Accurate and precise evaluation of the peak parameters of the recorded X-ray spectra requires the use of the correct peak shape. Usually, it is assumed that the shape of the X-ray peaks is a Voigt function, i.e., convolution of a Lorentzian distribution function of the emitted X-ray lines with a Gaussian response of the spectrometer, with additional terms for description of the tailing. This assumption is not exactly correct, because it employs a probability density function for description of a discrete signal, while, actually, the measurable parameter is the probability, i.e., the integral of the probability density function over the channel width. In trie present work, the distortion in the peak shape caused by the discrete sampling of the X-ray spectrum is studied and the significance of the introduced errors is evaluated. An improved fitting procedure for evaluation of the peak parameters is proposed.