Abstract: By means of the parameter estimation, we give the Bayesian estimation, the minimum risk equivalent estimation and the minimax estimation of scale parameter σ under the qsymmetric entropy loss function in the normal distribution, its mean of which is 0. Furthermore, when 0≤c*, d>0; c=c^*, d≥0, the estimator with the form of ［cT+d］^1/2 is admissible; when 0*, d=0; c>c^*, d>0, ［cT+d］^1/2 is inadmissible.

Key words: qsymmetric entropy loss function, equivalent estimation, Bayesian estimation, minimax estimation, admissibillity, scale parameter