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Frechet - Cramer -Rao lower bound on variance is a land mark in the history of Statistics. Obtaining uniformly minimum variance unbiased estimator via lower bound involves the problem of construction of bound and study Kiefer bound is the best lower bound of this type. Its computation involves complications. Therefore, its applications were restricted. In this book Kiefer bound is computed for parameters and some parametric functions in various truncated families of distributions. This book talks about the attainment of Kiefer bound. The natural forms of truncated densities are introduced....