We present an optimal coding scheme that parameterizes the maximum-likelihood estimate of variance for frequency spectra belonging to the generalized Gaussian distribution, the distribution covering the Laplacian and the Gaussian. By slightly modifying the all-pole model of the conventional linear prediction (LP), we can estimate the variance with the same method as in LP, which has low computational costs. Experimental results show that incorporating the coding scheme in a state-of-the-art wide-band audio coder enhances its objective and subjective quality in a low-bit-rate and low-delay situation by increasing the compression efficiency. Thus, this coding scheme will be useful in applications like mobile communications, which requires highly efficient compression.