On the Estimation of the Exponential Distribution of Parameters

Abstract

In the present paper, the problem of estimation of the exponential distribution of parameters is investigated.

In Sec. 1, the ordinary exponential distribution is considered, and the parameter λ is estimated by means of censored observations by the pseudomaximal likelihood method. It is shown that the estimator is asymptotically consistent and effective.

In Sec. 2, the problem of estimation of parameters of the truncated exponential distribution is considered using the maximal likelihood method. The existence and uniqueness of the solution corresponding to the likelihood equation are shown.

The practical application of the obtained results with the aid of computer realization is given. In particular, a sample of size n = 1000 is selected, which is distributed by the truncated exponential law. The sample mean \( \overline{x} \) = 1.3435 and the solution θ^∗ = 2.004 of the corresponding likelihood control are obtained.