Closed-Form Estimators for the Gamma Distribution Derived From Likelihood Equations
| Autor: | Zhi-Sheng Ye, Nan Chen |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Mathematical optimization 021103 operations research General Mathematics Generalized gamma distribution 0211 other engineering and technologies Estimator Asymptotic distribution 02 engineering and technology M-estimator 01 natural sciences Scaled inverse chi-squared distribution 010104 statistics & probability Gamma distribution Generalized integer gamma distribution Applied mathematics 0101 mathematics Statistics Probability and Uncertainty Mathematics Inverse-gamma distribution |
| Zdroj: | The American Statistician. 71:177-181 |
| ISSN: | 1537-2731 0003-1305 |
| DOI: | 10.1080/00031305.2016.1209129 |
| Popis: | It is well-known that maximum likelihood (ML) estimators of the two parameters in a gamma distribution do not have closed forms. This poses difficulties in some applications such as real-time signal processing using low-grade processors. The gamma distribution is a special case of a generalized gamma distribution. Surprisingly, two out of the three likelihood equations of the generalized gamma distribution can be used as estimating equations for the gamma distribution, based on which simple closed-form estimators for the two gamma parameters are available. Intuitively, performance of the new estimators based on likelihood equations should be close to the ML estimators. The study consolidates this conjecture by establishing the asymptotic behaviors of the new estimators. In addition, the closed-forms enable bias-corrections to these estimators. The bias-correction significantly improves the small-sample performance. |
| Databáze: | OpenAIRE |
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