What are the differences between different gaussian functions in Matlab?

Question

1. y = gauss(x,s,m)
2. Y = normpdf(X,mu,sigma)
3. R = normrnd(mu,sigma)

What are the basic differences between these three functions?

Answer 1

Y = normpdf(X,mu,sigma) is the probability density function for a normal distribution with mean mu and stdev sigma. Use this if you want to know the relative likelihood at a point X.

R = normrnd(mu,sigma) takes random samples from the same distribution as above. So use this function if you want to simulate something based on the normal distribution.

y = gauss(x,s,m) at first glance looks like the exact same function as normpdf(). But there is a slight difference: Its calculation is

Y = EXP(-(X-M).^2./S.^2)./(sqrt(2*pi).*S)

while normpdf() uses

Y = EXP(-(X-M).^2./(2*S.^2))./(sqrt(2*pi).*S)

This means that the integral of gauss() from -inf to inf is 1/sqrt(2). Therefore it isn't a legit PDF and I have no clue where one could use something like this.

For completeness we also have to mention p = normcdf(x,mu,sigma). This is the normal cumulative distribution function. It gives the probability that a value is between -inf and x.