We provide an estimation procedure of the two-parameter Gamma distribution based on the Algorithmic Inference approach. As a key feature of this approach, we compute the joint probability distribution of these parameters without assuming any prior. To this end, we propose a numerical algorithm which is often beneficial of a highly efficient speed up based on an approximate analytical expression of the probability distribution. We contrast our interval and point estimates with those recently obtained in Son and Oh (2006) for the same problem. From this benchmark we realize that our estimates are both unbiased and more accurate, albeit more dispersed, in some cases, than the competitors' methods, where the dispersion drawback is notably mitigated w.r.t. Bayesian methods by a greater estimate decorrelation. We also briefly discuss the theoretical novelty of the adopted inference paradigm which actually represents a brush up on a Fisher perspective dating to almost a century, made feasible today by the available computational tools.

Algorithmic Inference of Two-Parameter Gamma Distribution / B. Apolloni, S. Bassis. - In: COMMUNICATIONS IN STATISTICS. SIMULATION AND COMPUTATION. - ISSN 0361-0918. - 38:9(2009 Oct), pp. 1950-1968.

Algorithmic Inference of Two-Parameter Gamma Distribution

B. Apolloni
Primo
;
S. Bassis
Ultimo
2009

Abstract

We provide an estimation procedure of the two-parameter Gamma distribution based on the Algorithmic Inference approach. As a key feature of this approach, we compute the joint probability distribution of these parameters without assuming any prior. To this end, we propose a numerical algorithm which is often beneficial of a highly efficient speed up based on an approximate analytical expression of the probability distribution. We contrast our interval and point estimates with those recently obtained in Son and Oh (2006) for the same problem. From this benchmark we realize that our estimates are both unbiased and more accurate, albeit more dispersed, in some cases, than the competitors' methods, where the dispersion drawback is notably mitigated w.r.t. Bayesian methods by a greater estimate decorrelation. We also briefly discuss the theoretical novelty of the adopted inference paradigm which actually represents a brush up on a Fisher perspective dating to almost a century, made feasible today by the available computational tools.
Adaptive rejection sampling; Algorithmic inference; Gibbs sampling; Maximum likelihood estimator; Population bootstrap; Two-parameter Gamma distribution
Settore INF/01 - Informatica
ott-2009
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/67746
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