scholarly journals A New Version of the Exponentiated Exponential Distribution: Copula, Properties and Application to Relief and Survival Times

2021 ◽  
Vol 9 (2) ◽  
pp. 311-333
Author(s):  
Hanaa Elgohari
Keyword(s):  
Exponential Distribution ◽  
Hazard Function ◽  
Real Data ◽  
Likelihood Method ◽  
Type Model ◽  
Data Sets ◽  
Survival Times ◽  
Mathematical Properties ◽  
Mean Variance ◽  
New Distribution

In this paper, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index is performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "decreasing", "increasing", "increasing-constant", "upside down-constant", "decreasing nstant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The usefulness and flexibility of the new distribution is illustrated by means of two real data sets.

scholarly journals On Erlang-Truncated Exponential Distribution: Theory and Application

2021 ◽  
pp. 155-168
Author(s):  
Ibrahim Elbatal ◽  
A. Aldukeel
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Data Sets ◽  
Survival Times ◽  
New Distribution ◽  
Better Than

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

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 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 An extensive extension of exponentiated exponential distribution using alpha power transformation – statistical properties and applications in engineering science

2021 ◽  
Vol 17 (2) ◽  
pp. 59-74
Author(s):  
S. Qurat Ul Ain ◽  
K. Ul Islam Rather
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Statistical Properties ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean Variance ◽  
New Distribution ◽  
Extra Parameter

Abstract In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

scholarly journals TRANSMUTED ARCSINE DISTRIBUTION PROPERTIES AND APPLICATION

2018 ◽  
Vol 6 (10) ◽  
pp. 38-47
Author(s):  
Salma Omar Bleed ◽  
Arwa Elsunousi Ali Abdelali
Keyword(s):  
Maximum Likelihood Method ◽  
Risk Function ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Residual Function ◽  
Arcsine Distribution ◽  
New Distribution

The distribution of ArcSine will be developed to another new distribution using the Quadratic Rank Transmutation (QRT) method proposed by Shaw and Buckley (2007). The new distribution will be called the Transmuted ArcSine distribution, some of its mathematical characteristics such as variance, expectation, residual function, risk function, moments, moment generating function and characteristic function will be presented. The model parameters will be estimated by the maximum likelihood method. Finally, two real data sets are analyzed to illustrates the usefulness of the TAS distribution.

scholarly journals The Topp-Leone Generated Weibull Distribution: Regression Model, Characterizations and Applications

2016 ◽  
Vol 6 (1) ◽  
pp. 126 ◽  
Author(s):  
Gokarna R. Aryal ◽  
Edwin M. Ortega ◽  
G. G. Hamedani ◽  
Haitham M. Yousof
Keyword(s):  
Weibull Distribution ◽  
Regression Model ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Lifetime Model ◽  
First Time ◽  
Two Parameter ◽  
New Distribution

This paper introduces a new four-parameter lifetime model called the Topp Leone Generated Weibull (TLGW) distribution. This distribution is a generalization of the two parameter Weibull distribution using the genesis of Topp-Leone distribution.  We derive many of its structural properties including ordinary and incomplete moments, quantile and generating functions and order statistics. Parameter estimation using maximum likelihood method and simulation results to assess effectiveness of the distribution are discussed. Also, for the first time, we introduce a regression model based on the new distribution. We prove empirically the importance and flexibility of the new model in modeling various types of real data sets.

scholarly journals On the Alpha Power Kumaraswamy Distribution: Properties, Simulation and Application

2020 ◽  
Vol 43 (2) ◽  
pp. 285-313
Author(s):  
Mohamed Ali Ahmed
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Simulation Studies ◽  
Data Set ◽  
Kumaraswamy Distribution ◽  
Mathematical Properties

Adding  new  parameters to  classical distributions becomes one  of  the most  important methods  for  increasing distributions flexibility,  especially, in  simulation   studies   and real data sets. In this paper, alpha power  transformation (APT) is used  and  applied  to  the Kumaraswamy (K) distribution and a proposed distribution, so called the alpha power Kumaraswamy (AK) distribution, is presented.  Some important mathematical properties are derived, parameters estimation of the AK distribution using maximum likelihood  method  is considered. A simulation study and  a  real  data   set  are  used  to  illustrate the  flexibility of the  AK distribution compared with other  distributions.

scholarly journals A New One-parameter G Family of Compound Distributions: Copulas, Statistical Properties and Applications

2021 ◽  
Vol 9 (4) ◽  
pp. 942-962
Author(s):  
Mohamed Abo Raya
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Heavy Tail ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
New Family

This work introduces a new one-parameter compound G family. Relevant statistical properties are derived. The new density can be “asymmetric right skewed with one peak and a heavy tail”, “symmetric” and “left skewedwith one peak”. The new hazard function can be “upside-down”, “upside-down-constant”, “increasing”, “decreasing” and “decreasing-constant”. Many bivariate types have been also derived via different common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and flexibility of the new family is illustrated by means of two real data sets.

scholarly journals The long-term inverse Nakagami distribution: Properties, inference and application

2020 ◽  
Vol 42 ◽  
pp. e2
Author(s):  
Francisco Louzada Neto ◽  
Pedro Luiz Ramos ◽  
Paulo Henrique Ferreira da Silva
Keyword(s):  
Hazard Function ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Term Survival ◽  
Survival Distribution ◽  
Long Term Survival ◽  
Mathematical Properties ◽  
Nakagami Distribution ◽  
New Distribution

In this paper, a new long-term survival distribution, the so-called long-term inverse Nakagami distribution, is presented. The proposed distribution allows us to fit data with unimodal hazard function, where a part of the population is not susceptible to the event of interest, the so-called long-term survival. This distribution can be used, for instance, in clinical studies where a portion of the population can be cured during a treatment. Some mathematical properties of the new distribution are derived. The inferential procedures for the parameters are discussed under the maximum likelihood estimators. A numerical simulation study is carried out to verify the performance of these estimators. Finally, an application to real data on patients’ lifetime after acute myocardial infarction illustrates the usefulness of the proposed distribution.

scholarly journals On generalized classes of exponential distribution using T-X family framework

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1259-1272 ◽  
Author(s):  
Muhammad Zubair ◽  
Ayman Alzaatreh ◽  
Gauss Cordeiro ◽  
M.H. Tahir ◽  
Muhammad Mansoor
Keyword(s):  
Exponential Distribution ◽  
Shannon Entropy ◽  
Hazard Rate ◽  
Real Data ◽  
Quantile Function ◽  
Exponential Families ◽  
Data Sets ◽  
Mathematical Properties ◽  
New Models ◽  
Generalized Classes

We introduce new generalized classes of exponential distribution, called T-exponential {Y} class using the quantile functions of well-known distributions. We derive some general mathematical properties of this class including explicit expressions for the quantile function, Shannon entropy, moments and mean deviations. Some generalized exponential families are investigated. The shapes of the models in these families can be symmetric, left-skewed, right-skewed and reversed-J, and the hazard rate can be increasing, decreasing, bathtub, upside-down bathtub, J and reverse-J shaped. Two real data sets are used to illustrate the applicability of the new models.

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