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Hiba Z. Muhammed 한국신뢰성학회 2017 International Journal of Reliability and Applicati Vol.18 No.2
Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance- covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.
Muhammed, Hiba Z. The Korean Reliability Society 2017 International Journal of Reliability and Applicati Vol.18 No.2
Abstract. Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.
On the inverted Topp Leone distribution
Hiba Z Muhammed 한국신뢰성학회 2019 International Journal of Reliability and Applicati Vol.20 No.1
In this paper, a new distribution called inverted Topp-Leone distribution is introduced, which is useful for modeling lifetime phenomena. Some reliability measures of this distribution such as reliability, hazard and reversed hazard functions are studied. Some statistical properties for the inverted Topp-Leone distribution such as mode, median, quantile function and moments about zero are given. Order statistics from this distribution will be studied. Expressions for moments and product moments of order statistics are obtained in closed forms. Finally, the maximum likelihood estimation and confidence intervals for the shape parameter, reliability, hazard and reversed hazard functions are considered.
Bivariate generalized inverted Kumaraswamy distribution: properties and applications
Hiba Z Muhammed 한국신뢰성학회 2019 International Journal of Reliability and Applicati Vol.20 No.1
The inverted distributions have a wide range of applications in problems related to econometrics, biological sciences, survey sampling, engineering sciences, medical research and life testing problems. In addition, it is employed in financial literature, environmental studies, survival and reliability theory. The main aim of this paper is to define a bivariate generalized inverted Kumaraswamy distribution so that the marginals have generalized inverted Kumaraswamy distributions. And define a bivariate inverted Kumaraswamy distribution as a special case from the bivariate generalized inverted Kumaraswamy distribution. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in explicit forms. Different properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix are obtained. Bayesian estimators are also obtained for the unknown parameters of this model explicitly. Some simulations to see the performances of the MLEs are performed. One data analysis also has been performed for illustrative purpose.
Hiba Z. Muhammed,Essam A. Muhammed 한국신뢰성학회 2020 International Journal of Reliability and Applicati Vol.21 No.1
In this paper, we have discussed the Bayesian and Non Bayesian estimation of the unknown parameters of the inverse Weibull (IW) distribution and the exponential distribution under randomly censored data. The Bayes estimates (BEs) have been computed based on squared error loss (SEL) and general entropy loss (GEL) functions and by using Markov Chain Monte Carlo (MCMC) techniques. Asymptotic and bootstrap confidence intervals and highest posterior density (HPD) intervals are evaluated for the unknown parameters. Simulation study is carried out to see the performance of the maximum likelihood estimators (MLEs) and Bayes estimators. Finally, one real data set has been reanalyzed for illustrative purpose.
Statistical Properties of Kumaraswamy Exponentiated Gamma Distribution
Diab, L.S.,Muhammed, Hiba Z. The Korean Reliability Society 2015 International Journal of Reliability and Applicati Vol.16 No.2
The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.
Statistical Properties of Kumaraswamy Exponentiated Gamma Distribution
L. S. Diab,Hiba Z. Muhammed 한국신뢰성학회 2015 International Journal of Reliability and Applicati Vol.16 No.2
The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the r<SUP>th</SUP> moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.