scholarly journals The Generalized Odd Generalized Exponential Fréchet Model: Univariate, Bivariate and Multivariate Extensions with Properties and Applications to the Univariate Version

2020 ◽  
pp. 529-544 ◽  
Author(s):  
Hisham Abdel Hamid Elsayed ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Generating Functions ◽  
Residual Life ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Stochastic Properties

A new univariate extension of the Fréchet distribution is proposed and studied. Some of its fundamental statistical properties such as stochastic properties, ordinary and incomplete moments, moments generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering, Rényi, Shannon and q-entropies are derived. A simple type Copula based construction using Morgenstern family and via Clayton Copula is employed to derive many bivariate and multivariate extensions of the new model. We assessed the performance of the maximum likelihood estimators using a simulation study. The importance of the new model is shown by means of two applications to real data sets.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

scholarly journals Generalized Truncation Positive Normal Distribution

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1361
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Osvaldo Venegas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Data Sets ◽  
New Model ◽  
Positive Support

In this article we study the properties, inference, and statistical applications to a parametric generalization of the truncation positive normal distribution, introducing a new parameter so as to increase the flexibility of the new model. For certain combinations of parameters, the model includes both symmetric and asymmetric shapes. We study the model’s basic properties, maximum likelihood estimators and Fisher information matrix. Finally, we apply it to two real data sets to show the model’s good performance compared to other models with positive support: the first, related to the height of the drum of the roller and the second, related to daily cholesterol consumption.

scholarly journals The Odd Log-Logistic Poisson Inverse Rayleigh Distribution: Statistical Properties and Applications

2020 ◽  
pp. 775-787
Author(s):  
Ibrahim Elbatal
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Statistical Properties ◽  
Data Sets ◽  
New Model ◽  
Fundamental Properties

In this work, a new extension of the Inverse Rayleigh model is proposed and studied. We derive some of its fundamental properties. We assess the performance of the maximum likelihood estimators via a simulation study. The importance of the new model is shown via two applications to real data sets. The new model is better fit than other important competitive models based on two real data sets.

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 A Generalization of Reciprocal Exponential Model: Clayton Copula, Statistical Properties and Modeling Skewed and Symmetric Real Data Sets

2020 ◽  
pp. 373-386 ◽  
Author(s):  
M. M. Mansour ◽  
Nadeem Shafique Butt ◽  
Haitham Yousof ◽  
S. I. Ansari ◽  
Mohamed Ibrahim
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Extreme Values ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Exponential Model ◽  
Data Sets ◽  
Clayton Copula ◽  
Graphical Simulation ◽  
Better Than

We introduce a new extension of the reciprocal Exponential distribution for modeling the extreme values. We used the Morgenstern family and the clayton copula for deriving many bivariate and multivariate extensions of the new model. Some of its properties are derived. We assessed the performance of the maximum likelihood estimators (MLEs) via a graphical simulation study. The assessment was based on the sample size. The new reciprocal model is employed for modeling the skewed and the symmetric real data sets. The new reciprocal model is better than some other important competitive models in statistical modeling.

scholarly journals A Generalization of Binomial Exponential-2 Distribution: Copula, Properties and Applications

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1338
Author(s):  
Naif Alotaibi ◽  
Igor V. Malyk
Keyword(s):  
Residual Life ◽  
Real Life ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Conditional Moment ◽  
Failure Rate Function ◽  
New Model

In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used 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 Cubic Rank Transmuted Modified Burr III Pareto Distribution: Development, Properties, Characterizations and Applications

2018 ◽  
Vol 8 (1) ◽  
pp. 94
Author(s):  
Fiaz Ahmad Bhatti ◽  
G.G. Hamedani ◽  
Wenhui Sheng ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Residual Life ◽  
Glass Fibers ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Inequality Measures ◽  
P Distribution

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. The potentiality of CRTMBIII-P distribution is demonstrated via its application to the real data sets: tensile strength of carbon fibers and strengths of glass fibers. Goodness of fit of this distribution through different methods is studied.

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 A New Lindley-Burr XII Distribution: Model, Properties and Applications

2021 ◽  
Vol 10 (4) ◽  
pp. 33
Author(s):  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Morongwa Gabanakgosi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Distribution Model ◽  
Model Parameters ◽  
Data Sets ◽  
Mean Square ◽  
Conditional Moments ◽  
New Distribution

A new distribution called the Lindley-Burr XII (LBXII) distribution is proposed and studied. Some structural properties of the new distribution including moments, conditional moments, distribution of the order statistics and R´enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and applications to real data sets in order to illustrate the usefulness of the new distribution are given.

Sign in / Sign up

Export Citation Format

Share Document