A bimodal gamma distribution: properties, regression model and applications

Vila, Roberto; Ferreira, L. A.; Saulo, Helton; Prataviera, Fábio; Ortega, Edwin M. M.

doi:10.1080/02331888.2020.1764560

Cited by 15 publications

(12 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, we have some comparisons between the rates of random variables with known distributions: Inverse-gamma, Log-normal, Generalized-Pareto, BWeibull, BGamma [16], exponential and Normal;…”

Section: Characteristics Of Probability Denstiy Functionmentioning

confidence: 99%

“…MLqEs with BWeibull and BGamma distributions outperform when compared with parametric model in [39]. Example 4 : Wheaton River data are analyzed by [16] and references therein. The number of observation is 72.…”

Section: Application On Real Data Setsmentioning

confidence: 99%

“…MLqE with BWeibull give outperforming when we compare by MLqE with BGamma. BGamma from [16] has a good performance for fitting among the distributions [40] and references therein. The advantage of using MLqE is observed when we look at the p-values of KS and CVM in Table IV.…”

Section: Application On Real Data Setsmentioning

confidence: 99%

“…The section V introduces that the model parameters are estimated by maximum log and log q likelihood methods. Section VI gives numerial assessments of the proposed model and also provides the comparison between recently proposed Bimodal Gamma (BGamma) distribution [16] and the model in this paper. The conclusion is given by VI.…”

mentioning

confidence: 99%

See 3 more Smart Citations

A Bimodal Weibull Distribution: Properties and Inference

Vila¹,

Çankaya²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Modeling is a challenging topic and using parametric models is an important stage to reach flexible function for modeling. Weibull distribution has two parameters which are shape α and scale β. In this study, bimodality parameter is added and so bimodal Weibull distribution is proposed by using a quadratic transformation technique used to generate bimodal functions produced due to using the quadratic expression. The analytical simplicity of Weibull and quadratic form give an advantage to derive a bimodal Weibull via constructing normalizing constant. The characteristics and properties of the proposed distribution are examined to show its usability in modeling. After examination as first stage in modeling issue, it is appropriate to use bimodal Weibull for modeling data sets. Two estimation methods which are maximum log q likelihood and its special form including objective functions log q (f ) and log(f ) are used to estimate the parameters of shape, scale and bimodality parameters of the function. The second stage in modeling is overcome by using heuristic algorithm for optimization of function according to parameters due to fact that converging to global point of objective function is performed by heuristic algorithm based on the stochastic optimization.Real data sets are provided to show the modeling competence of the proposed distribution.

show abstract

Section: Characteristics Of Probability Denstiy Functionmentioning

confidence: 99%

Section: Application On Real Data Setsmentioning

confidence: 99%

Section: Application On Real Data Setsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A Bimodal Weibull Distribution: Properties and Inference

Vila¹,

Çankaya²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Olmos et al (2017) introduced recently a bimodal extension of the Birnbaum-Saunders distribution. Vila et al (2020) proposed the bimodal gamma distribution. Vila and C ¸ankaya (2021) considered a bimodal Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

A Model for Bimodal Rates and Proportions

Vila¹,

Alfaia²,

Menezes³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed by using an approach based on the alpha-skew-normal model. We discuss several properties of this distribution such as bimodality, real moments, entropy measures and identifiability. Furthermore, we propose a new regression model based on the proposed model and discuss residuals. Estimation is performed by maximum likelihood. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. An application is provided to show the modelling competence of the proposed distribution when the data sets show bimodality.

show abstract