Fast calculation of exponentially modified functions
Abstract
There is a great need for modelling experimental data represented as asymmetric peaks, for example those detected by chromatography. One of the most important models for these peaks is Exponentially Modified Gaussian (EMG) function. In statistics, EMG distribution describes the probability density of the sum or difference of two random variables, one of which has a normal distribution, and the other has an exponential distribution. Drawbacks of this distribution are I) rather complicated set of formulas used for its computation and II) lack of formulas that can be used for calculation of the density of the sum of one normal and more than one exponentially distributed variables. In this study a general method for rapidly calculating exponentially modified functions using the exponentially weighted moving average (EWMA) algorithm has been investigated. The algorithm allows very simple and fast way to calculate an approximate estimate of the exponential modification of Gaussian or any other function with required precision, as well as to make a double, triple, and more exponential modifications. New formulas relating the time constant of the exponential modification τ and the coefficient of the EWMA algorithm α are proposed and accuracy of these formulas depending on experimental data rate are evaluated.
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References
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