Using the approach of Roy and Mitra (1957), Jani (1984) has given an easy method for finding the uniformly minimum variance unbiased estimators (UMVUEs) of reliability and its variance in exponential life model. We extend these results under Type 1 and Type 2 censorings.
AbstractWe will discuss orthogonal models and error orthogonal models and their algebraic structure, using as background, commutative Jordan algebras. The role of perfect families of symmetric matrices will be emphasized, since they will play an important part in the construction of the estimators for the relevant parameters. Perfect families of symmetric matrices form a basis for the commutative Jordan algebra they generate. When normality is assumed, these perfect families of symmetric matrices will ensure that the models have complete and sufficient statistics. This will lead to uniformly minimum variance unbiased estimators for the relevant parameters.
Sampling theorem and efficiency comparison of three local minimum variance unbiased estimators of the mean and variance of the exponential distribution
