Estimating Scale and Truncation Parameters for the Truncated Exponential Distribution with Type-I Censored Sampling

Abstract

For time censored sampling from the truncated exponential distribution, maximum likelihood estimates (MLE) are derived for both the scale and truncation parameters. Both “conditional” and “unconditional” estimators are considered as well as estimators when the scale parameter is restricted to the positive axis. Asymptotic joint distributions of the estimators of scale and truncation point are found for all three versions of MLE. Small sample biases and mean squared errors of the estimators are studied by simulation. The estimators are applied to data on the size of forest fires. These data are also used to see how closely the estimates with censoring resemble the full sample estimates for varying degrees of censoring.