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 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 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 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 New Extension of Weibull Distribution: Copula, Mathematical Properties and Data Modeling

2020 ◽  
Vol 8 (4) ◽  
pp. 972-993
Author(s):  
Hanaa Elgohari ◽  
Haitham Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Model Parameters ◽  
Graphical Simulation ◽  
Mathematical Properties ◽  
Exponentiated Weibull ◽  
Lifetime Model ◽  
Simulation Results

This paper introduces a new flexible four-parameter lifetime model. Various of its structural properties are derived. The new density is expressed as a linear mixture of well-known exponentiated Weibull density. The maximum likelihood method is used to estimate the model parameters. Graphical simulation results to assess the performance of the maximum likelihood estimation are performed. We proved empirically the importance and flexibility of the new model in modeling four various types of 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 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.

Effects of covariates on alternating recurrent events in accelerated failure time models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Moumita Chatterjee ◽  
Sugata Sen Roy
Keyword(s):  
Recurrent Events ◽  
Failure Time ◽  
Likelihood Method ◽  
Model Parameters ◽  
Accelerated Failure Time ◽  
Survival Times ◽  
Copula Functions ◽  
Event Time ◽  
Accelerated Failure Time Models ◽  
Accelerated Failure

AbstractIn this article, we model alternately occurring recurrent events and study the effects of covariates on each of the survival times. This is done through the accelerated failure time models, where we use lagged event times to capture the dependence over both the cycles and the two events. However, since the errors of the two regression models are likely to be correlated, we assume a bivariate error distribution. Since most event time distributions do not readily extend to bivariate forms, we take recourse to copula functions to build up the bivariate distributions from the marginals. The model parameters are then estimated using the maximum likelihood method and the properties of the estimators studied. A data on respiratory disease is used to illustrate the technique. A simulation study is also conducted to check for consistency.

scholarly journals The Alpha Power Transformation Family: Properties and Applications

2019 ◽  
pp. 525-545 ◽  
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh
Keyword(s):  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Weibull Distributions ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Modified Weibull

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

scholarly journals Parametric Survival Modeling of Tuberculosis Data- A Case Study of Federal Medical Centre, Bida, Nigeria

2020 ◽  
Vol 14 (7) ◽  
pp. 37
Author(s):  
Vincent Abiodun Michael ◽  
Ismaila Adewale Bolarinwa
Keyword(s):  
Older Patients ◽  
Recovery Period ◽  
Selection Criterion ◽  
Weibull Model ◽  
Medical Centre ◽  
Likelihood Method ◽  
Outcome Variable ◽  
Survival Times ◽  
Lower Survival ◽  
Parametric Survival

The research performed parametric survival analysis of Tuberculosis (TB) data (covering 2010 to 2016) collected from the Federal Medical Centre, Bida, Niger State, Nigeria. Three parametric survival models (Exponential, Weibull and Log-logistic) were fitted. The outcome variable was time to recovery from TB infection and four covariates being age, gender, TB type and occupation were involved. Models were estimated by maximum likelihood method and model selection criterion used was the Akaike Information Criterion (AIC). The exponential and log-logistic models found all covariates statistically insignificant while Weibull found all covariates but TB type significant at 5% level. Based on AIC, Weibull model with AIC of 163.5731 performed best, followed by log-logistic model with AIC of 191.419 and exponential model performed worst, with AIC of 517.9652. The best of fitted models being Weibull suggested that older patients had higher hazards than younger ones, older patients hence, had lower survival times, holding other covariates constant. That is, the older the TB patient, the lower was the time to recovery from TB. Males had higher hazards and hence, lower survival times compared to females. That is, male TB patients recovered faster than the females. Pulmonary TB patients had lower (insignificant) hazards and hence, higher survival times than Respiratory TB patients. TB patients on technical occupation had lower hazards than others and hence, had higher survival times than those whose occupations were considered not technical. The research concluded that age, gender and occupation were the major determinants of recovery period of TB patients. It was recommended that the Management of Federal Medical Centre, Bida, and other organizations involved in TB management could make use of the Weibull model to fit and predict both the survival and hazard rates of TB patients.

scholarly journals Task-based programming in COMPSs to converge from HPC to big data

2017 ◽  
Vol 32 (1) ◽  
pp. 45-60 ◽  
Author(s):  
Javier Conejero ◽  
Sandra Corella ◽  
Rosa M Badia ◽  
Jesus Labarta
Keyword(s):  
Big Data ◽  
High Performance ◽  
Programming Model ◽  
Good Alternative ◽  
Programming Models ◽  
Suitable Model ◽  
Advantages And Disadvantages ◽  
Big Data Applications ◽  
And Performance ◽  
The Right

Task-based programming has proven to be a suitable model for high-performance computing (HPC) applications. Different implementations have been good demonstrators of this fact and have promoted the acceptance of task-based programming in the OpenMP standard. Furthermore, in recent years, Apache Spark has gained wide popularity in business and research environments as a programming model for addressing emerging big data problems. COMP Superscalar (COMPSs) is a task-based environment that tackles distributed computing (including Clouds) and is a good alternative for a task-based programming model for big data applications. This article describes why we consider that task-based programming models are a good approach for big data applications. The article includes a comparison of Spark and COMPSs in terms of architecture, programming model, and performance. It focuses on the differences that both frameworks have in structural terms, on their programmability interface, and in terms of their efficiency by means of three widely known benchmarking kernels: Wordcount, Kmeans, and Terasort. These kernels enable the evaluation of the more important functionalities of both programming models and analyze different work flows and conditions. The main results achieved from this comparison are (1) COMPSs is able to extract the inherent parallelism from the user code with minimal coding effort as opposed to Spark, which requires the existing algorithms to be adapted and rewritten by explicitly using their predefined functions, (2) it is an improvement in terms of performance when compared with Spark, and (3) COMPSs has shown to scale better than Spark in most cases. Finally, we discuss the advantages and disadvantages of both frameworks, highlighting the differences that make them unique, thereby helping to choose the right framework for each particular objective.

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