Normal cumulative distribution function
p = normcdf(x)
p = normcdf(x,mu,sigma)
[p,plo,pup] = normcdf(x,mu,sigma,pcov,alpha)
[p,plo,pup] = normcdf(___,'upper')
p = normcdf(x) returns the standard normal
cdf at each value in
x. The standard normal distribution
mu = 0 and
sigma = 1.
be a vector, matrix, or multidimensional array.
p = normcdf(x,mu,sigma) returns
the normal cdf at each value in
x using the specified
values for the 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.
[p,plo,pup] = normcdf(x,mu,sigma,pcov,alpha) returns
confidence bounds for
p when the input parameters
pcov is the covariance matrix of the
alpha specifies 100(1 -
confidence bounds. The default value of
pup are arrays
of the same size as
p containing the lower and
upper confidence bounds.
[p,plo,pup] = normcdf(___,'upper') returns
the complement of the normal cdf at each value in
using an algorithm that more accurately computes the extreme upper
tail probabilities. You can use
'upper' with any
of the previous syntaxes.
normcdf computes confidence
p using a normal approximation to the
distribution of the estimate
and then transforming those bounds to the scale of the output
The computed bounds give approximately the desired confidence level
when you estimate
pcov from large samples, but in smaller samples
other methods of computing the confidence bounds might be more accurate.
The normal cdf is
The result, p, is the probability that a single observation from a normal distribution with parameters µ and σ will fall in the interval (-∞ x].
The standard normal distribution has µ = 0 and σ = 1.
What is the probability that an observation from a standard normal distribution will fall on the interval [-1 1]?
p = normcdf([-1 1]); p(2)-p(1)
ans = 0.6827
More generally, about 68% of the observations from a normal distribution fall within one standard deviation, , of the mean, .