Mathematics

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Browsing Mathematics by Author "Alzaatreh, Ayman"

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    A New Weibull–Pareto Distribution: Properties and Applications
    (Communications in Statistics: Simulation and Computation, 2016-11-25) Tahir, M. H.; Cordeiro, Gauss M.; Alzaatreh, Ayman; Mansoor, M.; Zubair, M.
    Many distributions have been used as lifetime models. In this article, we propose a new three-parameter Weibull–Pareto distribution, which can produce the most important hazard rate shapes, namely, constant, increasing, decreasing, bathtub, and upsidedown bathtub. Various structural properties of the new distribution are derived including explicit expressions for the moments and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, and generating and quantile functions. The Rényi and q entropies are also derived. We obtain the density function of the order statistics and their moments. The model parameters are estimated by maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of two real datasets on Wheaton river flood and bladder cancer. In the two applications, the new model provides better fits than the Kumaraswamy–Pareto, beta-exponentiated Pareto, beta-Pareto, exponentiated Pareto, and Pareto models.
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    The gamma half-Cauchy distribution: Properties and applications
    (Hacettepe Journal of Mathematics and Statistics, 2016) Alzaatreh, Ayman; Mansoory, M.; Tahirz, M. H.; Zubair, M.; Ghazalik, Shakir Ali
    A new distribution, namely, the Gamma-Half-Cauchy distribution is proposed. Various properties of the Gamma-Half-Cauchy distribution are studied in detail such as limiting behavior, moments, mean deviations and Shannon entropy. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is obtained. Two data sets are used to illustrate the applications of Gamma-Half-Cauchy distribution.
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    The logistic-X family of distributions and its applications
    (Communications in Statistics - Theory and Methods, 2016-12-16) Tahir, M. H.; Cordeiro, Gauss M.; Alzaatreh, Ayman; Mansoor, M.; Zubair, M.
    The logistic distribution has a prominent role in the theory and practice of statistics. We introduce a new family of continuous distributions generated from a logistic random variable called the logistic-X family. Its density function can be symmetrical, left-skewed, right-skewed, and reversed-J shaped, and can have increasing, decreasing, bathtub, and upside-down bathtub hazard rates shaped. Further, it can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon entropy, and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. We also investigate the properties of one special model, the logistic-Fréchet distribution, and illustrate its importance by means of two applications to real data sets.