Inferential procedures for the truncated exponential distribution

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Abstract
Suppose that X1,X2,…,Xn are independent and identically distributed with density , 0≤x≤t and that inferences about θ are to be made. The exact distribution of is known but is quite complicated and so an approximation to its distribution is needed. It is shown here that the beta approximation for the density of (nt)−1U obtained by equating the first two moments performs better, for moderate n, than the normal approximation given by the central limit theorem and is asymptotically equivalent to it. The use of this approximation in making inferences in some life testing situations is discussed via an example.