Ibrahim Elbatal | Cairo University Egypt (original) (raw)

Papers by Ibrahim Elbatal

Journal of Statistical Theory and Applications, 2020

This paper proposes a new flexible four-parameter model called Marshall Olkin power generalized W... more This paper proposes a new flexible four-parameter model called Marshall Olkin power generalized Weibull (MOPGW) distribution which provides symmetrical, reversed-J shaped, left-skewed and right-skewed densities, and bathtub, unimodal, increasing, constant, decreasing, J shaped, and reversed-J shaped hazard rates. Some of the MOPGW structural properties are discussed. The maximum likelihood is utilized to estimate the MOPGW unknown parameters. Simulation results are provided to assess the performance of the maximum likelihood method. Finally, we illustrate the importance of the MOPGW model, compared with some rival models, via two real data applications from the engineering and medicine fields.

Journal of Statistical Planning and Inference, 2006

In this paper we consider some widely utilized classes of discrete distributions and aim to provi... more In this paper we consider some widely utilized classes of discrete distributions and aim to provide a systematic overview about their preservation under convolution. This paper will serve as a detailed reference for the study and applications of the preservation of the discrete NBU(2), NBUCA classes of discrete distributions.

A six parameter distribution so-called the McDonald modified Weibull distribution is defined and ... more A six parameter distribution so-called the McDonald modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the beta modified Weibull, Kumaraswamy modified Weibull, McDonald Weibull and modified Weibull distribution,among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments.We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

Mathematics

In this paper, we introduce a new continuous probability distribution with five parameters called... more In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz distribution. By investigating its mathematical and practical aspects, we prove that it is quite flexible and can be used effectively in modeling a wide variety of real phenomena. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, entropies and order statistics. We explore the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study testing the validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by the consideration of two real datasets.

Pakistan Journal of Statistics and Operation Research, 2016

The exponentiated gamma (EG) distribution is one of the important families of distributions in li... more 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 the beta exponentiated gamma (BEG) distribution has been introduced. The new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the BEG distribution has been provided. We derived the rth moment and moment generating function for this distribution. Moreover, we discussed the maximum likelihood estimation of this distribution under a simulation study.

Austrian Journal of Statistics

In this article a continuous distribution, the so-called transmuted additive Weibull distribution... more In this article a continuous distribution, the so-called transmuted additive Weibull distribution, that extends the additive Weibull distribution and some other distributions is proposed and studied. We will use the quadratic rank transmutation map proposed by Shaw and Buckley (2009) in order to generate the transmuted additive Weibull distribution. Various structural properties of the new distribution including explicit expressions for the moments, random number generation and order statistics are derived. Maximum likelihood estimation of the unknown parameters of the new model for complete sample is also discussed. It will be shown that the analytical results are applicable to model real world data. Zusammenfassung: In diesem Artikel wird eine stetige Verteilung vorgeschlagen und untersucht, die sogenannte additive umgewandelte Weibull-Verteilung, welche die additive Weibull-Verteilung und einige andere Verteilungen erweitert. Wir verwenden die quadratische Rang Transmutations-Abbildung, vorgeschlagen in Shaw and Buckley (2009), um die additive umgewandelte Weibull-Verteilung zu erzeugen. Verschiedene strukturelle Eigenschaften der neuen Verteilung einschließlich explizite Ausdrücke für die Momente, Erzeugung von Zufallszahlen, und Ordnungsstatistiken werden hergeleitet. Maximum Likelihood Schätzung der unbekannten Parameter dieses neuen Modells für die vollständige Stichprobe wird ebenfalls diskutiert. Es wird gezeigt, dass diese analytischen Ergebnisse verwendbar sind um reale Daten zu modellieren.

Pakistan Journal of Statistics and Operation Research

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential ... more In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

The linear exponential distribution is a very well-known distribution for modeling lifetime data ... more The linear exponential distribution is a very well-known distribution for modeling lifetime data in reliability and medical studies. We introduce in this paper a new four-parameter generalized version of the linear exponential distribution which is called Kumaraswamy linear exponential distribution. We provide a comprehensive account of the mathematical properties of the new distributions. In particular, a closed-form expressions for the density, cumulative distribution and hazard rate function of the distribution is given. Also, the rth order moment and moment generating function are derived. The maximum likelihood estimation of the unknown parameters is discussed.

Austrian Journal of Statistics, 2014

A generalization of the generalized inverse Weibull distribution the so-called transmuted general... more A generalization of the generalized inverse Weibull distribution the so-called transmuted generalized inverse Weibull distribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking the generalized inverse Weibull distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. Various structural properties including explicit expressions for the moments, quantiles, and moment generating function of the new distribution are derived. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the flexibility of the transmuted version versus the generalized inverse Weibull distribution.

In this paper we study a new broad class of distribution functions which is defined by means of r... more In this paper we study a new broad class of distribution functions which is defined by means of reflected generalized beta distribution. This class includes that of Beta-generated distribution as a special case. In particular, we extend the Generalized Inverse Weibull distribution proposed by Gusm\~ao et al. [2011], in order to obtain the Reflected Generalized Beta of Generalized Inverse Weibull Distribution. For this new distribution, moments, entropy, order statistics and a reliability measure are derived. The link between the InverseWeibull and the Dagum distribution is generalized. Then the maximum likelihood estimators of the parameters are examined and the observed Fisher information matrix provided. Finally, the usefulness of the model is illustrated by means of an application to real data.

Economic Quality Control, 2013

This paper introduces a transmuted generalized inverted exponential distribution. We generalize t... more This paper introduces a transmuted generalized inverted exponential distribution. We generalize the two parameter generalized inverted exponential distribution using the quadratic rank transmutation map proposed by to develop a transmuted generalized inverted exponential distribution. The properties of the transmuted generalized inverted exponential distribution are discussed. We derive the moments and examine the order statistics. Moreover, the maximum likelihood estimators for the parameters is briefly investigated and the information matrix is derived.

Journal of Statistics Applications & Probability, 2014

A functional composition of the cumulative distribution function of one probability distribution ... more A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking Lindley-geometric distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. It will be shown that the analytical results are applicable to model real world data.

Economic Quality Control, 2014

In this paper we introduce the so-called McDonald Exponentiated Pareto distribution. We provide a... more In this paper we introduce the so-called McDonald Exponentiated Pareto distribution. We provide a number of mathematical properties of this distribution and derive among others expressions for its momentgenerating function, the th moment, and the Renyi entropy. Finally, we present the likelihood equations to support the application of the McDonald Exponentiated Pareto distribution. The aim of the paper is to introduce an interesting distribution which is distinguished by high flexibility with respect to skewness and tail behavior.

METRON, 2014

A new class of lifetime distributions is introduced by compounding the modified Weibull and geome... more A new class of lifetime distributions is introduced by compounding the modified Weibull and geometric distributions, the so-called modified Weibull geometric distribution. It includes as special submodels such as linear failure rate geometric distribution, Weibull geometric distribution, exponential geometric distribution, among others. We study its structural properties including probability density function, hazard functions, moments, generating and quantile functions. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. Estimation by maximum likelihood and inference for a large sample are presented. An expectation-maximization algorithm is used to determine the maximum likelihood estimates of the parameters. Finally, a real data set is analyzed for illustrative purposes.

A generalization of the exponentiated Weibull geometric model called the transmuted exponentiated... more A generalization of the exponentiated Weibull geometric model called the transmuted exponentiated Weibull geometric distribution is proposed and studied. It includes as special cases at least ten models. Some of its structural properties including order statistics, explicit expressions for the ordinary and incomplete moments and generating function are derived. The estimation of the model parameters is performed by the maximum likelihood method. The use of the new lifetime distribution is illustrated with an example. We hope that the proposed distribution will serve as a good alternative to other models available in the literature for modeling positive real data in several areas.