scholarly journals Beta Kumaraswamy Burr Type X Distribution and Its Properties

2018 ◽  
Author(s):  
Umar Yusuf Madaki ◽  
Mohd Rizam Abu Bakar ◽  
Laba Handique
Keyword(s):  
Maximum Likelihood ◽  
Reliability Analysis ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Likelihood Methods ◽  
Proposed Model ◽  
Maximum Likelihood Methods ◽  
True Values

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densi- ties and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on dierent set of true values. Some real data sets were employed to show the usefulness and  exibility of the model which serves as generalization to many sub-models in the elds of engineering, medical, survival and reliability analysis.

scholarly journals Beta Kumaraswamy Burr Type X Distribution and Its Properties

2018 ◽  
Author(s):  
Umar Yusuf Madaki ◽  
Mohd Rizam Abu Bakar ◽  
Laba Handique
Keyword(s):  
Maximum Likelihood ◽  
Reliability Analysis ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Likelihood Methods ◽  
Proposed Model ◽  
Maximum Likelihood Methods ◽  
True Values

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densities and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on different set of true values. Some real data sets were employed to show the usefulness and flexibility of the model which serves as generalization to many sub-models in the field of engineering, medical, survival and reliability analysis.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1537
Author(s):  
Juan M. Astorga ◽  
Jimmy Reyes ◽  
Karol I. Santoro ◽  
Osvaldo Venegas ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Exponential Function ◽  
Real Data ◽  
Data Sets ◽  
Reliability Model ◽  
Likelihood Methods ◽  
Parameter Recovery ◽  
High Coefficient ◽  
Positive Data ◽  
Maximum Likelihood Methods

This article introduces an extension of the Power Muth (PM) distribution for modeling positive data sets with a high coefficient of kurtosis. The resulting distribution has greater kurtosis than the PM distribution. We show that the density can be represented based on the incomplete generalized integro-exponential function. We study some of its properties and moments, and its coefficients of asymmetry and kurtosis. We apply estimations using the moments and maximum likelihood methods and present a simulation study to illustrate parameter recovery. The results of application to two real data sets indicate that the new model performs very well in the presence of outliers.

The Reflected-Shifted-Truncated Lindley Distribution with Applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sanku Dey ◽  
Sophia Waymyers ◽  
Devendra Kumar
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Real Data ◽  
Comprehensive Treatment ◽  
Model Parameters ◽  
Data Sets ◽  
Right Censored Data ◽  
Lindley Distribution ◽  
Failure Data ◽  
Maximum Likelihood Methods

AbstractIn this paper, a new probability density function with bounded domain is presented. The new distribution arises from the Lindley distribution proposed in 1958. It presents the advantage of not including any special function in its formulation. The new transformed model, called the reflected-shifted-truncated Lindley distribution can be used to model left-skewed data. We provide a comprehensive treatment of general mathematical and statistical properties of this distribution. We estimate the model parameters by maximum likelihood methods based on complete and right-censored data. To assess the performance and consistency of the maximum likelihood estimators, we conduct a simulation study with varying sample sizes. Finally, we use the distribution to model left-skewed survival and failure data from two real data sets. For the real data sets containing complete data and right-censored data, this distribution is superior in its ability to sufficiently model the data as compared to the power Lindley, exponentiated power Lindley, generalized inverse Lindley, generalized weighted Lindley and the well-known Gompertz distributions.

scholarly journals Bayesian and non-Bayesian estimation of four-parameter of bivariate discrete inverse Weibull distribution with applications to model failure times, football and biological data

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2511-2531 ◽  
Author(s):  
M.S. Eliwa ◽  
M. El-Morshedy
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Discrete Analogue ◽  
Biological Data ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Inverse Weibull Distribution ◽  
Detailed Simulation

In this paper we have considered one model, namely the bivariate discrete inverse Weibull distribution, which has not been considered in the statistical literature yet. The proposed model is a discrete analogue of Marshall-Olkin inverse Weibull distribution. Some of its important statistical properties are studied. Maximum likelihood and Bayesian methods are used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. Finally, three real data sets are analyzed to illustrate the importance of the proposedmodel.

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 Odd Power Lindley Generator of Probability Distributions: Properties, Characterizations and Regression Modeling

2019 ◽  
Vol 8 (2) ◽  
pp. 70 ◽  
Author(s):  
Mustafa C. Korkmaz ◽  
Emrah Altun ◽  
Haitham M. Yousof ◽  
G.G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Simulation Studies ◽  
Proposed Model ◽  
Family Of Distributions

In this study, a new flexible family of distributions is proposed with its statistical properties as well as some useful characterizations. The maximum likelihood method is used to estimate the unknown model parameters by means of two simulation studies. A new regression model is proposed based on a special member of the proposed family called, the log odd power Lindley Weibull distribution. Residual analysis is conducted to evaluate the model assumptions. Four applications to real data sets are given to demonstrate the usefulness of the proposed model.

Generalized Flexible Weibull Extension Distribution

2017 ◽  
Vol 2 (4) ◽  
pp. 68-75
Author(s):  
Zubair Ahmad ◽  
Brikhna Iqbal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Suggested Model ◽  
Proposed Model ◽  
Parameter Values ◽  
Family Of Distributions

In this article, a four parameter generalization of the flexible Weibull extension distribution so-called generalized flexible Weibull extension distribution is studied. The proposed model belongs to T-X family of distributions proposed by Alzaatreh et al. [5]. The suggested model is much flexible and accommodates increasing, unimodal and modified unimodal failure rates. A comprehensive expression of the numerical properties and the estimates of the model parameters are obtained using maximum likelihood method. By appropriate choice of parameter values the new model reduces to four sub models. The proposed model is illustrated by means of three real 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.

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