The following functions return numbers from pseudo-random distributions of the specified shapes and parameters. Except for enoise and gnoise where you have an option to select a random number generator, the remaining noise functions use a Mersenne Twister algorithm for the initial uniform pseudo-random distribution. Note that whenever you need repeatable results you should use SetRandomSeed prior to executing any of the noise functions.

Built-in noise functions and distributions

Noise Function Distribution
binomialNoise Binomial distribution
enoise Uniform distribution
expNoise Exponential distribution
gammaNoise Gamma distribution
gnoise Gaussian distribution
HyperGNoise Hypergeometric distribution
logNormalNoise Lognormal distribution
poissonNoise Poisson distribution
StatsPowerNoise Power distribution
StatsVonMisesNoise Von Mises distribution
WNoise Two-parameter Weibull distribution

You can easily verify that the various noise functions indeed generate the desired distribution. For example, suppose you generated 10000 data points from a Gamma distribution as in:

Make/O/N=1e4 noiseWave=gammaNoise(10,2)

Make/O/N=100/O W_Hist
Histogram/P/B={0,1,100} noiseWave,W_Hist

To fit this to a gamma distribution we write the following user function:

Function myFit(w,x) : FitFunc
    Wave w
    Variable x

    return x^(w[0]-1)*exp(-x/w[1])/((w[1]^w[0])*Gamma(w[0]))

To determine the initial guesses for the fitting coefficients we note that the average of noiseWave is 19.8681. This average should be equal to the product a*b of the two parameters of the gamma distribution. Our guess is therefore a=b=sqrt(19.8)

Make/O/D/N=2 W_coef={4.48,4.48}
FuncFit/NTHR=0/TBOX=768 myFit W_coef  W_Hist[1,50] /D

The resulting fit to a Gamma distribution is drawn below in blue plotted over the calculated distribution (red).




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