TITLE:
Moved Score Confidence Intervals for Means of Discrete Distributions
AUTHORS:
Yu Guan
KEYWORDS:
Confidence Interval; Confidence Level; Coverage Probability; Discrete Distribution;
Moved Score Confidence Interval
JOURNAL NAME:
Open Journal of Statistics,
Vol.1 No.2,
July
26,
2011
ABSTRACT: Let X denote a discrete distribution as Poisson, binomial or negative binomial variable. The score confidence interval for the mean of X is obtained based on inverting the hypothesis test and the central limit theorem is discussed and recommended widely. But it has sharp downward spikes for small means. This paper proposes to move the score interval left a little (about 0.04 unit), called by moved score confidence interval. Numerical computation and Edgeworth expansion show that the moved score interval is analogous to the score interval completely and behaves better for moderate means; for small means the moved interval raises the infimum of the coverage probability and improves the sharp spikes significantly. Especially, it has unified explicit formulations to compute easily.