scholarly journals A New Extension of the Lomax Distribution with Properties and Applications to Failure Times Data

2019 ◽  
pp. 461-479
Author(s):  
Mohamed Abo Raya
Keyword(s):  
Estimation Method ◽  
Likelihood Estimation ◽  
Good Alternative ◽  
Model Parameters ◽  
Data Sets ◽  
New Model ◽  
Lomax Distribution ◽  
Failure Times ◽  
Lifetime Model ◽  
Better Than

A new lifetime model is introduced and studied. The major justi…cation for the practicality of the new model is based on the wider use of the Lomax model. We are also motivated to introduce the new model since the density of the new distribution exhibits various important shapes such as the unimodal, right skewed and left skewed. The new model can be viewed as a mixture of the exponentiated Lomax distribution. It can also be considered as a suitablemodel for testing the symmetric, left skewed, right skewed and unimodal data. The maximum likelihood estimation method is used to estimate the model parameters. We prove empirically the importance and ‡exibility of the new model in modeling two types of aircraft windshield lifetime data sets. The proposed lifetime model is much better than gamma Lomax, beta Lomax, exponentiated Lomax and Lomax models so the exponentiated Lomax, model is a good alternative to these models in modeling aircraft windshield data.

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 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 Odd Lindley-Lomax Model: Statistical Properties and Applications

1970 ◽  
pp. 419-430
Author(s):  
M. Masoom Ali ◽  
Mustafa Ç. Korkmaz ◽  
Haitham M. Yousof ◽  
Nadeem Shafique Butt
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Good Alternative ◽  
Model Parameters ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Computational Aspects ◽  
Maximum Likelihood Estimation Method ◽  
Better Than

 In this work, we focus on some new theoretical and computational aspects of the Odd Lindley-Lomax model. The maximum likelihood estimation method is used to estimate the model parameters. We show empirically the importance and flexibility of the new model in modeling two types of aircraft windshield lifetime data. This model is much better than exponentiated Lomax, gamma Lomax, beta Lomax and Lomax models so the Odd Lindley-Lomax lifetime model is a good alternative to these models in modeling aircraft windshield data. A Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators. 

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals On the inferences and applications of transmuted exponential Lomax distribution

2018 ◽  
Vol 6 (1) ◽  
pp. 30
Author(s):  
Umar Kabir ◽  
Terna Godfrey IEREN
Keyword(s):  
Real Life ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Probability Density Function Pdf ◽  
New Distribution ◽  
Better Than

This article proposed a new distribution referred to as the transmuted Exponential Lomax distribution as an extension of the popular Lomax distribution in the form of Exponential Lomax by using the Quadratic rank transmutation map proposed and studied in earlier research. Using the transmutation map, we defined the probability density function (PDF) and cumulative distribution function (CDF) of the transmuted Exponential Lomax distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Lomax distribution using three real-life data sets. The results obtained indicated that TELD performs better than the other distributions comprising power Lomax, Exponential-Lomax, and the Lomax distributions.

scholarly journals A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Pelumi E. Oguntunde ◽  
Mundher A. Khaleel ◽  
Mohammed T. Ahmed ◽  
Adebowale O. Adejumo ◽  
Oluwole A. Odetunmibi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Real Life ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Lomax Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Better Than

Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution.

scholarly journals Extended Reciprocal Rayleigh Distribution: Copula, Properties and Real Data Modeling

2020 ◽  
pp. 35-52
Author(s):  
Hoda Ragab Rezk
Keyword(s):  
Simulation Study ◽  
Estimation Method ◽  
Data Modeling ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Graphical Simulation ◽  
Better Than

Abstract: A new extension of the reciprocal Rayleigh distribution is introduced. Simple type copula-based construction is presented for deriving and many bivariate and multivariate type distributions of the reciprocal Rayleigh model. The new reciprocal Rayleigh model generalizes another three reciprocal Rayleigh distributions. The performance of the estimation method is assessed using a graphical simulation study. The new model is better than some other important competitive models in modeling different real data sets.

scholarly journals The Odd Log-Logistic Dagum Distribution: Properties and Applications

2018 ◽  
Vol 41 (1) ◽  
pp. 109-135 ◽  
Author(s):  
Filippo Domma ◽  
Abbas Eftekharian ◽  
Ahmed Afify ◽  
Morad Alizadeh ◽  
Indranil Ghosh
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Failure Criteria ◽  
Likelihood Method ◽  
Model Parameters ◽  
New Model ◽  
Dagum Distribution ◽  
Lifetime Model

This paper introduces a new four-parameter lifetime model called the odd log-logistic Dagum distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some structural properties of the model odd log-logistic Dagum such as order statistics and incomplete moments. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling real data.

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.

An NHPP Software Reliability Model and Its Comparison

1997 ◽  
Vol 04 (03) ◽  
pp. 269-282 ◽  
Author(s):  
Hoang Pham ◽  
Xuemei Zhang
Keyword(s):  
Software Reliability ◽  
Visual Basic ◽  
Model Parameters ◽  
Data Sets ◽  
New Model ◽  
Reliability Models ◽  
Failure Data ◽  
Software Reliability Models ◽  
Software Reliability Model ◽  
Better Than

In this paper, software reliability models based on a nonhomogeneous Poisson process (NHPP) are summarized. A new model based on NHPP is presented. All models are applied to two widely used data sets. It can be shown that for the failure data used here, the new model fits and predicts much better than the existing models. A software program is written, using Excel & Visual Basic, which can be used to facilitate the task of obtaining the estimators of model parameters.

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