This paper introduces a generalized formulation of linear prediction (LP), including both conventional and temporally weighted LP analysis methods as special cases. The temporally weighted methods have recently been successfully applied to noise robust spectrum analysis in speech and speaker recognition applications. In comparison to those earlier methods, the new generalized approach allows more versatility in weighting different parts of the data in the LP analysis. Two such weighted methods are evaluated and compared to the conventional spectrum modeling methods FFT and LP, as well as the temporally weighted methods WLP and SWLP, by substituting each of them in turn as the spectrum estimation method of the MFCC feature extraction stage of a GMM-UBM based speaker verification system. The new methods are shown to lead to performance improvement in several cases involving channel distortion and additive noise mismatch between the training and recognition conditions.