Advances and Applications in Statistics
Volume 14, Issue 1, Pages 49 - 55
(January 2010)
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A COMPARATIVE STUDY OF PARAMETER INFERENCE METHODS FOR POISSON DISTRIBUTION:
SMALL SAMPLE SIZES
Manlika Tanusit
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Abstract: The objective of this study is to compare point
estimation methods and interval estimation methods for the Poisson distribution
with small sample sizes. Three methods of point estimation: maximum likelihood
method, Bayesian method and minimax method, and three methods of interval
estimation: normal method, normal-Bayesian method and score-Bayesian method are
considered. The lowest mean absolute error and the lowest average width are used
as the criteria of selection for point estimation and interval estimation,
respectively. The scopes of this study consist of sample sizes: 5, 6, 7, 8, 9,
10 and the parameter l is equal to 0.02,
0.04, 0.06, 0.08 and 0.1. Data is simulated 1,000 times generated by using the
JAVA software. The results of this research are as follows: For point
estimation, we recommend that for all sample sizes and parameter l, the Bayesian method should be used. In case of
interval estimation, normal-Bayesian method is
recommended for sample sizes are 5 to 8, l between 0.2 to 0.4 and sample sizes are 9 to 10,
l is
equal to 0.2 whereas score-Bayesian method should be considered for sample sizes
are 5 to 8, values of l
ranging from 0.6 to 1 and sample sizes are 9 to 10, l between 0.4 to 1.0. |
Keywords and phrases: Poisson distribution, interval estimation, sample size. |
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