1026036c-0e2a-40b8-a662-a54bf62c135c 13 3 12 decimal

&[DATE] &[TIME] - &[FILENAME]

Gaussian from convolution . . .

The complete convolution of two Gaussian is a slightly skewed Gaussian.

Very useful for fitting data sets of convolving underlying properties, from which

no PDF model can be found. Such a demand was done with great success Mathcad .

In addition to the [3] base parameters [W1, W2, m], The resulting Gaussian can be

shifted/magified [±]. Set properly L(t), U(t) to avoid cigar convolution !

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t U 2 t 21 mat min :

t L 2 - t 2 - 21 mat max :

W1 1 : W2 0.75 : m 0.5 : 13 mat

<= 'm' =>

t X 1.5 2 ln sqrt * W1 π sqrt * / 42 ln * t W1 / (2^* - exp * : t H 1.5 2 ln sqrt * W2 π sqrt * / 42 ln * t W2 / (2^* - exp * : t Convol u X t u - H * u t L t U int eval : green Gaussian model convolution 41 sys

Gaussian from complete convolution

x X m x - H x Convol m 1 m 0.5 - 2 2 mat m 0.75 m 14 green 1 5 mat 5 1 sys x U x L 2 1 sys

sanity MCD 0.25 - Convol 0.75 Convol 21 mat 0.137 0.1333 21 mat

Experiment a cigar solution

W1 1 : W2 0.75 : m 0.5 : 13 mat

<= 'm' =>

λ 0.625 :

t U λ t 21 mat min :

t L λ - t λ - 21 mat max :

t X 1.5 2 ln sqrt * W1 π sqrt * / 42 ln * t W1 / (2^* - exp * : t H 1.5 2 ln sqrt * W2 π sqrt * / 42 ln * t W2 / (2^* - exp * : t Convol u X t u - H * u t L t U int eval : green Gaussian cigar convolution 41 sys

Gaussian "cigar" convolution

x X m x - H x Convol m 1 m 0.5 - 2 2 mat m 0.75 m 14 green 1 5 mat 5 1 sys x U x L 2 1 sys