  The estimation of the signal location and intensity of a peak in a pulse
height spectrum is important for x-ray and $\gamma$-ray spectroscopy,
charged-particle spectrometry, liquid chromatography, and many other subfields.
However, both the "centroid" and "signal intensity" of a peak in a pulse-height
spectrum are ill-defined quantities and different methods of analysis will
yield different numerical results. Here, we apply three methods of analysis.
Method A is based on simple count summation and is likely the technique most
frequently applied in practice. The analysis is straightforward and fast, and
does not involve any statistical modeling. We find that it provides reliable
results only for high signal-to-noise data, but has severe limitations in all
other cases. Method B employs a Bayesian model to extract signal counts and
centroid from the measured total and background counts. The resulting values
are derived from the respective posteriors and, therefore, have a rigorous
statistical meaning. The method makes no assumptions about the peak shape. It
yields reliable and relatively small centroid uncertainties. However, it
provides relatively large signal count uncertainties. Method C makes a strong
assumption regarding the peak shape by fitting a Gaussian function to the data.
The fit is based again on a Bayesian model. Although Method C requires careful
consideration of the Gaussian width (usually given by the detector resolution)
used in the fitting, it provides reliable values and relatively small
uncertainties both for the signal counts and the centroid.
