ESTIMATING THE MEAN OF AN EXPONENTIAL-DISTRIBUTION FROM GROUPED OBSERVATIONS

In a number of industrial situations, it is more economical to record the number of observations within preset categories instead of recordi ng the observations exactly. Using more than two categories serves as a good alternative to dichotomous data, such as the case where test un its are merely characterized as ''failed'' or ''unfailed'' in a single time interval. In this paper, we consider estimating the mean of the exponential distribution when the data are grouped into three categori es. Various estimators are presented and compared via simulations. The results are then extended to the estimation of the parameters of the Weibull distribution.