Far East Journal of Theoretical Statistics
Volume 21, Issue 2, Pages 137 - 156
(March 2007)
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SEQUENTIAL CONFIDENCE INTERVALS FOR A FUNCTION OF THE
PARAMETERS OF AN EXPONENTIAL DISTRIBUTION
Eiichi Isogai (Japan) and Chikara Uno (Japan)
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Abstract: We consider the sequential
fixed-width confidence interval estimation problem for a function q
of location parameter m and scale parameter s
of a negative exponential distribution. We propose a fully sequential procedure
and construct sequential confidence intervals for q.
Their asymptotic consistency is shown. As an application of q
we consider the problem of estimating the ratio
with
and give the asymptotic consistency of the fully sequential procedure. We also
give the second-order asymptotic expansion of the average sample size of the
above procedure as the width of confidence interval approaches zero. Some
simulation results are presented. |
Keywords and phrases: fixed-width confidence interval, negative exponential,
asymptotic consistency, Anscombe’s theorem, asymptotic expansion, nonlinear
renewal theory. |
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