Abstract
This paper is concerned with sequential estimation of the probability of a random variable falling a specified number of standard deviations away from the mean, when the mean, the standard deviation and the underlying distribution are unknown. We consider both point and interval estimation of tail probability under some broad assumptions on the underlying distribution,we establish asymptotic collsistency of the sequential fixed-width interval procedure and risk-efficiency of the sequential point-estimation procedure. We also carry out a simulation study for the fixed-width interval estimation when the underlying distribution is normal or exponential.
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