The Marshall-Olkin Modified Lindley Distribution: Properties and Applications

Likelihood Method ◽

Lindley Distribution ◽

New Model ◽

Simulation Procedure ◽

Recent Modification ◽

This article is devoted to a new Marshall-Olkin distribution by using a recent modification of the Lindley distribution. Mathematical features of the new model are described. Utilizing maximum likelihood method, the parameters of the new model are estimated. Performance of the estimation approach is discussed by means of a simulation procedure. Moreover, applications of the new distribution are presented which reveal its superiority over other three competing Marshall-Olkin extended distributions of the literature.

Zero-truncated Poisson-Lindley distribution

ICSA - International Conference on Statistics and Analytics 2019 ◽

10.29244/icsa.2019.pp40-50 ◽

2021 ◽

pp. 40-50

Author(s):

Afida Nurul Hilma ◽

Dian Lestari ◽

Sindy Devila

Keyword(s):

Maximum Likelihood ◽

Real Data ◽

Likelihood Method ◽

Lindley Distribution ◽

Count Distribution ◽

Distribution Parameters ◽

Counting Distribution ◽

Over Dispersion

In order to find a counting distribution that can handle the condition when the data has no zero-count. Distribution named Zero-truncated Poisson-Lindley distribution is developed. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero-truncated Poisson-Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method. Then, the application of the model to real data is given.

A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽

10.3390/sym12030440 ◽

2020 ◽

Vol 12 (3) ◽

pp. 440 ◽

Cited By ~ 8

Author(s):

Abdulhakim A. Al-babtain ◽

I. Elbatal ◽

Haitham M. Yousof

Keyword(s):

Maximum Likelihood ◽

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.

A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-678 ◽

2020 ◽

Vol 8 (2) ◽

pp. 610-630 ◽

Cited By ~ 2

Author(s):

Mohamed Ibrahim ◽

Emrah Altun EA ◽

Haitham M. Yousof

Keyword(s):

Maximum Likelihood ◽

Estimation Method ◽

Least Square Method ◽

Least Square ◽

Likelihood Method ◽

Survival Times ◽

New Model ◽

Von Mises ◽

Bootstrapping Method

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

The Weibull-Gamma Distribution: Properties and Applications

Entropy ◽

10.3390/e21050438 ◽

2019 ◽

Vol 21 (5) ◽

pp. 438 ◽

Cited By ~ 2

Author(s):

Hadeel S. Klakattawi

Keyword(s):

Maximum Likelihood ◽

Gamma Distribution ◽

Data Distribution ◽

Likelihood Method ◽

Parameter Distribution ◽

Great Flexibility ◽

Special Cases ◽

New Distribution ◽

Family Of Distributions

A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications

Symmetry ◽

10.3390/sym11121459 ◽

2019 ◽

Vol 11 (12) ◽

pp. 1459 ◽

Cited By ~ 3

Author(s):

Ramadan A. ZeinEldin ◽

Farrukh Jamal ◽

Christophe Chesneau ◽

Mohammed Elgarhy

Keyword(s):

Maximum Likelihood ◽

Probability Density ◽

Goodness Of Fit ◽

Information Criteria ◽

Likelihood Method ◽

Type Ii ◽

Asymptotic Results ◽

Kumaraswamy Distribution ◽

In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics.

Slashed Exponentiated Rayleigh Distribution

Revista Colombiana de Estadística ◽

10.15446/rce.v38n2.51673 ◽

2015 ◽

Vol 38 (2) ◽

pp. 453-466 ◽

Cited By ~ 1

Author(s):

Hugo S. Salinas ◽

Yuri A. Iriarte ◽

Heleno Bolfarine

Keyword(s):

Maximum Likelihood ◽

Real Data ◽

Random Variable ◽

Rayleigh Distribution ◽

Likelihood Method ◽

Independent Random Variables ◽

Parameter Estimates ◽

Positive Data ◽

<p>In this paper we introduce a new distribution for modeling positive data with high kurtosis. This distribution can be seen as an extension of the exponentiated Rayleigh distribution. This extension builds on the quotient of two independent random variables, one exponentiated Rayleigh in the numerator and Beta(q,1) in the denominator with q>0. It is called the slashed exponentiated Rayleigh random variable. There is evidence that the distribution of this new variable can be more flexible in terms of modeling the kurtosis regarding the exponentiated Rayleigh distribution. The properties of this distribution are studied and the parameter estimates are calculated using the maximum likelihood method. An application with real data reveals good performance of this new distribution.</p>

The Odd Log-Logistic Dagum Distribution: Properties and Applications

Revista Colombiana de Estadística ◽

10.15446/rce.v41n1.66542 ◽

2018 ◽

Vol 41 (1) ◽

pp. 109-135 ◽

Cited By ~ 1

Author(s):

Filippo Domma ◽

Abbas Eftekharian ◽

Ahmed Afify ◽

Morad Alizadeh ◽

Indranil Ghosh

Keyword(s):

Maximum Likelihood ◽

Likelihood Estimation ◽

Real Data ◽

Failure Criteria ◽

Likelihood Method ◽

Model Parameters ◽

New Model ◽

Dagum Distribution ◽

Lifetime Model

This paper introduces a new four-parameter lifetime model called the odd log-logistic Dagum distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some structural properties of the model odd log-logistic Dagum such as order statistics and incomplete moments. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling real data.

A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation

Symmetry ◽

10.3390/sym13020269 ◽

2021 ◽

Vol 13 (2) ◽

pp. 269

Author(s):

Yuri A. Iriarte ◽

Mário de Castro ◽

Héctor W. Gómez

Keyword(s):

Parameter Estimation ◽

Maximum Likelihood ◽

Structural Properties ◽

Bimodal Distribution ◽

Symmetric Distribution ◽

Likelihood Method ◽

Simulation Experiments ◽

Special Cases ◽

The generalized bimodal distribution is especially efficient in modeling univariate data exhibiting symmetry and bimodality. However, its performance is poor when the data show important levels of skewness. This article introduces a new unimodal/bimodal distribution capable of modeling different skewness levels. The proposal arises from the recently introduced Lambert transformation when considering a generalized bimodal baseline distribution. The bimodal-normal and generalized bimodal distributions can be derived as special cases of the new distribution. The main structural properties are derived and the parameter estimation is carried out under the maximum likelihood method. The behavior of the estimators is assessed through simulation experiments. Finally, two applications are presented in order to illustrate the utility of the proposed distribution in data modeling in different real settings.