Cubic Transmuted-G Family of Distributions and Its Properties

2018 ◽  
Vol 33 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Information Criteria ◽  
Data Sets ◽  
New Family ◽  
Family Of Distributions

Abstract In this article, a new family of distributions is introduced by using transmutation maps. The proposed family of distributions is expected to be useful in modeling real data sets. The genesis of the proposed family, including several statistical and reliability properties, is presented. Methods of estimation like maximum likelihood, least squares, weighted least squares, and maximum product spacing are discussed. Maximum likelihood estimation under censoring schemes is also considered. Further, we explore some special models of the proposed family of distributions and examined different properties of these special models. We compare three particular models of the proposed family with several existing distributions using different information criteria. It is observed that the proposed particular models perform better than different competing models. Applications of the particular models of the proposed family of distributions are finally presented to establish the applicability in real life situations.

scholarly journals New General Transmuted Family of Distributions with Applications

2018 ◽  
pp. 807-829
Author(s):  
Md. Mahabubur Rahman ◽  
Bander Al-Zahrani ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
New Class ◽  
New Family ◽  
Family Of Distributions

In this paper, we have introduced a new family of general transmuted distributions and have studied the cubic transmuted family of distributions in detail. This new class of distributions oers more distributional exibility when bi-modality appear in the data sets. Some special members of the proposed cubic transmuted family of distributions have been discussed. We have investigated, in detail, the proposed cubic transmuted family of distributions for parent exponential distribution. The statistical properties along with the reliability behavior for the cubic transmuted exponential distribution have been studied. We have obtained the expressions for single and joint order statistics when a sample is available from the cubic transmuted exponential distribution. Maximum likelihood estimation of parameters for cubic transmuted exponential distribution has also been discussed. We have also discussed the simulation and real data applications of the proposed distribution.

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

scholarly journals The Weibull-G Poisson Family for Analyzing Lifetime Data

2020 ◽  
pp. 131-148 ◽  
Author(s):  
Haitham Yousof ◽  
Muhammad Mansoor ◽  
Morad Alizadeh ◽  
Ahmed Afify ◽  
Indranil Ghosh
Keyword(s):  
Generating Functions ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
New Family ◽  
Mathematical Properties ◽  
Independent Identically Distributed ◽  
Family Of Distributions

We study a new family of distributions defined by the minimum of the Poissonrandom number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al. (2014)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Three special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of theproposed family.

scholarly journals Modified generalized marshall-olkin family of distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 18
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Goodness Of Fit Tests ◽  
New Family ◽  
Family Of Distributions

In this article, we propose a new family of distributions using the T-X family named as modified generalized Marshall-Olkin family of distributions. Comprehensive mathematical and statistical properties of this family of distributions are provided. The model parameters are estimated by maximum likelihood method. The maximum likelihood estimation under Type-II censoring is also discussed. Two lifetime data sets are used to show the suitability and applicability of the new family of distributions. For comparison purposes, different goodness of fit tests are used.  

scholarly journals A New Parametric Life Family of Distributions: Properties, Copula and Modeling Failure and Service Times

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1462
Author(s):  
Mansour Shrahili ◽  
Naif Alotaibi
Keyword(s):  
Maximum Likelihood ◽  
Probability Distributions ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
New Family ◽  
Renyi’S Entropy

A new family of probability distributions is defined and applied for modeling symmetric real-life datasets. Some new bivariate type G families using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. Moreover, some of its statistical properties are presented and studied. Next, the maximum likelihood estimation method is used. A graphical assessment based on biases and mean squared errors is introduced. Based on this assessment, the maximum likelihood method performs well and can be used for estimating the model parameters. Finally, two symmetric real-life applications to illustrate the importance and flexibility of the new family are proposed. The symmetricity of the real data is proved nonparametrically using the kernel density estimation method.

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 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 Generalized Odd Gamma-G Family of Distributions: Properties and Applications

2018 ◽  
Vol 47 (2) ◽  
pp. 69-89 ◽  
Author(s):  
Bistoon Hosseini ◽  
Mahmoud Afshari ◽  
Morad Alizadeh
Keyword(s):  
Maximum Likelihood ◽  
Test Validity ◽  
Estimation Method ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Data Sets ◽  
Maximum Likelihood Estimation Method ◽  
Family Of Distributions

Recently, new continuous distributions have been proposed to apply in statistical analysis. In this paper, the Generalized Odd Gamma-G distribution is introduced. In particular, G has been considered as the Uniform distribution and some statistical properties such as quantile function, asymptotics, moments, entropy and order statistics have been calculated.The fitness capability of this model has been investigated  by fitting this model and others based on real data sets. The  parameters of this model are estimated by the maximum likelihood estimation method with simulated  real data in order to test validity of maximum likelihood estimators .

scholarly journals The Alpha-Beta Skew Logistic Distribution: Properties and Applications

2020 ◽  
Vol 8 (1) ◽  
pp. 304-317 ◽  
Author(s):  
Hamid Esmaeili ◽  
Fazlollah Lak ◽  
Morad Alizadeh ◽  
Mohammad esmail Dehghan monfared
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Real Data ◽  
Logistic Distribution ◽  
Data Sets ◽  
New Family ◽  
Alpha Beta ◽  
Family Of Distributions ◽  
Skewness And Kurtosis

A new family of skew distributions is introduced by extending the alpha skew logistic distribution proposed by Hazarika-Chakraborty [9]. This family of distributions is called the alpha-beta skew logistic (ABSLG) distribution.Density function, moments, skewness and kurtosis coefficients are derived. The parameters of the new family are estimated by maximum likelihood and moments methods. The performance of the obtained estimators examined via a Monte carlo simulation. Flexibility, usefulness and suitability of ABSLG is illustrated by analyzing two real data sets.

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