Abstract: The present paper presents the general form of the symmetric entropy loss function, (λ/δ)^q+(δ/λ)^q-2(q>0), which is called the q-symmetric entropy loss function, and deals with the Byaesian estimation, the minimum risk equivalent estimation and the minimax estimation for the scale parameter of the exponential istribution under the loss function, the conclusion is generalized. The admissbility and inadmissibility of estimator with the form of (cT+d)^-1 are discussed.

Key words: Bayesian estimation, equivalent estimation, minimax estimation, scale parameter, admissibility, q-symmetric entropy loss function