scholarly journals A New Extended-F Family: Properties and Applications to Lifetime Data

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Saima K. Khosa ◽  
Ahmed Z. Afify ◽  
Zubair Ahmad ◽  
Mi Zichuan ◽  
Saddam Hussain ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Model Parameters ◽  
Additional Parameter ◽  
Alpha Power ◽  
New Approach ◽  
New Class ◽  
Mathematical Properties ◽  
Extended Weibull Distribution

In this article, a new approach is used to introduce an additional parameter to a continuous class of distributions. The new class is referred to as a new extended-F family of distributions. The new extended-Weibull distribution, as a special submodel of this family, is discussed. General expressions for some mathematical properties of the proposed family are derived, and maximum likelihood estimators of the model parameters are obtained. Furthermore, a simulation study is provided to evaluate the validity of the maximum likelihood estimators. Finally, the flexibility of the proposed method is illustrated via two applications to real data, and the comparison is made with the Weibull and some of its well-known extensions such as Marshall–Olkin Weibull, alpha power-transformed Weibull, and Kumaraswamy Weibull distributions.

scholarly journals The Complementary Generalized Transmuted Poisson-G Family of Distributions

2018 ◽  
Vol 47 (4) ◽  
pp. 60-80 ◽  
Author(s):  
Morad Alizadeh ◽  
Haitham M. Yousof ◽  
Ahmed Z. Afify ◽  
Gauss M. Cordeiro ◽  
M. Mansoor
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Family Of Distributions

We introduce a new class of continuous distributions called the complementary generalized transmuted Poisson-G family, which extends the transmuted class pioneered by Shaw and Buckley (2007). We provide some special models and derive general mathematical properties including quantile function, explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies and order statistics. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the new family is illustrated 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 The Ristic-Balakrishnan odd log-logistic family of distributions: Properties and Applications

2020 ◽  
Vol 8 (1) ◽  
pp. 17-35
Author(s):  
Hamid Esmaeili ◽  
Fazlollah Lak ◽  
Emrah Altun
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Mathematical Properties ◽  
Proposed Model ◽  
The Family ◽  
Logistic Family ◽  
Family Of Distributions ◽  
Extra Parameter

This paper investigates general mathematical properties of a new generator of continuous distributions with two extra parameter called the Ristic-Balakrishnan odd log-logistic family of distributions. We present some special models and investigate the asymptotes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Explicit expressions for the ordinary and incomplete moments, generating functions and order statistics, which hold for any baseline model, are determined. Further, we discuss the estimation of the model parameters by maximum likelihood and present a simulation study based on maximum likelihood estimation. A regression model based on proposed model was introduced. Finally, three applications to real data were provided to illustrate the potentiality of the family of distributions.

scholarly journals The Zeta-G Class: Some Computational and Analytical Aspects

2020 ◽  
Vol 42 ◽  
pp. e111
Author(s):  
Ana Carla Percontini ◽  
Frank Gomes-Silva ◽  
Gauss Moutinho Crdeiro ◽  
Pedro Rafael Marinho
Keyword(s):  
Maximum Likelihood ◽  
Generating Function ◽  
Real Data ◽  
Data Set ◽  
R Language ◽  
New Class ◽  
Mathematical Properties ◽  
Special Cases ◽  
Computational Aspects

We define a new class of distributions with one extra shapeparameter including some special cases. We provide numerical and computational aspects of the new class. We proposefunctions using the \textsf{R} language to fit any distribution in this family to a data set. In addition, such functions are implemented efficientlyusing the library \textsf{Rcpp} that enables the incorporation of the codes \textsf{C++} in \textsf{R} automatically. Some examples are presentedfor using the implemented routines in practice. We derive some mathematical properties of this class including explicit expressionsfor the moments, generating function and mean deviations. We discuss the estimation of the model parametersby maximum likelihood and provide an application to a real data set.

scholarly journals The Gumbel- Pareto Distribution: Theory and Applications

2019 ◽  
Vol 16 (4) ◽  
pp. 0937
Author(s):  
Saad Et al.
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Numerical Illustration ◽  
Data Set ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
First Time ◽  
New Distribution

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

The Marshall–Olkin Transmuted-G Family of Distributions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmed Z. Afify ◽  
Haitham M. Yousof ◽  
Morad Alizadeh ◽  
Indranil Ghosh ◽  
Samik Ray ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Statistics And Probability ◽  
Family Of Distributions

AbstractWe introduce a new family of univariate continuous distributions called the Marshall–Olkin transmuted-G family which extends the transmuted-G family pioneered by Shaw and Buckley (2007). Special models for the new family are provided. Some of its mathematical properties including quantile measure, explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of two applications to real data sets.

scholarly journals The Exponentiated Kumaraswamy-G Class: General Properties and Application

2019 ◽  
Vol 42 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Ronaldo Silva ◽  
Frank Gomes-Silva ◽  
Manoel Ramos ◽  
Gauss Moutinho Cordeiro ◽  
Pedro Marinho ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Quantile Function ◽  
Weibull Model ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood

We propose a new family of distributions called the exponentiated Kumaraswamy-G class with three extra positive parameters, which generalizes the Cordeiro and de Castro's family. Some special distributions in the new class are discussed. We derive some mathematical properties of the proposed class including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, mean deviations, reliability, Rényi entropy and Shannon entropy. The method of maximum likelihood is used to fit the distributions in the proposed class. Simulations are performed in order to assess the asymptotic behavior of the maximum likelihood estimates. We illustrate its potentiality with applications to two real data sets which show that the extended Weibull model in the new class provides a better fit than other generalized Weibull distributions.

scholarly journals A New Extreme Value Model with Different Copula, Statistical Properties and Applications

2021 ◽  
pp. 1015-1035
Author(s):  
Hanaa Elgohari ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Extreme Value ◽  
Model Parameters ◽  
Finite Sample ◽  
Mathematical Properties ◽  
Maximum Likelihood Estimations ◽  
Extreme Value Model ◽  
Value Model

In this article, we defined and studied a new distribution for modeling extreme value. Some of its mathematical properties are derived and analyzed. Simple types copula is employed for proposing many bivariate and multivariate type extensions. Method of the maximum likelihood estimation is employed to estimate the model parameters. Graphically, we perform the simulation experiments to assess of the finite sample behavior of the maximum likelihood estimations. Three applications are presented for measuring the flexibility of the new model is illustrated using three real data applications.

scholarly journals Weibull Inverse Lomax Distribution

2019 ◽  
pp. 587-603 ◽  
Author(s):  
Amal S Hassan ◽  
Rokaya E Mohamed
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Reliability Function ◽  
Model Parameters ◽  
Asymptotic Confidence Intervals ◽  
Censored Sample ◽  
Inverse Lomax Distribution ◽  
Sample Maximum ◽  
Type Ii Censored Sample

A four-parameter lifetime model, named the Weibull inverse Lomax (WIL) is presented and studied. Some structural properties are derived. The estimation of the model parameters is performed based on Type II censored sample. Maximum likelihood estimators along with asymptotic confidence intervals of population parameters and reliability function are constructed. The property of consistency of maximum likelihood estimators has been verified on the basis of simulated samples.  Further, the results are applied on two real data.

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.

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