Multivariate Gamma Regression: Parameter Estimation, Hypothesis Testing, and Its Application

Rahayu, Anita; Purhadi, Purhadi; Sutikno, Sutikno; Prastyo, Dedy Dwi

doi:10.3390/sym12050813

Cited by 19 publications

(10 citation statements)

References 17 publications

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“…We can refer to Kotz et al [31] (Chapter 48) for an overview of multivariate Gamma distributions. We can also refer to Rahayu et al [32] for statistical applications with multivariate Gamma distributions. In such a case of dependent univariate Gamma distributions, the result in Theorem 1 still holds so that we now have dependent negative multinomial counts.…”

Section: Sampling Theory Resultsmentioning

confidence: 99%

Cox Processes Associated with Spatial Copula Observed through Stratified Sampling

Oscar

Vaillant²

2021

Mathematics

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Cox processes, also called doubly stochastic Poisson processes, are used for describing phenomena for which overdispersion exists, as well as Poisson properties conditional on environmental effects. In this paper, we consider situations where spatial count data are not available for the whole study area but only for sampling units within identified strata. Moreover, we introduce a model of spatial dependency for environmental effects based on a Gaussian copula and gamma-distributed margins. The strength of dependency between spatial effects is related with the distance between stratum centers. Sampling properties are presented taking into account the spatial random field of covariates. Likelihood and Bayesian inference approaches are proposed to estimate the effect parameters and the covariate link function parameters. These techniques are illustrated using Black Leaf Streak Disease (BLSD) data collected in Martinique island.

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Section: Sampling Theory Resultsmentioning

confidence: 99%

Cox Processes Associated with Spatial Copula Observed through Stratified Sampling

Oscar

Vaillant²

2021

Mathematics

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“…He also stated that the maximum likelihood method is widely used because it is more precise especially when dealing with large samples since it yields an excellent estimator when the sample is large. Maximum likelihood function C D of M is a solution to the maximization problem given as [9,10,12,15,16,[22][23][24][25].…”

Section: Maximum Likelihood Estimation Methods (Mle)mentioning

confidence: 99%

Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique

Troon¹

2021

Preprint

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Kenya is one of the countries in the world with a good quantity of wind. This makes the country to work ontechnologies that can help in harnessing the wind with a vision of achieving a total capacity of 2GW of wind energy by 2030.The objective of this research is to find the best three-parameter wind speed distribution for examining wind speed using the maximum likelihood fitting technique. To achieve the objective, the study used hourly wind speed data collected for a period of three years (2016 – 2018) from five sites within Narok County. The study examines the best distributions that the data fits and then conducted a suitability test of the distributions using the Kolmogorov-Smirnov test. The distribution parameters were fitted using maximum likelihood technique and model comparison test conducted using Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values with the decision rule that the best distribution relies on the distribution with the smaller AIC and BIC values. The research showed that the best distribution is the gamma distribution with the shape parameter of 2.071773, scale parameter of 1.120855, and threshold parameter of 0.1174. A conclusion that gamma distribution is the best three-parameter distribution for examining the Narok country wind speed data

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“…Regarding Lemma 1 and Lemma 2, an iteration process can be carried out using the BHHH method. Following [33], the BHHH algorithm in this study is as follows:…”

Section: Proof Of Lemmamentioning

confidence: 99%

A Logit Model for Bivariate Binary Responses

Purhadi

Fathurahman

2021

Symmetry

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This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 × 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt–Hall–Hall–Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.

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Multivariate Gamma Regression: Parameter Estimation, Hypothesis Testing, and Its Application

Cited by 19 publications

References 17 publications

Cox Processes Associated with Spatial Copula Observed through Stratified Sampling

Cox Processes Associated with Spatial Copula Observed through Stratified Sampling

Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique

A Logit Model for Bivariate Binary Responses

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