Closed-form estimators and bias-corrected estimators for the Nakagami distribution

Jun, Zhao; Kim, SungBum; Kim, Hyoung-Moon

doi:10.1016/j.matcom.2020.12.026

Cited by 7 publications

(1 citation statement)

References 21 publications

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“…Based on this weakness of MLE, Ye and Chen (2017) obtained closed‐form estimators for the univariate gamma distribution derived from likelihood equations. Inspired by this simple idea, Zhao, Kim, and Kim (2021) derived closed‐form estimators for the Nakagami distribution. Kim and Jang (2021) obtained new closed‐form estimators for the weighted Lindley distribution.…”

Section: Introductionmentioning

confidence: 99%

New closed‐form efficient estimator for multivariate gamma distribution

Jang

Zhao

Kim

et al. 2023

Statistica Neerlandica

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Maximum likelihood estimation is used widely in classical statistics. However, except in a few cases, it does not have a closed form. Furthermore, it takes time to derive the maximum likelihood estimator (MLE) owing to the use of iterative methods such as Newton–Raphson. Nonetheless, this estimation method has several advantages, chief among them being the invariance property and asymptotic normality. Based on the first approximation to the solution of the likelihood equation, we obtain an estimator that has the same asymptotic behavior as the MLE for multivariate gamma distribution. The newly proposed estimator, denoted as , is also in closed form as long as the ‐consistent initial estimator is in the closed form. Hence, we develop some closed‐form ‐consistent estimators for multivariate gamma distribution to improve the small‐sample property. is an alternative to MLE and performs better compared to MLE in terms of computation time, especially for large datasets, and stability. For the bivariate gamma distribution, the is over 130 times faster than the MLE, and as the sample size increasing, the is over 200 times faster than the MLE. Owing to the instant calculation of the proposed estimator, it can be used in state–space modeling or real‐time processing models.

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Section: Introductionmentioning

confidence: 99%

New closed‐form efficient estimator for multivariate gamma distribution

Jang

Zhao

Kim

et al. 2023

Statistica Neerlandica

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Novel Closed‐Form Point Estimators for a Weighted Exponential Family Derived From Likelihood Equations

Vila,

Nakano,

Saulo

2024

Stat

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In this paper, we propose and investigate closed‐form point estimators for a weighted exponential family. We also develop a bias‐reduced version of these proposed closed‐form estimators through bootstrap methods. Estimators are assessed using a Monte Carlo simulation, revealing favourable results for the proposed bootstrap bias‐reduced estimators. We illustrate the proposed methodology with the use of two real data sets.

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New closed-form estimator and its properties

Kim

Jang

et al. 2021

J. Korean Stat. Soc.

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Closed-form estimators and bias-corrected estimators for the Nakagami distribution

Cited by 7 publications

References 21 publications

New closed‐form efficient estimator for multivariate gamma distribution

New closed‐form efficient estimator for multivariate gamma distribution

Novel Closed‐Form Point Estimators for a Weighted Exponential Family Derived From Likelihood Equations

New closed-form estimator and its properties

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