We consider the density of right truncated family of distributions in its natural form. We compute the Kiefer bound on variance of unbiased estimators of the parametric function involved in the density of right truncated distribution. Type II right truncated and doubly censored samples are taken into consideration. It is shown that the variances of estimators based on the samples attain their Kiefer bounds. Results are illustrated through examples. Bounds based on complete and censored samples are compared.

Kiefer bound, variance bound, minimum variance unbiased estimator, right truncated distribution, parametric function, ideal estimation equation, censored samples.