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A new generalization of exponentiated Frechet distribution
L. S. Diab,I. Elbatal 한국신뢰성학회 2016 International Journal of Reliability and Applicati Vol.17 No.1
Motivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy exponentiated Frechet distribution (KEF). We derive some mathematical properties of the (KEF) including moment generating function, moments, quantile function and incomplete moment. We provide explicit expressions for the density function of the order statistics and their moments. In addition, the method of maximum likelihood and least squares and weighted least squares estimators are discuss for estimating the model parameters. A real data set is used to illustrate the importance and flexibility of the new distribution.
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.
A new generalization of exponentiated Frechet distribution
Diab, L.S.,Elbatal, I. The Korean Reliability Society 2016 International Journal of Reliability and Applicati Vol.17 No.1
Motivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy exponentiated Frechet distribution (KEF). We derive some mathematical properties of the (KEF) including moment generating function, moments, quantile function and incomplete moment. We provide explicit expressions for the density function of the order statistics and their moments. In addition, the method of maximum likelihood and least squares and weighted least squares estimators are discuss for estimating the model parameters. A real data set is used to illustrate the importance and flexibility of the new distribution.
Testing exponentiality against RNBRUE based on laplace transform order
S. M. El-Arishy,L. S. Diab,E. S. El-Atfy 한국신뢰성학회 2019 International Journal of Reliability and Applicati Vol.20 No.1
In this paper, a new hypothesis test is constructed to test exponentiality against RNBRUE based on Laplace transform order and another test based on goodness of fit approach follows as a special case. Pitman asymptotic efficiency (PAE) are studied, the critical values of the tests are tabulated for sample sizes n=5(5)50, and the power estimates are calculated to assess the performance of the tests. Also a test of exponentiality versus RNBRUE for right censored data is considered. The power estimates of the tests are simulated for some commonly used distributions in reliability. Finally, sets of real data are used as examples to elucidate the use of the proposed test statistic for practical problems in case of complete and uncompleted data in the reliability analysis.
Exponentiated Quasi Lindley distribution
I. Elbatal,L. S. Diab,M. Elgarhy 한국신뢰성학회 2016 International Journal of Reliability and Applicati Vol.17 No.1
The Exponentiated Quasi Lindley (EQL) distribution which is an extension of the quasi Lindley Distribution is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density and hazard rate functions, the moments and moment generating function, the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally an application of the model with a real data set is presented for the illustration of the usefulness of the proposed distribution.
Exponentiated Quasi Lindley distribution
Elbatal, I.,Diab, L.S.,Elgarhy, M. The Korean Reliability Society 2016 International Journal of Reliability and Applicati Vol.17 No.1
The Exponentiated Quasi Lindley (EQL) distribution which is an extension of the quasi Lindley Distribution is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density and hazard rate functions, the moments and moment generating function, the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally an application of the model with a real data set is presented for the illustration of the usefulness of the proposed distribution.
Testing NRBU Class of Life Distributions Using a Goodness of Fit Approach
El-Arishy, S.M.,Diab, L.S.,Alim, N.A. Abdul The Korean Reliability Society 2006 International Journal of Reliability and Applicati Vol.7 No.2
In this paper, we present the U-Statistic test for testing exponentiality against new renewal better than used (NRBU) based on a goodness of fit approach. Selected critical values are tabulated for sample sizes n=5(1)30(10)50. The asymptotic Pitman relative efficiency relative to (NRBU) test given in the work of Mahmoud et all (2003) is studied. The power estimates of this test for some commonly used life distributions in reliability are also calculated. Some of real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. The problem in case of right censored data is also handled.