scholarly journals Extended Poisson-Pareto Type II Distribution: Theoretical and Computational Aspects

2019 ◽  
pp. 713-730
Author(s):  
Rania Hassan Abd El Khaleq
Keyword(s):  
Poisson Model ◽  
Real Data ◽  
Continuous Model ◽  
Data Sets ◽  
Type Ii ◽  
Unknown Parameters ◽  
New Model ◽  
Method Of Maximum Likelihood ◽  
Computational Aspects ◽  
Better Than

We introduce a new continuous model with strong physical motivations and wide applications upon compounding the diecreate zero truncated Poisson model and a new continuous model called the Burr X Pareto type II distribution. Some of its mathematical and statistical properties are derived as well as four applications to real data sets are provided with detailes to illustrate the wide importance of the new model. We conclude that the new model is better than other nine competitive models via the four applications. Method of maximum likelihood is used to estimate the unknown parameters of the new model. The new model provide adequate Öts as compared to other related models in the four applications.

scholarly journals A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated T-X Distributions Family

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 412 ◽  
Author(s):  
Hadeel S. Klakattawi ◽  
Wedad H. Aljuhani
Keyword(s):  
Hazard Function ◽  
Real Data ◽  
Parameter Distribution ◽  
Data Sets ◽  
Alpha Power ◽  
Simulation Studies ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Exponentiated Weibull ◽  
A New Technique

In the following article, a new five-parameter distribution, the alpha power exponentiated Weibull-exponential distribution is proposed, based on a newly developed technique. It is of particular interest because the density of this distribution can take various symmetric and asymmetric possible shapes. Moreover, its related hazard function is tractable and showing a great diversity of asymmetrical shaped, including increasing, decreasing, near symmetrical, increasing-decreasing-increasing, increasing-constant-increasing, J-shaped, and reversed J-shaped. Some properties relating to the proposed distribution are provided. The inferential method of maximum likelihood is employed, in order to estimate the model’s unknown parameters, and these estimates are evaluated based on various simulation studies. Moreover, the usefulness of the model is investigated through its application to three real data sets. The results show that the proposed distribution can, in fact, better fit the data, when compared to other competing distributions.

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 Extended Poisson-Log-Logistic Distribution

2019 ◽  
Vol 8 (2) ◽  
pp. 56
Author(s):  
Jehan. A. Almamy
Keyword(s):  
Physical Interpretation ◽  
Real Data ◽  
Logistic Distribution ◽  
Data Sets ◽  
New Model ◽  
Wide Applicability ◽  
Essential Properties ◽  
Compound Model ◽  
Better Than

In this work, we introduce a new Poisson-log-logistic distribution with a physical interpretation and some applications. Some essential properties are derived. Modeling of four real data sets are provided to illustrate the wide applicability of the new model in differnt fields like finance, reliability, economy and medicine. The new compound model is better than other well-known competitive models which have at least the same number of parameters.

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 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 Statistical inference for Kumaraswamy-exponential distribution based on progressive Type-II censored data with binomial removals

2020 ◽  
Vol 53 (2) ◽  
pp. 147-163
Author(s):  
RAKHI MOHAN ◽  
MANOJ CHACKO
Keyword(s):  
Exponential Distribution ◽  
Loss Function ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Type Ii ◽  
Bayes Estimators ◽  
Estimation Of Parameters ◽  
Unknown Parameters ◽  
Data Set ◽  
Better Than

In this paper, estimation of parameters of Kumaraswamy-exponential distribution with shape parameters α and β is considered based on a progressively type-II censored sample with binomial removals. Together with the unknown parameters, the removal probability p is also estimated. Bayes estimators are obtained using different loss functions such as squared error, LINEX loss function and entropy loss function. All Bayesian estimates are compared with the corresponding maximum likelihood estimates numerically in terms of their bias and mean square error values and found that Bayes estimators perform better than MLE’s for β and p and MLEs perform better than Bayes estimators for α. A real data set is also used for illustration.

scholarly journals On A New Two Parameter Fréchet Distribution with Applications

2021 ◽  
pp. 99-112
Author(s):  
Rania Hassan Abd El Khaleq
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Real Data ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Maximum Likelihood Estimations ◽  
Two Parameter ◽  
New Distribution ◽  
Better Than

A new ‡exible extension of the Fréchet model is proposed and studied. Some of itsfundamental statistical properties are derived. The importance of the new model is shown via two applications to real data sets. A simple type Copula based construction are also presented.We assess the performance of the maximum likelihood estimations of the new distribution with respect to sample size n. The assessment was based on a simulation study.The new model is much better than other important competitive models.

scholarly journals THE POWER MUTH DISTRIBUTION∗

2017 ◽  
Vol 22 (2) ◽  
pp. 186-201 ◽  
Author(s):  
Pedro Jodra ◽  
Hector Wladimir Gomez ◽  
Maria Dolores Jimenez-Gamero ◽  
Maria Virtudes Alba-Fernandez
Keyword(s):  
Probability Distributions ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Failure Rate Function ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Practical Usefulness ◽  
Method Of Maximum Likelihood

Muth introduced a probability distribution with application in reliability theory. We propose a new model from the Muth law. This paper studies its statistical properties, such as the computation of the moments, computer generation of pseudo-random data and the behavior of the failure rate function, among others. The estimation of parameters is carried out by the method of maximum likelihood and a Monte Carlo simulation study assesses the performance of this method. The practical usefulness of the new model is illustrated by means of two real data sets, showing that it may provide a better fit than other probability distributions.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

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.

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