The Effect of a Random Noise Background upon the Amplitude Distribution Function of Random Events†

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Abstract
Statistical properties of a sum of continuous noise and random discrete events having gamma and Gaussian amplitude distributions, respectively, have been analysed. An expression is derived for the probability density function of this sum as a function of gamma and Gaussian distribution parameters. Attention is paid to the mode value, especially interesting in pulse-height spectrometry. The probability density function of the sum and its mode values are calculated and plotted in a normalized dimensionless form, suitable to direct application. The results can be applied for evaluation of errors in pulse-height spectrometry, especially when multi-channel pulse-height analysers are used.

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