Papers by Ayman Alzaatreh
Journal of Statistical Distributions and Applications, 2014
Communications in Statistics - Theory and Methods, 2015
The logistic distribution and the S-shaped pattern of its cumulative distribution and quantile fu... more The logistic distribution and the S-shaped pattern of its cumulative distribution and quantile functions have been extensively used in many di↵erent spheres a↵ecting human life. By far the most well-known application of logistic distribution is in the logistic regression which is used for modeling categorical response variables. The exponentiated-exponential logistic distribution, a generalization of the logistic distribution is obtained using the technique by of mixing two distributions hereafter called as the EEL distribution. This distribution subsumes various types of logistic distribution. The structural analysis of the distribution in this paper includes limiting behavior, quantiles, moments, mode, skewness, kurtosis, order statistics, the large sample distributions of the sample maximum and the sample minimum and the distribution of the sample median. For illustrative purposes, a real life data set is considered as an application of the EEL distribution.
Communications in Statistics - Simulation and Computation, 2014
Many distributions have been used as lifetime models. Recently, a generator of distributions call... more Many distributions have been used as lifetime models. Recently, a generator of distributions called the Weibull-G class was proposed by . 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 data sets 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.
Communication in Statistics- Simulation and Computation
Many distributions have been used as lifetime models. Recently, a generator of dis-tributions cal... more Many distributions have been used as lifetime models. Recently, a generator of dis-tributions called the Weibull-G class was proposed by Bourguignon et al. (2014). 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 mo-ments 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 pa-rameters 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 data sets on Wheaton river flood and bladder cancer. In the two applications, the ne...
Communication in Statistics- Theory and Methods
The logistic distribution has a prominent role in the theory and practice of statistics. We intro... more 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.
Statistical Methodology, 2012
and sharing with colleagues.
METRON, 2013
In this paper, a new method is proposed for generating families of continuous distributions. A ra... more In this paper, a new method is proposed for generating families of continuous distributions. A random variable X , "the transformer", is used to transform another random variable T , "the transformed". The resulting family, the T -X family of distributions, has a connection with the hazard functions and each generated distribution is considered as a weighted hazard function of the random variable X . Many new distributions, which are members of the family, are presented. Several known continuous distributions are found to be special cases of the new distributions.
Computational Statistics & Data Analysis, 2014
In this paper, some properties of gamma-X family are discussed and a member of the family, the ga... more In this paper, some properties of gamma-X family are discussed and a member of the family, the gamma-normal distribution, is studied in detail. The limiting behaviors, moments, mean deviations, dispersion, and Shannon entropy for the gamma-normal distribution are provided. Bounds for the non-central moments are obtained. The method of maximum likelihood estimation is proposed for estimating the parameters of the gamma-normal distribution. Two real data sets are used to illustrate the applications of the gamma-normal distribution.
A new distribution, namely, the Gamma-Half-Cauchy distribution is proposed. Various properties of... more 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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Papers by Ayman Alzaatreh
is obtained. Two data sets are used to illustrate the applications of Gamma-Half-Cauchy distribution.
is obtained. Two data sets are used to illustrate the applications of Gamma-Half-Cauchy distribution.