Parameter Estimation in Multivariate Gamma Distribution

Vaidyanathan, V. S.; Lakshmi, R.

doi:10.19139/95

Cited by 7 publications

(4 citation statements)

References 6 publications

(10 reference statements)

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“…In this part, a real-life data given by Dumonceaux and Antle (1973) is considered. The data known as flood data represent the maximum flood levels of Susquehanna River at Harrisburg, Pennsylvania over four periods years between 1969 and 1980 in millions of cubic feet per second and given as: 0.654, 0.613, 0.315, 0.449, 0.297, 0.402, 0.379, 0.423, 0.379, 0.3235, 0.269, 0.740, 0.418, 0.412, 0.494, 0.416, 0.338, 0.392, 0.484, 0.265 (Balakrishnan and Wang, 2000;Lakshmi and Vaidyanathan, 2016;Vaidyanathan and Lakshmi, 2015).…”

Section: Real Life Examplementioning

confidence: 99%

“…Gamma distribution is one of the extensively used distributions for modeling skewed data in various fields such as hydrology, finance, especially for reliability or lifetime (Basak and Balakrishnan, 2012;Hirose, 1995;Vaidyanathan and Lakshmi, 2015). Let be a random variable with shape parameter , scale parameter and location (or threshold) parameter .…”

Section: Introductionmentioning

confidence: 99%

“…In Eq. ( 2), indicates incomplete Gamma function (Balakrishnan and Wang, 2000; N. L. Johnson et al, 1994, Vaidyanathan andLakshmi, 2015).…”

Section: Introductionmentioning

confidence: 99%

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Gamma Dağılımının Parametrelerinin Tahmini için Metasezgisel Yöntemlerin Değerlendirilmesi ve Karşılaştırılması

Yonar

Pehlivan

2022

Nicel Bilimler Dergisi

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Parameter estimation of three parameter (3-p) Gamma distribution is very important as it is one of the most popular distributions used to model skewed data. Maximum Likelihood (ML) method based on finding estimators that maximize the likelihood function, is a well-known parameter estimation method. It is rather difficult to maximize the likelihood function formed for the parameter estimation of the 3-p Gamma distribution. In this study, five well known metaheuristic methods, Simulated Annealing (SA), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and Artificial Bee Colony (ABC), are suggested to obtain ML estimates of the parameters for the 3-p Gamma distribution. Monte-Carlo simulations are performed to examine efficiencies of the metaheuristic methods for the parameter estimation problem of the 3-p Gamma distribution. Also, differences between solution qualities and computation time of the algorithms are investigated by statistical tests. Moreover, one of the multi-criteria decision-making methods, Technique for Order Performance by Similarity to Ideal Solution (TOPSIS), is preferred for ranking the metaheuristic algorithms according to their performance in parameter estimation. Results show that Differential Evolution is superior to the others for this problem in consideration of all the criteria of solution quality, computation time, simplicity, and robustness of the metaheuristic algorithms. In addition, an analysis of real-life data is presented to demonstrate the implementation of the suggested metaheuristic methods.

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Section: Real Life Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gamma Dağılımının Parametrelerinin Tahmini için Metasezgisel Yöntemlerin Değerlendirilmesi ve Karşılaştırılması

Yonar

Pehlivan

2022

Nicel Bilimler Dergisi

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“…A common method of estimation for the bivariate gamma distribution in (1) is the method of moments since its moments can be readily calculated (Yue et al, 2001;Vaidyanathan & Lakshmi, 2015). Tsionas (2004) proposed the use of Bayesian Monte Carlo methods for estimating this type of multivariate gamma distribution.…”

Section: Bivariate Gamma Distributionmentioning

confidence: 99%

Bivariate Gamma Mixture of Experts Models for Joint Insurance Claims Modeling

Hu¹,

Murphy²,

O’Hagan³

2019

Preprint

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In general insurance, risks from different categories are often modeled independently and their sum is regarded as the total risk the insurer takes on in exchange for a premium. The dependence from multiple risks is generally neglected even when correlation could exist, for example a single car accident may result in claims from multiple risk categories. It is desirable to take the covariance of different categories into consideration in modeling in order to better predict future claims and hence allow greater accuracy in ratemaking. In this work multivariate severity models are investigated using mixture of experts models with bivariate gamma distributions, where the dependence structure is modeled directly using a GLM framework, and covariates can be placed in both gating and expert networks. Furthermore, parsimonious parameterisations are considered, which leads to a family of bivariate gamma mixture of experts models. It can be viewed as a model-based clustering approach that clusters policyholders into sub-groups with different dependencies, and the parameters of the mixture models are dependent on the covariates. Clustering is shown to be important in separating the data into sub-groupings where strong dependence is often present, even if the overall data set exhibits only weak dependence. In doing so, the correlation within different components features prominently in the model. It is shown that, by applying to both simulated data and a real-world Irish GI insurer data set, claim predictions can be improved.

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