Physical Sciences and Mathematics Commons^™

Estimation In Truncated Exponential Family Of Distributions, Laxman M. Hegde

Mathematics & Statistics Theses & Dissertations

Estimating the parameters of a truncated distribution is a well known problem in statistical inference. The non-existence of the maximum likelihood estimator (m.l.e.) with positive probability in certain truncated distributions is not well known. To mention a few results in the literature:

(i) Deemer and Votaw 1955 show that the maximum likelihood estimator does not exist in a truncated negative exponential distribution on 0,T , T > 0 known, whenever the sample mean x (GREATERTHEQ) T/2.

(ii) Broeder 1955 shows that the maximum likelihood estimator of the scale parameter of a truncated gamma distribution, with the shape parameter being known, becomes …

Estimating The Parameters Of Truncated Distributions, Mukul Mohan Mittal

Mathematics & Statistics Theses & Dissertations

The problem considered here is the estimation of the parameters of some special truncated distributions. If the sample observations are restricted to the interval {O, T} with T known, then it is well known in the literature that the method of maximum likelihood fails to provide a finite estimate, for the mean of an exponential distribution, whenever the sample mean is greater than T/2 (Deemer and Votaw, 1955, Ann. Math. Statist. 26, 498-504). Not so well known is the nonexistence of the maximum likelihood estimator (m.l.e.), under certain conditions, for the scale parameter of a gamma distribution from a truncated …