Probability Generating Function Based Jeffrey's Divergence for Statistical Inference |
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Authors: | Maryam Sharifdoust Seng-Huat Ong |
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Affiliation: | 1. Department of Mathematics, Khomeinishahr Branch, Islamic Azad University, Esfahan, Iran;2. Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia |
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Abstract: | Statistical inference procedures based on transforms such as characteristic function and probability generating function have been examined by many researchers because they are much simpler than probability density functions. Here, a probability generating function based Jeffrey's divergence measure is proposed for parameter estimation and goodness-of-fit test. Being a member of the M-estimators, the proposed estimator is consistent. Also, the proposed goodness-of-fit test has good statistical power. The proposed divergence measure shows improved performance over existing probability generating function based measures. Real data examples are given to illustrate the proposed parameter estimation method and goodness-of-fit test. |
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Keywords: | Bias Goodness-of-fit Kullback–Liebler divergence Maximum likelihood Mean squared error M-estimation Minimum Hellinger distance Monte Carlo simulation Parameter estimation |
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