We consider the problem of estimating a quantile ξ + bσ of an exponential distribution on the basis of a random sample of size n ≥ 2. Here ξ and σ are unknown location and scale parameters and b is a given constant. For quadratic loss, it is established that the best equivariant estimator (Equation presented) is inadmissible if 0 ≤ b < n-1or b > 1 + n1. For b > 1 + n1the estimator (Equation presented) elsewhere, provides a noticeable improvement over δ0.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Best equivariant estimator
- Location-scale parameter
- Quadratic loss
- Quantile of the exponential distribution