Univariate and bivariate extensions of the generalized exponential distributions

2021 ◽  
Vol 71 (6) ◽  
pp. 1581-1598
Author(s):  
Vahid Nekoukhou ◽  
Ashkan Khalifeh ◽  
Hamid Bidram
Keyword(s):  
Em Algorithm ◽  
Exponential Distribution ◽  
Bivariate Distribution ◽  
Generalized Exponential Distribution ◽  
Exponential Distributions ◽  
Unknown Parameters ◽  
Data Set ◽  
New Class ◽  
Special Cases ◽  
Univariate Distribution

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

scholarly journals The Beta Weibull-G Family of Distributions: Model, Properties and Application

2018 ◽  
Vol 7 (2) ◽  
pp. 12 ◽  
Author(s):  
Boikanyo Makubate ◽  
Broderick O. Oluyede ◽  
Gofaone Motobetso ◽  
Shujiao Huang ◽  
Adeniyi F. Fagbamigbe
Keyword(s):  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Exponential Distributions ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Generalized Distributions ◽  
Special Cases

A new family of generalized distributions called the beta Weibull-G (BWG) distribution is proposed and developed. This new class of distributions has several new and well known distributions including exponentiated-G, Weibull-G, Rayleigh-G, exponential-G, beta exponential-G, beta Rayleigh-G, beta Rayleigh exponential, beta-exponential-exponential, Weibull-log-logistic distributions, as well as several other distributions such as beta Weibull-Uniform, beta Rayleigh-Uniform, beta exponential-Uniform, beta Weibull-log logistic and beta Weibull-exponential distributions as special cases. Series expansion of the density function, hazard function, moments, mean deviations, Lorenz and Bonferroni curves, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates of the model parameters are given. Application of the model to real data set is presented to illustrate the importance and usefulness of the special case beta Weibull-log-logistic distribution.

scholarly journals New Generalizations of Exponential Distribution with Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
N. A. Rather ◽  
T. A. Rather
Keyword(s):  
Exponential Distribution ◽  
Generating Functions ◽  
Weibull Distributions ◽  
Generalized Exponential Distribution ◽  
Special Cases ◽  
Moment Generating Functions

The main purpose of this paper is to present k-Generalized Exponential Distribution which among other things includes Generalized Exponential and Weibull Distributions as special cases. Besides, we also obtain three-parameter extension of Generalized Exponential Distribution. We shall also discuss moment generating functions (MGFs) of these newly introduced distributions.

scholarly journals On the Estimation Problems for Exponentiated Exponential Distribution under Generalized Progressive Hybrid Censoring

2021 ◽  
Vol 50 (1) ◽  
pp. 24-40
Author(s):  
Aakriti Pandey ◽  
Arun Kaushik ◽  
Sanjay K. Singh ◽  
Umesh Singh
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Expected Number ◽  
Unknown Parameters ◽  
Data Set ◽  
Mean Squared Errors ◽  
Entropy Measures ◽  
Estimation Problems ◽  
Censored Sample ◽  
Termination Time

In this article, we considered the statistical inference for the unknown parameters of exponentiated exponential distribution based on a generalized progressive hybrid censored sample under classical paradigm. We have obtained maximum likelihood estimators of the unknown parameters and confidence intervals utilizing asymptotic theory. Entropy measures, such as Shannon entropy and Awad sub-entropy, have been obtained to measure loss of information owing to censoring. Further, the expected total time of the test and expected number of failures, which are useful during the execution of an experiment, also have been computed. The performance of the estimators have been discussed based on mean squared errors. Moreover, the effect of choice of parameters, termination time T, and m on the ETTT and ETNFs also have been observed. For illustrating the proposed methodology, a real data set is considered.

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 Adjusted Log-logistic Generalized Exponential Distribution with Application to Lifetime Data

2017 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
I. E. Okorie ◽  
A. C. Akpanta ◽  
J. Ohakwe ◽  
D. C. Chikezie ◽  
C. U. Onyemachi ◽  
...  
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
Generalized Exponential Distribution ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
The One ◽  
Special Case

This paper introduces a new generator of probability distribution-the adjusted log-logistic generalized (ALLoG) distribution and a new extension of the standard one parameter exponential distribution called the adjusted log-logistic generalized exponential (ALLoGExp) distribution. The ALLoGExp distribution is a special case of the ALLoG distribution and we have provided some of its statistical and reliability properties. Notably, the failure rate could be monotonically decreasing, increasing or upside-down bathtub shaped depending on the value of the parameters $\delta$ and $\theta$. The method of maximum likelihood estimation was proposed to estimate the model parameters. The importance and flexibility of he ALLoGExp distribution was demonstrated with a real and uncensored lifetime data set and its fit was compared with five other exponential related distributions. The results obtained from the model fittings shows that the ALLoGExp distribution provides a reasonably better fit than the one based on the other fitted distributions. The ALLoGExp distribution is therefore ecommended for effective modelling of lifetime data sets.

scholarly journals The complementary Poisson-Lindley class of distributions

2015 ◽  
Vol 3 (2) ◽  
pp. 146 ◽  
Author(s):  
Amal Hassan ◽  
Salwa Assar ◽  
Kareem Ali
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Formal Proof ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Data Set ◽  
Lifetime Distributions ◽  
New Class ◽  
Rate Functions

<p>This paper proposed a new general class of continuous lifetime distributions, which is a complementary to the Poisson-Lindley family proposed by Asgharzadeh et al. [3]. The new class is derived by compounding the maximum of a random number of independent and identically continuous distributed random variables, and Poisson-Lindley distribution. Several properties of the proposed class are discussed, including a formal proof of probability density, cumulative distribution, and reliability and hazard rate functions. The unknown parameters are estimated by the maximum likelihood method and the Fisher’s information matrix elements are determined. Some sub-models of this class are investigated and studied in some details. Finally, a real data set is analyzed to illustrate the performance of new distributions.</p>

A bivariate Kumaraswamy-exponential distribution with application

2019 ◽  
Vol 69 (5) ◽  
pp. 1185-1212
Author(s):  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Abdus Saboor ◽  
Haniya Samad
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Information Matrix ◽  
Bivariate Distribution ◽  
Conditional Density ◽  
Estimation Methods ◽  
Density Functions ◽  
Marginal Density ◽  
Data Set ◽  
Expected Information

Abstract In this paper, we introduce a new bivariate Kumaraswamy exponential distribution, whose marginals are univariate Kumaraswamy exponential. Some probabilistic properties of this bivariate distribution are derived, such as joint density function, marginal density functions, conditional density functions, moments and stress-strength reliability. Also, we provide the expected information matrix with its elements in a closed form. Estimation of the parameters is investigated by the maximum likelihood, Bayesian and least squares estimation methods. A simulation study is carried out to compare the performance of the estimators by estimation methods. Further, one data set have been analyzed to show how the proposed distribution works in practice.

scholarly journals Bayesian Analysis of Topp-Leone Generalized Exponential Distribution

2018 ◽  
Vol 47 (4) ◽  
pp. 1-15
Author(s):  
Najrullah Khan ◽  
Athar Ali Khan
Keyword(s):  
Bayesian Analysis ◽  
Exponential Distribution ◽  
Bayesian Approach ◽  
Survival Data ◽  
Survival Model ◽  
Generalized Exponential Distribution ◽  
Data Set ◽  
Simulation Tools ◽  
Support Set ◽  
Optimization And Simulation

The Topp-Leone distribution was introduced by Topp-Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized Exponential distribution. Since, Topp-Leone distribution contains only one parameter and its support set is restricted to (0,1), because of this, in most practical situations it is not a better fit for the lifetime modelling. So an extension of this distribution is required. A Bayesian approach has been adopted to fit this model as survival model. A real survival data set is used to illustrate. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools.

scholarly journals A New Class of Generalized Modified Weibull Distribution with Applications

2015 ◽  
Vol 44 (3) ◽  
pp. 45-68
Author(s):  
Broderick Oluyede ◽  
Shujiao Huang ◽  
Tiantian Yang
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Estimation Technique ◽  
Exponential Distributions ◽  
New Class ◽  
Mathematical Properties ◽  
Special Cases ◽  
Generalized Modified Weibull ◽  
Modified Weibull

A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented.

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