Normal probability density function
Y = normpdf(X,mu,sigma)
Y = normpdf(X)
Y = normpdf(X,mu)
Y = normpdf(X,mu,sigma) computes
the pdf at each of the values in
X using the normal
distribution with mean
mu and standard deviation
sigma can be vectors, matrices, or multidimensional
arrays that all have the same size. A scalar input is expanded to
a constant array with the same dimensions as the other inputs. The
sigma must be positive.
The normal pdf is
The likelihood function is the pdf viewed
as a function of the parameters. Maximum likelihood estimators (MLEs)
are the values of the parameters that maximize the likelihood function
for a fixed value of
The standard normal distribution has µ = 0 and σ = 1.
If x is standard normal, then xσ + µ is also normal with mean µ and standard deviation σ. Conversely, if y is normal with mean µ and standard deviation σ, then x = (y – µ) / σ is standard normal.
Y = normpdf(X) uses the standard normal
mu = 0,
sigma = 1).
Y = normpdf(X,mu) uses the normal distribution
with unit standard deviation (
sigma = 1).
mu = [0:0.1:2]; [y i] = max(normpdf(1.5,mu,1)); MLE = mu(i) MLE = 1.5000