Averaging the spectral shapes

The methods of obtaining the average spectral shape in a low statistics regime are presented. Different approaches to averaging are extensively tested with simulated spectra, based on the ASCA responses. The issue of binning up the spectrum before fitting is discussed together with the choice of statistic used to model the spectral shape. The best results are obtained with methods in which input data are represented by probability density functions. Application of weights, representing the coverage between the input and output bins, slightly improves the resolution of averaging.