scholarly journals Box-Cox Gamma-G Family of Distributions: Theory and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1801
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Maximum Likelihood ◽  
Statistical Model ◽  
Cauchy Distribution ◽  
Natural Generalization ◽  
Power Parameter ◽  
New Class ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Box Cox Transformation ◽  
Family Of Distributions

This paper is devoted to a new class of distributions called the Box-Cox gamma-G family. It is a natural generalization of the useful Ristić–Balakrishnan-G family of distributions, containing a wide variety of power gamma-G distributions, including the odd gamma-G distributions. The key tool for this generalization is the use of the Box-Cox transformation involving a tuning power parameter. Diverse mathematical properties of interest are derived. Then a specific member with three parameters based on the half-Cauchy distribution is studied and considered as a statistical model. The method of maximum likelihood is used to estimate the related parameters, along with a simulation study illustrating the theoretical convergence of the estimators. Finally, two different real datasets are analyzed to show the fitting power of the new model compared to other appropriate models.

scholarly journals The Exponentiated Generalized-G Poisson Family of Distributions

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Gokarna R. Aryal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Real World ◽  
Generating Functions ◽  
Real World Data ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

AbstractIn this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.

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 On the Topp Leone Exponentiated-G Family of Distributions: Properties and Applications

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Sule Ibrahim ◽  
Sani Ibrahim Doguwa ◽  
Isah Audu ◽  
Jibril Haruna Muhammad
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Quantile Function ◽  
Data Sets ◽  
Shape Parameters ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
Family Of Distributions

We proposed a new family of distributions called the Topp Leone exponentiated-G family of distributions with two extra positive shape parameters, which generalizes and also extends the Topp Leone-G family of distributions. We derived some mathematical properties of the proposed family including explicit expressions for the quantile function, ordinary and incomplete moments, generating function and reliability. Some sub-models in the new family were discussed. The method of maximum likelihood was used to estimate the parameters of the sub-model. Further, the potentiality of the family was illustrated by fitting two real data sets to the mentioned sub-models.

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 The New rT - X Family of Distributions: Some Properties with Applications

2019 ◽  
pp. 409-432
Author(s):  
Clement Boateng Ampadu ◽  
Abdulzeid Yen Anafo
Keyword(s):  
Data Sets ◽  
Statistical Distributions ◽  
Unknown Parameters ◽  
Related Data ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Modeling And Forecasting ◽  
Family Of Distributions

The rT - X family of distributions induced by V which have been introduced in [1] is further explored in this paper. In particular, we have obtained some basic mathematical properties of this new family. The simulation study shows the method of maximum likelihood is adequate in estimating the unknown parameters in sub-models of this new class of statistical distributions. Further, the application shows that sub-models of this new family of distributions are useful in material science engineering and related disciplines that call for modeling and forecasting of related data sets. Finally, inspired by the Ampadu-G family of distributions [2], we propose a new class of distributions that have never appeared in the literature, and ask the reader to investigate some properties and applications of this new class of distributions.

scholarly journals A New Generalized Cauchy Distribution with an Application to Annual One Day Maximum Rainfall Data

2021 ◽  
Vol 9 (1) ◽  
pp. 123-136
Author(s):  
Cory Ball ◽  
Binod Rimal ◽  
Sher Chhetri
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Cauchy Distribution ◽  
Maximum Rainfall ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Map Approach

In this article, we introduce a new three-parameter transmuted Cauchy distribution using the quadratic rank transmutation map approach. Some mathematical properties of the proposed model are discussed. A simulation study is conducted using the method of maximum likelihood estimation to estimate the parameters of the proposed model. We used two real datasets and compare various statistics to show the fitting and versatility of the model.

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 General Results for the Transmuted Family of Distributions and New Models

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Marcelo Bourguignon ◽  
Indranil Ghosh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Generating Functions ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
New Models ◽  
Family Of Distributions

The transmuted family of distributions has been receiving increased attention over the last few years. For a baselineGdistribution, we derive a simple representation for the transmuted-Gfamily density function as a linear mixture of theGand exponentiated-Gdensities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Rényi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.

scholarly journals The Nadarajah Haghighi Topp Leone-G Family of Distributions ‎with Mathematical Properties and Applications

2019 ◽  
Vol 15 (4) ◽  
pp. 849
Author(s):  
Hesham Reyad‎ ◽  
Mahmoud Ali Selim ◽  
Soha Othman
Keyword(s):  
Information Matrix ◽  
Quantile Function ◽  
Model Parameters ◽  
Lorenz Curves ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Statistics And Probability ◽  
Method Of Maximum Likelihood

Based on the Nadarajah Haghighi distribution and the Topp Leone-G family in view of the T-X family, we introduce a new generator of continuous distributions with three extra parameters called the Nadarajah Haghighi Topp Leone-G family. Three sub-models of the new class are discussed. Main mathematical properties of the new family are investigated such as; quantile function, raw and incomplete moments, Bonferroni and Lorenz curves, moment and probability generating functions, stress-strength model, Shanon and Rényi entropies, order statistics and probability weighted moments. The model parameters of the new family is estimated by using the method of maximum likelihood and the observed information matrix is also obtained. We introduce two real applications to show the importance of the new family.

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.

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