Confidence interval for the mean of the exponential distribution, based on grouped data

Abstract

When the available data from an exponential distribution are grouped, the maximum likelihood estimator (MLE) for the mean and several modified MLE have been discussed in literature. However, little work has been done on interval estimators based on such grouped data. This paper derives the asymptotic property of a statistic which is used to construct an approximate confidence interval for the mean. The width of this approximate confidence interval, based on grouped data, is compared with those based on complete samples, and samples with type-I and type-II censoring. The limits of the ratios of these widths are derived when the sample size approaches infinity. The approximate confidence interval from grouped data is wider than those from complete and censored samples. However, Monte Carlo simulation indicates that the proposed method based on grouped data is adequate, considering the restricted information in this case.