scholarly journals A New Extremely Flexible Version of the Exponentiated Weibull Model: Theorem and Applications to Reliability and Medical Data Sets

2019 ◽  
pp. 195-215
Author(s):  
Mohamed Abo Raya
Keyword(s):  
Weibull Model ◽  
Hazard Rates ◽  
Data Sets ◽  
Suitable Model ◽  
New Model ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull ◽  
Weibull Models ◽  
Lifetime Model ◽  
New Distribution

In this work, a new lifetime model is introduced and studied. The major justification for the practicality of the new model is based on the wider use of the exponentiated Weibull and Weibull models. We are also motivated to introduce the new lifetime model since it exhibits decreasing, upside down-increasing, constant, increasing-constant and J shaped hazard rates also the density of the new distribution exhibits various important shapes. The new model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be considered as a suitable model for fitting the symmetric, left skewed, right skewed and unimodal data. The importance and flexibility of the new model is illustrated by four read data applications.

scholarly journals A New Flexible Lifetime Model with Statistical Properties and Applications

2018 ◽  
pp. 881-901
Author(s):  
Mohamed Abo Raya
Keyword(s):  
Survival Times ◽  
New Model ◽  
Proposed Model ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull ◽  
Weibull Models ◽  
Lifetime Model ◽  
Modified Weibull ◽  
The Right ◽  
Better Than

In this article, we introduce a new lifetime model which exhibits the increasing, the decreasing and the bathtub hazard rates. The considerable justification for the practicality of the new lifetime model is depended on the wider use of the exponentiated Weibull and Weibull lifetime models. The new lifetime model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be viewed as a appropriate model for fitting the right skewed, the symmetric, the left skewed and the unimodal data. We prove empirically the importance and flexibility of the new model in modeling two types of lifetime data. The new lifetime model is a superior on the Marshall Olkin extended-Weibull, the Poisson Topp Leone-Weibull, the Burr X Exponentiated-Weibull, the Kumaraswamy-Weibull, the Gamma-Weibull, the Transmuted modified-Weibull, the Weibull-Fréchet, the Beta-Weibull, the Mcdonald-Weibull, the transmuted exponentiated generalized-Weibull, the Kumaraswamy transmuted-Weibull, and the Modified beta-Weibull models so the new model is a good substitutional to these models in modeling the aircraft windshield data. The new lifetime model is much better than the Mcdonald-Weibull, the transmuted linear exponential, the Weibull, the transmuted modified-Weibull, the Modified beta-Weibull,the transmuted additive-Weibull, the exponentiated transmuted generalized Rayleig models in modeling cancer patient data. In modeling the survival times of Guinea pigs data we deduced that the proposed model is much better than the Odd Weibull-Weibull, the Weibull Logarithmic-Weibull and the gamma exponentiated-exponential models. Finally, the new model is a preferable model than the exponentiated-Weibull, the transmuted-Weibull, the Odd Log Logistic-Weibull models, and a good alternate to these models in modeling Glass fibres data.

scholarly journals The Burr X Exponentiated Weibull Model: Characterizations,Mathematical Properties and Applications to Failure and Survival Times Data

2019 ◽  
pp. 141-160 ◽  
Author(s):  
Mohamed G. Khalil ◽  
G. G. Hamedani ◽  
Haitham M. Yousof
Keyword(s):  
Weibull Model ◽  
Good Alternative ◽  
Likelihood Method ◽  
Model Parameters ◽  
Suitable Model ◽  
Survival Times ◽  
Exponentiated Weibull ◽  
Weibull Models ◽  
Lifetime Model ◽  
The Right

In this article, we introduce a new three-parameter lifetime model called the Burr X exponentiated Weibull model. The major justification for the practicality of the new lifetime model is based on the wider use of the exponentiated Weibull and Weibull models. We are motivated to propose this new lifetime model because it exhibits increasing, decreasing, bathtub, J shaped and constant hazard rates. The new lifetime model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be viewed as a suitable model for fitting the right skewed, symmetric, left skewed and unimodal data. We provide a comprehensive account of some of its statistical properties. Some useful characterization results are presented. The maximum likelihood method is used to estimate the model parameters. We prove empirically the importance and flexibility of the new model in modeling two types of lifetime data. The proposed model is a better fit than the Poisson Topp Leone-Weibull, the Marshall Olkin extended-Weibull, gamma-Weibull , Kumaraswamy-Weibull , Weibull-Fréchet, beta-Weibull, transmuted modified-Weibull, Kumaraswamy transmuted- Weibull, modified beta-Weibull, Mcdonald-Weibull and transmuted exponentiated generalized-Weibull models so it is a good alternative to these models in modeling aircraft windshield data as well as the new lifetime model is much better than the Weibull-Weibull, odd Weibull-Weibull, Weibull Log-Weibull, the gamma exponentiated-exponential and exponential exponential-geometric models so it is a good alternative to these models in modeling the survival times of Guinea pigs. We hope that the new distribution will attract wider applications in reliability, engineering and other areas of research.

scholarly journals A New Flexible Version of the Lomax Distribution with Applications

2018 ◽  
Vol 7 (5) ◽  
pp. 120
Author(s):  
T. H. M. Abouelmagd
Keyword(s):  
Estimation Method ◽  
Good Alternative ◽  
Model Parameters ◽  
Data Sets ◽  
Suitable Model ◽  
Lifetime Data ◽  
New Model ◽  
The Right ◽  
New Distribution ◽  
Better Than

A new version of the Lomax model is introduced andstudied. The major justification for the practicality of the new model isbased on the wider use of the Lomax model. We are also motivated tointroduce the new model since the density of the new distribution exhibitsvarious important shapes such as the unimodal, the right skewed and the leftskewed. The new model can be viewed as a mixture of the exponentiated Lomaxdistribution. It can also be considered as a suitable model for fitting thesymmetric, left skewed, right skewed, and unimodal data sets. The maximumlikelihood estimation method is used to estimate the model parameters. Weprove empirically the importance and flexibility of the new model inmodeling two types of aircraft windshield lifetime data sets. The proposedlifetime model is much better than gamma Lomax, exponentiated Lomax, Lomaxand beta Lomax models so the new distribution is a good alternative to thesemodels in modeling aircraft windshield data.

scholarly journals The four-parameter exponentiated Weibull model with Copula, properties and real data modeling.

2021 ◽  
pp. 649-667
Author(s):  
Wahid Shehata ◽  
Haitham M. Yousof
Keyword(s):  
Estimation Method ◽  
Real Data ◽  
Weibull Model ◽  
Hazard Rates ◽  
Survival Times ◽  
New Model ◽  
Clayton Copula ◽  
Failure Times ◽  
Mathematical Properties ◽  
Exponentiated Weibull

A new four-parameter lifetime model is introduced and studied. The new model derives its flexibility and wide applicability from the well-known exponentiated Weibull model. Many bivariate and the multivariate type versions are derived using the Morgenstern family and Clayton copula. The new density can exhibit many important shapes with different skewness and kurtosis which can be unimodal and bimodal. The new hazard rate can be decreasing, J-shape, U-shape, constant, increasing, upside down and increasing-constant hazard rates. Various of its structural mathematical properties are derived. Graphical simulations are used in assessing the performance of the estimation method. We proved empirically the importance and flexibility of the new model in modeling various types of data such as failure times, remission times, survival times and strengths data.

scholarly journals The Two-Parameter Odd Lindley Weibull Lifetime Model with Properties and Applications

2018 ◽  
Vol 7 (4) ◽  
pp. 57 ◽  
Author(s):  
Jehhan. A. Almamy ◽  
Mohamed Ibrahim ◽  
M. S. Eliwa ◽  
Saeed Al-mualim ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Weibull Model ◽  
Good Alternative ◽  
Model Parameters ◽  
Data Sets ◽  
New Model ◽  
Lifetime Model ◽  
Two Parameter ◽  
Better Than

In this work, we study the two-parameter Odd Lindley Weibull lifetime model. This distribution is motivated by the wide use of the Weibull model in many applied areas and also for the fact that this new generalization provides more flexibility to analyze real data. The Odd Lindley Weibull density function can be written as a linear combination of the exponentiated Weibull densities. We derive explicit expressions for the ordinary and incomplete moments, moments of the (reversed) residual life, generating functions and order statistics. We discuss the maximum likelihood estimation of the model parameters. We assess the performance of the maximum likelihood estimators in terms of biases, variances, mean squared of errors by means of a simulation study. The usefulness of the new model is illustrated by means of two real data sets. The new model provides consistently better fits than other competitive models for these data sets. The Odd Lindley Weibull lifetime model is much better than \ Weibull, exponential Weibull, Kumaraswamy Weibull, beta Weibull, and the three parameters odd lindly Weibull with three parameters models so the Odd Lindley Weibull model is a good alternative to these models in modeling glass fibres data as well as the Odd Lindley Weibull model is much better than the Weibull, Lindley Weibull transmuted complementary Weibull geometric and beta Weibull models so it is a good alternative to these models in modeling time-to-failure data.

scholarly journals The Three-parameters Marshall-Olkin Generalized Weibull Model with Properties and Different Applications to Real Data Sets

2020 ◽  
pp. 675-688
Author(s):  
Mohamed G. Khalil ◽  
Wagdy M. Kamel
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Weibull Model ◽  
Parametric Model ◽  
Data Sets ◽  
Unknown Parameters ◽  
Graphical Simulation ◽  
Method Of Maximum Likelihood ◽  
New Distribution

A new three-parameter life parametric model called the Marshall-Olkin generalized Weibull is defined and studied. Relevant properties are mathematically derived and analyzed. The new density exhibits various important symmetric and asymmetric shapes with different useful kurtosis. The new failure rate can be “constant”, “upside down-constant (reversed U-HRF-constant)”, “increasing then constant”, “monotonically increasing”, “J-HRF” and “monotonically decreasing”. The method of maximum likelihood is employed to estimate the unknown parameters. A graphical simulation is performed to assess the performance of the maximum likelihood estimation. We checked and proved empirically the importance, applicability and flexibility of the new Weibull model in modeling various symmetric and asymmetric types of data. The new distribution has a high ability to model different symmetric and asymmetric types of data.

scholarly journals The Topp-Leone Generated Weibull Distribution: Regression Model, Characterizations and Applications

2016 ◽  
Vol 6 (1) ◽  
pp. 126 ◽  
Author(s):  
Gokarna R. Aryal ◽  
Edwin M. Ortega ◽  
G. G. Hamedani ◽  
Haitham M. Yousof
Keyword(s):  
Weibull Distribution ◽  
Regression Model ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Lifetime Model ◽  
First Time ◽  
Two Parameter ◽  
New Distribution

This paper introduces a new four-parameter lifetime model called the Topp Leone Generated Weibull (TLGW) distribution. This distribution is a generalization of the two parameter Weibull distribution using the genesis of Topp-Leone distribution.  We derive many of its structural properties including ordinary and incomplete moments, quantile and generating functions and order statistics. Parameter estimation using maximum likelihood method and simulation results to assess effectiveness of the distribution are discussed. Also, for the first time, we introduce a regression model based on the new distribution. We prove empirically the importance and flexibility of the new model in modeling various types of real data sets.

scholarly journals Stress-Strength Reliability Model with The Exponentiated Weibull Distribution: Inferences and Applications

2018 ◽  
Vol 7 (4) ◽  
pp. 78
Author(s):  
Fathy Helmy Eissa
Keyword(s):  
Real Data ◽  
Credible Interval ◽  
Model Parameters ◽  
Data Sets ◽  
Empirical Bayesian ◽  
Bootstrap Confidence Intervals ◽  
Linex Loss ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull ◽  
Unit Stress

In this paper, we deal with the estimation of the reliability $R=P(Y<X)$ where $X$, a unit strength, and $Y$, a unit stress, are independent exponentiated Weibull random variables. The maximum likelihood and Bayesian methods are used to make inference about $R$. We obtain the Baysian estimator using Lindely's procedure under squared error loss and LINEX loss functions with gamma prior for the unknown model parameters. The asymptotic and bootstrap confidence intervals are obtained as well as the credible interval for R is constructed in view of the empirical Bayesian procedure. For illustrative purposes, analysis of real data sets is presented. Mont Carlo simulations are carried out to compare the performances of the different estimators.

scholarly journals The Logarithmic Burr-Hatke Exponential Distribution for Modeling Reliability and Medical Data

2018 ◽  
Vol 7 (5) ◽  
pp. 73
Author(s):  
T. H. M. Abouelmagd
Keyword(s):  
Exponential Distribution ◽  
Exponential Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Suitable Model ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Weibull Models ◽  
Modified Weibull ◽  
Family Of Distributions

In this work, we introduced a new one-parameter exponential distribution. Some of its structural properties are derived% \textbf{.} The maximum likelihood method is used to estimate the model parameters by means of numerical Monte Carlo simulation study. The justification for the practicality of the new lifetime model is based on the wider use of the exponential model. The new model can be viewed as a mixtureof the exponentiated exponential distribution. It can also be considered as a suitable model for fitting right skewed data.\textbf{\ }We prove empirically the importance and flexibility of the new model in modelingcancer patients data, the new model provides adequate fits as compared to other related models with small values for $W^{\ast }$\ \ and $A^{\ast }$. The new model is much better than the Modified beta-Weibull, Weibull, exponentiated transmuted generalized Rayleig, the transmuted modified-Weibull, and transmuted additive Weibull models in modeling cancer patients data. We are also motivated to introduce this new model because it has only one parameter and we can generate some new families based on it such as the the odd Burr-Hatke exponential-G family of distributions, the logarithmic\textbf{\ }Burr-Hatke exponential-G family of distributions and the generalized\textbf{\ }Burr-Hatke exponential-G family of distributions, among others.

scholarly journals A New Lifetime Model: Copulas, Properties and Real Lifetime Data Applications

2021 ◽  
pp. 195-211
Author(s):  
Wahid Shehata
Keyword(s):  
Maximum Likelihood ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Finite Sample ◽  
Failure Rate Function ◽  
Failure Times ◽  
Lifetime Model ◽  
New Distribution

A new four parameter lifetime model called the Weibullgeneralized Lomax is proposed and studied.  The new density function can be "right skewed", "symmetric" and "left skewed" and its corresponding failure rate function can be "monotonically decreasing", " monotonically increasing" and "constant". The skewness of the new distribution can negative and positive. The maximum likelihood method is employed and used for estimating the model parameters. Using the "biases" and "mean squared errors", we performed simulation experiments for assessing the finite sample behavior of the maximum likelihood estimators. The new model deserved to be chosen as the best model among many well-known Lomax extension such as exponentiated Lomax, gamma Lomax, Kumaraswamy Lomax, odd log-logistic Lomax, Macdonald Lomax, beta Lomax, reduced odd log-logistic Lomax, reduced Burr-Hatke Lomax, reduced WG-Lx, special generalized mixture Lomax and the standard Lomax distributions in modeling the "failure times" and the "service times" data sets.

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