A.I. Shawky - Academia.edu (original) (raw)

Papers by A.I. Shawky

International Journal of Mathematical Analysis, 2014

Advances and Applications in Statistics

In this study, we propose a new family of distributions called the Gompertz general (Gom-G) distr... more In this study, we propose a new family of distributions called the Gompertz general (Gom-G) distribution. Some properties of the new family of distributions are discussed. Explicit expressions for the ordinary and incomplete moments, quantile function, entropies

Recently Gupta et al. (1998) introduced a new distribution, called exponentiated Pareto distribut... more Recently Gupta et al. (1998) introduced a new distribution, called exponentiated Pareto distribution. In this paper, we consider the exponentiated Pareto mixture distribution (EPMD) as a possible model for a life time distribution. The moments about zero, median, mode and measures of variation, skewness and kurtosis of random variable have EPMD are derived. We establish recurrence relation between moments about mean of random variable having EPMD. Based on Type II censored samples from a heterogeneous population that can be represented by a finite mixture of exponentiated Pareto life time model, the maximum likelihood and Bayes estimates of the parameters are obtained. An approximation form due to Lindley (1980) is used to obtain the corresponding Bayes estimates.

This article examines statistical inference for   X Y P R   where X and Y are independent but... more This article examines statistical inference for   X Y P R   where X and Y are independent but not identically distributed Pareto of the first kind (Pareto (I)) random variables with same scale parameter but different shape parameters. The Maximum likelihood, uniformly minimum variance unbiased and Bayes estimators with Gamma prior are used for this purpose. Simulation studies which compare the estimators are presented. Moreover, sensitivity of Bayes estimator to the prior parameters is considered.

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 2004

Journal of Statistical Research of Iran, 2009

Journal of Computational and Theoretical Nanoscience, 2015

Explicit expressions are derived for the kth moment of the rth order statistics arising from inde... more Explicit expressions are derived for the kth moment of the rth order statistics arising from independent and nonidentically distributed Pearson III random variables. Applications to reliability analysis and stochastic activity networks are given. An upper and lower bound estimate for the network completion times when activity times follow Pearson III as well as the gamma random variables is presented. Mathematica 7 codes to perform the calculations are also given.

Journal of Computational and Theoretical Nanoscience, 2016

In this paper, we study the lower record values from an exponentiated gamma distribution and deri... more In this paper, we study the lower record values from an exponentiated gamma distribution and derive explicit expressions for the single, product, triple and quadruple moments. We also, establish recurrence relations for the single, product, triple and quadruple moments and moment generating function.

Journal of Computational and Theoretical Nanoscience, 2017

SpringerPlus, 2016

Background The log-logistic (LL) distribution (branded as the Fisk distribution in economics) pos... more Background The log-logistic (LL) distribution (branded as the Fisk distribution in economics) possesses a rather supple functional form. The LL distribution is among the class of survival time parametric models where the hazard rate initially increases and then decreases and at times can be hump-shaped. The LL distribution can be used as a suitable substitute for Weibull distribution. It is in fact a mixture of Gompertz distribution and Gamma distribution with the value of the mean and the variance coincide-equal to one. The LL distribution as a life testing model has its own standing; it is an increasing failure rate (IFR) model and also is viewed as a weighted exponential distribution. Scrolling through the literature on the subject distribution we see that Bain (1974) modeled LL distribution by a transformation of a well-known logistic variate. The properties of LL distribution have been deliberated upon by Ragab and Green (1984) who also worked on the order statistics for the said distribution. Kantam et al. (2001) proposed acceptance sampling plan using the LL distribution. Kantam et al. (2006) designed economic acceptance sampling plan using the LL distribution. Kantam and Rao (2002) derived the modified maximum likelihood estimation (MLE) of this distribution.

Pakistan Journal of Statistics and Operation Research, 2016

In this paper we have proposed a new family of distributions; the Topp-Leone family of distributi... more In this paper we have proposed a new family of distributions; the Topp-Leone family of distributions. We have given general expression for density and distribution function of the new family. Expression for moments and hazard rate has also been given. We have also given an example of the proposed family.

Journal of Computational and Theoretical Nanoscience, 2015

In this paper, we consider the exponentiated Pareto (EP) distribution with two shape parameters θ... more In this paper, we consider the exponentiated Pareto (EP) distribution with two shape parameters θ and λ. We first derive the exact forms of means, variances and covariances of record values. The maximum likelihood estimators (MLE's) of the two shape parameters θ and λ are derived. Based on the moments of lower record values, we obtained the necessary coefficients for the best linear unbiased estimators (BLUE's) of the location and scale parameters of EP distribution. The variances and covariances of these estimators are also given. The best linear unbiased predictor (BLUP) of the future record value is also discussed.

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1999

Life Science Journal

The reliability equivalence factors of parallel and series systems with n independent non-identic... more The reliability equivalence factors of parallel and series systems with n independent non-identical components are obtained. Three different methods are used to improve such systems: (i) improving the quality of several components by decreasing their failure rates, (ii) adding a hot component to the system, and (iii) adding a cold redundant component to the system. The survival function is used as a performance measure of the system reliability to compare different system designs. The rth moment time to failures will be derived in parallel and series systems in Weibull Distribution.

The International Journal of Contemporary …, 2009

Order statistics from an exponentiated gamma (EG) distribution are considered. Exact expression f... more Order statistics from an exponentiated gamma (EG) distribution are considered. Exact expression for the single and double moments of order statistics from EG distribution are derived. Based on the moments of order statistics, the best linear unbiased estimators (BLUE's) for the location and scale parameters of EG distribution under Type-II censoring are obtained. The variances and covariances of these estimators are also presented. The maximum likelihood estimator (MLE) for the shape parameter is derived. Also, estimators based on order statistics for the shape parameter are obtained. Finally, comparisons between the estimators are made based on simulation study.

Stochastics and Stochastic Reports, 2000

Production Planning & Control, 2001

In this paper our main objective is to investigate a deterministic inventory production lot-size ... more In this paper our main objective is to investigate a deterministic inventory production lot-size model with a permissible delay in payment under a restriction. We analyse our deterministic inventory model under a restriction which will be assumed as the average inventory level. ...

International Journal of Mathematical Analysis, 2014

Advances and Applications in Statistics

In this study, we propose a new family of distributions called the Gompertz general (Gom-G) distr... more In this study, we propose a new family of distributions called the Gompertz general (Gom-G) distribution. Some properties of the new family of distributions are discussed. Explicit expressions for the ordinary and incomplete moments, quantile function, entropies

Recently Gupta et al. (1998) introduced a new distribution, called exponentiated Pareto distribut... more Recently Gupta et al. (1998) introduced a new distribution, called exponentiated Pareto distribution. In this paper, we consider the exponentiated Pareto mixture distribution (EPMD) as a possible model for a life time distribution. The moments about zero, median, mode and measures of variation, skewness and kurtosis of random variable have EPMD are derived. We establish recurrence relation between moments about mean of random variable having EPMD. Based on Type II censored samples from a heterogeneous population that can be represented by a finite mixture of exponentiated Pareto life time model, the maximum likelihood and Bayes estimates of the parameters are obtained. An approximation form due to Lindley (1980) is used to obtain the corresponding Bayes estimates.

This article examines statistical inference for   X Y P R   where X and Y are independent but... more This article examines statistical inference for   X Y P R   where X and Y are independent but not identically distributed Pareto of the first kind (Pareto (I)) random variables with same scale parameter but different shape parameters. The Maximum likelihood, uniformly minimum variance unbiased and Bayes estimators with Gamma prior are used for this purpose. Simulation studies which compare the estimators are presented. Moreover, sensitivity of Bayes estimator to the prior parameters is considered.

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 2004

Journal of Statistical Research of Iran, 2009

Journal of Computational and Theoretical Nanoscience, 2015

Explicit expressions are derived for the kth moment of the rth order statistics arising from inde... more Explicit expressions are derived for the kth moment of the rth order statistics arising from independent and nonidentically distributed Pearson III random variables. Applications to reliability analysis and stochastic activity networks are given. An upper and lower bound estimate for the network completion times when activity times follow Pearson III as well as the gamma random variables is presented. Mathematica 7 codes to perform the calculations are also given.

Journal of Computational and Theoretical Nanoscience, 2016

In this paper, we study the lower record values from an exponentiated gamma distribution and deri... more In this paper, we study the lower record values from an exponentiated gamma distribution and derive explicit expressions for the single, product, triple and quadruple moments. We also, establish recurrence relations for the single, product, triple and quadruple moments and moment generating function.

Journal of Computational and Theoretical Nanoscience, 2017

SpringerPlus, 2016

Background The log-logistic (LL) distribution (branded as the Fisk distribution in economics) pos... more Background The log-logistic (LL) distribution (branded as the Fisk distribution in economics) possesses a rather supple functional form. The LL distribution is among the class of survival time parametric models where the hazard rate initially increases and then decreases and at times can be hump-shaped. The LL distribution can be used as a suitable substitute for Weibull distribution. It is in fact a mixture of Gompertz distribution and Gamma distribution with the value of the mean and the variance coincide-equal to one. The LL distribution as a life testing model has its own standing; it is an increasing failure rate (IFR) model and also is viewed as a weighted exponential distribution. Scrolling through the literature on the subject distribution we see that Bain (1974) modeled LL distribution by a transformation of a well-known logistic variate. The properties of LL distribution have been deliberated upon by Ragab and Green (1984) who also worked on the order statistics for the said distribution. Kantam et al. (2001) proposed acceptance sampling plan using the LL distribution. Kantam et al. (2006) designed economic acceptance sampling plan using the LL distribution. Kantam and Rao (2002) derived the modified maximum likelihood estimation (MLE) of this distribution.

Pakistan Journal of Statistics and Operation Research, 2016

In this paper we have proposed a new family of distributions; the Topp-Leone family of distributi... more In this paper we have proposed a new family of distributions; the Topp-Leone family of distributions. We have given general expression for density and distribution function of the new family. Expression for moments and hazard rate has also been given. We have also given an example of the proposed family.

Journal of Computational and Theoretical Nanoscience, 2015

In this paper, we consider the exponentiated Pareto (EP) distribution with two shape parameters θ... more In this paper, we consider the exponentiated Pareto (EP) distribution with two shape parameters θ and λ. We first derive the exact forms of means, variances and covariances of record values. The maximum likelihood estimators (MLE's) of the two shape parameters θ and λ are derived. Based on the moments of lower record values, we obtained the necessary coefficients for the best linear unbiased estimators (BLUE's) of the location and scale parameters of EP distribution. The variances and covariances of these estimators are also given. The best linear unbiased predictor (BLUP) of the future record value is also discussed.

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1999

Life Science Journal

The reliability equivalence factors of parallel and series systems with n independent non-identic... more The reliability equivalence factors of parallel and series systems with n independent non-identical components are obtained. Three different methods are used to improve such systems: (i) improving the quality of several components by decreasing their failure rates, (ii) adding a hot component to the system, and (iii) adding a cold redundant component to the system. The survival function is used as a performance measure of the system reliability to compare different system designs. The rth moment time to failures will be derived in parallel and series systems in Weibull Distribution.

The International Journal of Contemporary …, 2009

Order statistics from an exponentiated gamma (EG) distribution are considered. Exact expression f... more Order statistics from an exponentiated gamma (EG) distribution are considered. Exact expression for the single and double moments of order statistics from EG distribution are derived. Based on the moments of order statistics, the best linear unbiased estimators (BLUE's) for the location and scale parameters of EG distribution under Type-II censoring are obtained. The variances and covariances of these estimators are also presented. The maximum likelihood estimator (MLE) for the shape parameter is derived. Also, estimators based on order statistics for the shape parameter are obtained. Finally, comparisons between the estimators are made based on simulation study.

Stochastics and Stochastic Reports, 2000

Production Planning & Control, 2001

In this paper our main objective is to investigate a deterministic inventory production lot-size ... more In this paper our main objective is to investigate a deterministic inventory production lot-size model with a permissible delay in payment under a restriction. We analyse our deterministic inventory model under a restriction which will be assumed as the average inventory level. ...