Three-parameter gamma distribution: Estimation using likelihood, spacings and least squares approach

Lakshmi, R.; Vaidyanathan, V. S.

doi:10.1080/09720510.2014.986927

Cited by 11 publications

(10 citation statements)

References 8 publications

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“…where θ = (σ, β, µ) is a vector of representing unknown parameters [4,12]. To obtain the ML estimates of the parameters σ, β and µ, the likelihood function (or the log likelihood function) is maximized as follows:…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…Three parameters (3-p) Gamma distribution is one of the commonly used distributions for modeling skewed data in the field of reliability, hydrology, and finance [3,6,12,18]. The probability density function and cumulative distribution function of the 3-p Gamma distribution are defined by…”

Section: Introductionmentioning

confidence: 99%

“…Tzavelas [27] introduced a program in Mathematica to obtain the solutions of the likelihood equations in the ML parameter estimation for the 3-p Gamma distributions. Lakshmi and Vaidyanathan [12] proposed a novel approach for the ML, the least square (LS) and the maximum product spacing (MPS) methods to estimate the parameters of the 3-p Gamma distribution by using an extensive search over three-dimensional parameter space.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres

Yonar

Pehlivan

2020

Hacettepe Journal of Mathematics and Statistics

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Three-parameter (3-p) Gamma distribution is widely used to model for skewed data in the reliability field. Thus, the problem of parameter estimation for the Gamma distribution has remained significant and interesting in all times. The maximum likelihood (ML) and the least square (LS) are the most popular methods in the parameter estimation. In this study, a novel Differential Evolution (DE) algorithm is proposed for the ML and LS estimation of the parameters of the 3-p Gamma distribution. This approach overcomes the problem of how to determine the search space of the DE by utilizing a new search space based on the confidence interval. The modified maximum likelihood and the profile likelihood methods are considered to constitute the confidence interval. In order to examine the performance of the proposed approach, an extensive Monte Carlo simulation study and a real data application are performed. The results show that this proposed approach is effective for estimating the parameters of the 3-p Gamma distribution with respect to mean square error and deficiency criteria.

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Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres

Yonar

Pehlivan

2020

Hacettepe Journal of Mathematics and Statistics

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“…al. [26] estimated the three-parameter gamma distribution by using likelihood, spacings and least squares approach. Upadhyay et.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Inference on the Generalized Gamma Distribution using Conjugate Priors

Riffi

El-Masri

2020

IUGNS

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This paper focuses on the three-parameter generalized gamma distribution and uses Bayesian techniques to estimate its parameters. Many authors con-sidered estimating the parameters of the generalized gamma distribution in a Bayesian framework using Jeﬀrey’s priors. Others used diﬀerent loss functions and the least squares approach. This study uses Bayesian techniques to estimate the three-parameter generalized gamma distribution by using conjugate priors. The random Metropolis algorithm is used to simulate the Bayesian estimates of the three parameters. Then these estimates are compared to the maximum like-lihood estimates using the mean error through simulation. It has been shown in this paper that the obtained estimates using this approach is more accurate than the traditional methods of estimation such as the Maximum likelihood method. The same approach is then used to estimate the parameters of mixtures of the generalized gamma parameters using conjugate priors.

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“…The generalized gamma distribution (GG) was introduced by [1] and carefully analyzed by [2]. The GG has three-parameters and the techniques to find them is a matter of research, see among others [3,4,5]. A significant role in astrophysics is played by the luminosity function (LF) for galaxies and we present some models, among others, the Schechter LF, see [6], a two-component Schechter-like LF, see [7], and the double Schechter LF with five parameters, see [8].…”

Section: Introductionmentioning

confidence: 99%

New Probability Distributions in Astrophysics: I. The Truncated Generalized Gamma

Zaninetti¹

2019

IJAA

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The gamma function is a good approximation to the luminosity function of astrophysical objects, and a truncated gamma distribution would permit a more rigorous analysis. This paper examines the generalized gamma distribution (GG) and then introduces the scale and the new double truncation. The magnitude version of the truncated GG distribution with scale is adopted in order to fit the luminosity function (LF) for galaxies or quasars. The new truncated GG LF is applied to the five bands of SDSS galaxies, to the 2dF QSO Redshift Survey in the range of redshifts between 0.3 and 0.5, and to the COSMOS QSOs in the range of redshifts between 3.7 and 4.7. The average absolute magnitude versus redshifts for SDSS galaxies and QSOs of 2dF was modeled adopting a redshift dependence for the lower and upper absolute magnitude of the new truncated GG LF.

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Three-parameter gamma distribution: Estimation using likelihood, spacings and least squares approach

Cited by 11 publications

References 8 publications

A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres

A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres

Bayesian Inference on the Generalized Gamma Distribution using Conjugate Priors

New Probability Distributions in Astrophysics: I. The Truncated Generalized Gamma

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