- Iam a doctur in mathimatical statisticsedit
Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime... more
Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared to many distributions in analysis real data.
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This paper deals with the problem of estimation of the stress–strength function $$R = P(Y < X)$$R=P(Y<X), when X and Y are two independent but not identically distributed random variables belonging to the exponentiated Frechet (EF)... more
This paper deals with the problem of estimation of the stress–strength function $$R = P(Y < X)$$R=P(Y<X), when X and Y are two independent but not identically distributed random variables belonging to the exponentiated Frechet (EF) distribution. Different estimators of R, namely, maximum likelihood, uniformly minimum variance unbiased, and Bayes, are derived in closed form. In addition, two-sided confidence interval for R is obtained. We discuss the reliability in multi-component model. Simulation studies are performed to compare the different estimates of $$R$$R and $$R_{s, k}$$Rs,k. Real data are used as a practical application of the proposed procedure.
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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... 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.
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The purpose of this study is to introduce a new T-X family lifetime distribution known as exponentiated exponential-inverse Weibull, and we refer to this distribution as EE-IW. The new model’s basic mathematical characteristics are... more
The purpose of this study is to introduce a new T-X family lifetime distribution known as exponentiated exponential-inverse Weibull, and we refer to this distribution as EE-IW. The new model’s basic mathematical characteristics are studied. The maximum likelihood (ML) estimator (MLE) approach is used to estimate the parameters. A Monte Carlo simulation is done to examine the behavior of the estimators. Finally, a real-world dataset is utilized to show the utility of the proposed model in many industries and to compare it to well-known distributions.
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In this paper, we will discuss the mixture distribution consists of two components from exponentiated Frechet distribution (EFD) based on upper record values. We will study the maximum likelihood estimator (MLE) and Bayes estimation under... more
In this paper, we will discuss the mixture distribution consists of two components from exponentiated Frechet distribution (EFD) based on upper record values. We will study the maximum likelihood estimator (MLE) and Bayes estimation under quadratic loss and LINEX loss functions for two parameters �� and �� of distribution, reliability and failure rate functions. Through Monte Carlo simulation, the root mean square errors (RMSEs) of the estimators are computed and compared between them. (M.M. Badr. Mixture of exponentiated Frechet distribution based on upper record values. J Am Sci
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The performance and potential of a process of industrial products is assessed under lower specification limit L by lifetime performance index (CL). In this paper, under consideration the independent lifetimes Chen products with known one... more
The performance and potential of a process of industrial products is assessed under lower specification limit L by lifetime performance index (CL). In this paper, under consideration the independent lifetimes Chen products with known one shape parameters the CL of the performance of a process is evaluated. For the hybrid censoring scheme the maximum likelihood (ML) estimate of CL is constructed as well as confidence interval for CL is developing. Also, Bayesian approach is adopted to estimates CL and credibly interval is constructed. Some theoretical results of hypothesis tests of CL is adopted. Finally, our obtaining results will be assessed and compared through Monte Carlo simulation study and numerical example.
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This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on upper record values. We have derived the maximum likelihood (ML) and Bayesian estimators for the unknown two parameters, as... more
This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on upper record values. We have derived the maximum likelihood (ML) and Bayesian estimators for the unknown two parameters, as well as the reliability and hazard functions. We obtained Bayes estimators on the basis of the symmetric (squared error) and asymmetric (linear exponential (LINEX) and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Furthermore, Bayesian prediction interval of the future upper record values are discussed and obtained. Finally, estimation of the parameters, practical examples of real record values and simulated record values are given to illustrate the theoretical results of prediction interval.
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This problem is of importance in the following physical situation. Suppose that X is the strength of a component which is subjected to a stress Y. Then, the component fails whenever X &lt; Y and there is no failure when Y &lt; X.... more
This problem is of importance in the following physical situation. Suppose that X is the strength of a component which is subjected to a stress Y. Then, the component fails whenever X &lt; Y and there is no failure when Y &lt; X. In addition, the stresses may be expensive to sample, such ...
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Recently, several writers have extended the exponentiated Weibull distribution. The five-parameter exponentiated Weibull-exponentiated Weibull (EW-EW) distribution is introduced. In terms of fit, the EW-EW distribution outperforms the EW... more
Recently, several writers have extended the exponentiated Weibull distribution. The five-parameter exponentiated Weibull-exponentiated Weibull (EW-EW) distribution is introduced. In terms of fit, the EW-EW distribution outperforms the EW distribution. Some EW-EW distribution features, such as precise formulas for ordinary moments, quantile, median, and order statistics, are found. Model parameters were estimated using the maximum likelihood technique (ML). The behavior of the various estimators was investigated using a simulated exercise. A medical dataset was utilized to evaluate the practical importance of the EW-EW distribution using additional criteria such as the Akaike information criterion (AKINC), the correct AKINC (COAKINC), the Bayesian INC (BINC), and the Hannan-Quinn INC (HQINC). In terms of performance, we show that the EW-EW distribution beats other models.
In this article we introduce a new six - parameters model called the Beta Generalized Exponentiated-Frechet (BGEF) distribution which exhibits decreasing hazard rate. Many models such as Beta Frechet (BF), Beta ExponentiatedFrechet (BEF),... more
In this article we introduce a new six - parameters model called the Beta Generalized Exponentiated-Frechet (BGEF) distribution which exhibits decreasing hazard rate. Many models such as Beta Frechet (BF), Beta ExponentiatedFrechet (BEF), Generalized Exponentiated-Frechet (GEF), ExponentiatedFrechet (EF), Frechet (F) are sub models. Some of its properties including rth moment, reliability and hazard rate are investigated. The method of maximum likelihood isproposed to estimate the model parameters. The observed Fisher’s information matrix is given. Moreover, we give the advantage of the (BGEF) distribution by an application using two real datasets
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Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime... more
Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared...
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The paper addresses a new four-parameter probability distribution called the Exponentiated Exponential Burr XII or abbreviated as EE-BXII. We derive various statistical properties in addition to the parameter estimation, moments, and... more
The paper addresses a new four-parameter probability distribution called the Exponentiated Exponential Burr XII or abbreviated as EE-BXII. We derive various statistical properties in addition to the parameter estimation, moments, and asymptotic confidence bounds. We estimate the precision of the maximum likelihood estimators via a simulation study. Furthermore, the utility of the proposed distribution is evaluated by using two lifetime data sets and the results are compared with other existing probability distributions. The results clarify that the proposed distribution provides a better fit to these data sets as compared to the existing probability distributions.
In this article, we introduce a new three-parameter lifetime model, which is called truncated Cauchy power Log-Logistic (TCPLL) model. The TCPLL model has many applications in different sciences, such as physics and medicine, and we show... more
In this article, we introduce a new three-parameter lifetime model, which is called truncated Cauchy power Log-Logistic (TCPLL) model. The TCPLL model has many applications in different sciences, such as physics and medicine, and we show that in the application section. We used two real-life datasets related to physics and medicine to show the flexibility of the TCPLL model. The TCPLL distribution is more flexible than some well-known models. The TCPLL parameters are estimated using maximum likelihood method for estimation. The numerical study is displayed to show the effectiveness of the estimates. At the end, we calculated some important properties like, quantile function, moments, order statistics and moment generating function of the proposed model.
The last years, the odd Fréchet-G family has been considered with success in various statistical applications. This notoriety can be explained by its simple and flexible exponential-odd structure quite different to the other existing... more
The last years, the odd Fréchet-G family has been considered with success in various statistical applications. This notoriety can be explained by its simple and flexible exponential-odd structure quite different to the other existing families, with the use of only one additional parameter. In counter part, some of its statistical properties suffer of a lack of adaptivity in the sense that they really depend on the choice of the baseline distribution. Hence, efforts have been made to relax this subjectivity by investigating extensions or generalizations of the odd transformation at the heart of the construction of this family, with the aim to reach new perspectives of applications as well. This study explores another possibility, based on the transformation of the whole cumulative distribution function of this family (while keeping the odd transformation intact), through the use of the quadratic rank transmutation that has proven itself in other contexts. We thus introduce and study ...