two real data sets.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1275-1301
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• 2023

This paper introduced the Weibull Marshall-Olkin Power Lomax (WMOPL) distribution. The statistical aspects of the proposed model are presented, such as the quantiles function, moments, mean residual life and mean deviations, variance, skewness, kurtosis, and reliability measures like the residual life function, and stress-strength reliability. The parameters of the new model are estimated using six different methods, and simulation research is illustrated to compare the six estimation methods. In the end, two real data sets show that the Weibull Marshall-Olkin Power Lomax distribution is flexible and suitable for modeling data.

• Communications for Statistical Applications and Methods
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• 제25권3호
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• pp.245-261
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• 2018

Attempts have been made to define new classes of distributions that provide more flexibility for modelling skewed data in practice. In this work we define a new extension of the generalized gamma distribution (Stacy, The Annals of Mathematical Statistics, 33, 1187-1192, 1962) for Marshall-Olkin generalized gamma (MOGG) distribution, based on the generator pioneered by Marshall and Olkin (Biometrika, 84, 641-652, 1997). This new lifetime model is very flexible including twenty one special models. The main advantage of the new family relies on the fact that practitioners will have a quite flexible distribution to fit real data from several fields, such as engineering, hydrology and survival analysis. Further, we also define a MOGG mixture model, a modification of the MOGG distribution for analyzing lifetime data in presence of cure fraction. This proposed model can be seen as a model of competing causes, where the parameter associated with the Marshall-Olkin distribution controls the activation mechanism of the latent risks (Cooner et al., Statistical Methods in Medical Research, 15, 307-324, 2006). The asymptotic properties of the maximum likelihood estimation approach of the parameters of the model are evaluated by means of simulation studies. The proposed distribution is fitted to two real data sets, one arising from measuring the strength of fibers and the other on melanoma data.