scidemo_normaldist

Parameters

mu :: a 1-by-1 matrix of doubles, the mean
sigma :: a 1-by-1 matrix of doubles, the variance
nrandx :: a 1-by-1 matrix of doubles, the number of generated random numbers
nhclass :: a 1-by-1 matrix of doubles, the number of classes in the histogram
xmin :: a 1-by-1 matrix of doubles, the minimum x
xmax :: a 1-by-1 matrix of doubles, the maximum x

Description

Computes the exact distribution function of the Normal (Laplace-Gauss) distribution function in the range [xmin,xmax] and draw it. Then generate nrandx points and draw the histogram with nhclass classes. Then plots the intervals [mu-n*sigma,mu+n*sigma] for n=1,2,3. In the legend, display the corresponding integrals approximated from the intg function.

The current function is a demonstration of the following functions.

Uses the grand function to generate the random numbers.
Uses the histo function to draw the histogram.
Uses the intg function to compute the approximate integrals.
Uses the erf function to compute the exact integrals.

The Normal distribution function definition is:

This implies that, if X is a random variable from the Normal distribution, the probability that X is inside the interval [a,b] is

The previous equality can be associated with the erf function, which satisfies the equality

where n=1,2,3,....

Examples

// Compare generated Normal random numbers with exact PDF.
mu = 10;
sigma = 5;
xmin = mu-6*sigma;
xmax = mu+6*sigma;
nrandx = 10000;
nhclass = 100;
scf();
scidemo_normaldist ( mu , sigma , nrandx , nhclass , xmin , xmax );
// Uses erf and compare with approximate computations
erf([1 2 3]/sqrt(2))

Authors

Bibliography

distfun/normpdf, 2009-2010 - DIGITEO - Michael Baudin, http://forge.scilab.org/index.php/p/distfun/source/tree/HEAD/macros/normpdf.sci