In this paper, we define and study a new lifetime model called the Kumaraswamy Marshall-Olkin log-logistic distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. The new model contains some well-known distributions as special cases such as the Marshall-Olkin loglogistic, log-logistic, lomax, Pareto type II and Burr XII distributions. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary moments, skewness, kurtosis are derived. The maximum likelihood estimators of the unknown parameters are obtained. The importance and flexibility of the new model is proved empirically using a real data set.
Abstract. This paper introduces a new five-parameter lifetime model called the exponentiated Kumaraswamy power Lindley distribution, that extends the power Lindley distribution and some well-known distributions. Various structural properties of the new model including expansions for the density function, explicit expressions for the ordinary and conditional moments, residual and reversed residual life functions and mean deviations are derived. The maximum likelihood method is used to estimate the model parameters. The usefulness and flexibility of the proposed model are illustrated empirically by means of two real data sets.Résumé. Ce papier introduit un modèle de durée de vieà cinq variables appelée exponentiation du modèle puissance Kumaraswamy de Lindley, qui généralise le modèle puissance de la distribution de Lindley et cetaines distribitions connues. Y sontétablies différentes propriétés structurelles di mouveau modèle, y compris des dévelopments en série de la densité de probabilité, une expression explicite des moments conditionnels et inconditionnels, les fonction de durée de vie (résiduelles et résiduelles inverses), et des propriétés relativesà la déviation par rapportà la moyenne. Les paramètres ontété estimés par la méthode du maximum de vraisemblance. L'utilité et la flexibility de la méthode aété montrée sur deux jeux de données réelles.
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