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.
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.
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 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 moments and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time and generating and quantile functions. The R´enyi 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.
To appear in Communications in Statistics-Simulation and Computation (USA) DOI:10.1080/03610918.2014.948190 Impact factor (2013) = 0.288
We introduce a new model called the Weibull-Lomax distribution which extends the Lomax distribut... more We introduce a new model called the Weibull-Lomax distribution which extends the Lomax distribution and has increasing and decreasing shapes for the hazard rate function. 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, probability weighted moments, generating and quantile function. The R´enyi and q entropies are also obtained.
We provide the density function of the order statistics and their moments. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of two real life data sets. For these data, the new model outperforms the McDonald-Lomax,
Kumaraswamy-Lomax, gamma-Lomax, beta-Lomax, exponentiated Lomax and Lomax models.
To appear in Hacettepe Journal of Mathematics and Statistics (Turkey), 42. Doi: 10.15672/HJMS.2014147465
Impact factor (2013) = 0.433
We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to... more We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set shows that it can give consistently better fit than other important lifetime models.
Recently, several attempts have been made to define new models that extend well-known distributio... more Recently, several attempts have been made to define new models that extend well-known distributions and at the same time provide great flexibility in modelling real data. We propose a new four-parameter model named the Weibull-power function (WPF) distribution which exhibits bathtub-shaped hazard rate. Some of its statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, R´enyi and Shannon entropies, reliability and order statistics. The model parameters are estimated by the method of maximum likelihood. A bivariate extension is also proposed. The new distribution can be implemented easily using statistical software packages. We investigate the potential usefulness of the proposed model by means of two real data sets. In fact, the new model provides a better fit to these data than the additive Weibull, modified Weibull, Sarahan-Zaindin modified Weibull and beta-modified Weibull distributions, suggesting that it is a reasonable candidate for modeling survival data.
To appear in Hacettepe Journal of Mathematics and Statistics (Turkey), 42. Doi: 10.15672/HJMS.2014428212
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.
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.
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 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 moments and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time and generating and quantile functions. The R´enyi 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.
To appear in Communications in Statistics-Simulation and Computation (USA) DOI:10.1080/03610918.2014.948190 Impact factor (2013) = 0.288
We introduce a new model called the Weibull-Lomax distribution which extends the Lomax distribut... more We introduce a new model called the Weibull-Lomax distribution which extends the Lomax distribution and has increasing and decreasing shapes for the hazard rate function. 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, probability weighted moments, generating and quantile function. The R´enyi and q entropies are also obtained.
We provide the density function of the order statistics and their moments. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of two real life data sets. For these data, the new model outperforms the McDonald-Lomax,
Kumaraswamy-Lomax, gamma-Lomax, beta-Lomax, exponentiated Lomax and Lomax models.
To appear in Hacettepe Journal of Mathematics and Statistics (Turkey), 42. Doi: 10.15672/HJMS.2014147465
Impact factor (2013) = 0.433
We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to... more We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set shows that it can give consistently better fit than other important lifetime models.
Recently, several attempts have been made to define new models that extend well-known distributio... more Recently, several attempts have been made to define new models that extend well-known distributions and at the same time provide great flexibility in modelling real data. We propose a new four-parameter model named the Weibull-power function (WPF) distribution which exhibits bathtub-shaped hazard rate. Some of its statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, R´enyi and Shannon entropies, reliability and order statistics. The model parameters are estimated by the method of maximum likelihood. A bivariate extension is also proposed. The new distribution can be implemented easily using statistical software packages. We investigate the potential usefulness of the proposed model by means of two real data sets. In fact, the new model provides a better fit to these data than the additive Weibull, modified Weibull, Sarahan-Zaindin modified Weibull and beta-modified Weibull distributions, suggesting that it is a reasonable candidate for modeling survival data.
To appear in Hacettepe Journal of Mathematics and Statistics (Turkey), 42. Doi: 10.15672/HJMS.2014428212
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Papers by Mansoor Abbasi
is obtained. Two data sets are used to illustrate the applications of Gamma-Half-Cauchy distribution.
Kumaraswamy-Pareto, beta-exponentiated Pareto, beta-Pareto, exponentiated-Pareto and Pareto
models.
To appear in Communications in Statistics-Simulation and Computation (USA) DOI:10.1080/03610918.2014.948190
Impact factor (2013) = 0.288
distribution are derived including explicit expressions for the moments and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments, generating and quantile function. The R´enyi and q entropies are also obtained.
We provide the density function of the order statistics and their moments. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of two real life data sets. For these data, the new model outperforms the McDonald-Lomax,
Kumaraswamy-Lomax, gamma-Lomax, beta-Lomax, exponentiated Lomax and Lomax models.
To appear in Hacettepe Journal of Mathematics and Statistics (Turkey), 42. Doi: 10.15672/HJMS.2014147465
Impact factor (2013) = 0.433
measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set
shows that it can give consistently better fit than other important lifetime models.
bathtub-shaped hazard rate. Some of its statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, R´enyi and Shannon entropies, reliability and order statistics.
The model parameters are estimated by the method of maximum likelihood. A bivariate extension is also proposed. The new distribution can be implemented easily using statistical software packages. We investigate the potential usefulness of the proposed model by means of two
real data sets. In fact, the new model provides a better fit to these data than the additive Weibull, modified Weibull, Sarahan-Zaindin modified Weibull and beta-modified Weibull distributions, suggesting that it is a reasonable candidate for modeling survival data.
To appear in Hacettepe Journal of Mathematics and Statistics (Turkey), 42. Doi: 10.15672/HJMS.2014428212
is obtained. Two data sets are used to illustrate the applications of Gamma-Half-Cauchy distribution.
Kumaraswamy-Pareto, beta-exponentiated Pareto, beta-Pareto, exponentiated-Pareto and Pareto
models.
To appear in Communications in Statistics-Simulation and Computation (USA) DOI:10.1080/03610918.2014.948190
Impact factor (2013) = 0.288
distribution are derived including explicit expressions for the moments and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments, generating and quantile function. The R´enyi and q entropies are also obtained.
We provide the density function of the order statistics and their moments. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of two real life data sets. For these data, the new model outperforms the McDonald-Lomax,
Kumaraswamy-Lomax, gamma-Lomax, beta-Lomax, exponentiated Lomax and Lomax models.
To appear in Hacettepe Journal of Mathematics and Statistics (Turkey), 42. Doi: 10.15672/HJMS.2014147465
Impact factor (2013) = 0.433
measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set
shows that it can give consistently better fit than other important lifetime models.
bathtub-shaped hazard rate. Some of its statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, R´enyi and Shannon entropies, reliability and order statistics.
The model parameters are estimated by the method of maximum likelihood. A bivariate extension is also proposed. The new distribution can be implemented easily using statistical software packages. We investigate the potential usefulness of the proposed model by means of two
real data sets. In fact, the new model provides a better fit to these data than the additive Weibull, modified Weibull, Sarahan-Zaindin modified Weibull and beta-modified Weibull distributions, suggesting that it is a reasonable candidate for modeling survival data.
To appear in Hacettepe Journal of Mathematics and Statistics (Turkey), 42. Doi: 10.15672/HJMS.2014428212