Normal inverse cumulative distribution function
X = norminv(P,mu,sigma)
[X,XLO,XUP] = norminv(P,mu,sigma,pcov,alpha)
X = norminv(P,mu,sigma) computes
the inverse of the normal cdf using the corresponding mean
sigma at the corresponding probabilities
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, and the values
P must lie in the interval [0 1].
[X,XLO,XUP] = norminv(P,mu,sigma,pcov,alpha) produces
confidence bounds for
X when the input parameters
pcov is the covariance matrix of the
alpha specifies 100(1 -
confidence bounds. The default value of
arrays of the same size as
X containing the lower
and upper confidence bounds.
norminv computes confidence
P using a normal approximation to the
distribution of the estimate
where q is the
from a normal distribution with mean 0 and standard deviation 1. The
computed bounds give approximately the desired confidence level when
large samples, but in smaller samples other methods of computing the
confidence bounds may be more accurate.
The normal inverse function is defined in terms of the normal cdf as
The result, x, is the solution of the integral equation above where you supply the desired probability, p.
Find an interval that contains 95% of the values from a standard normal distribution.
x = norminv([0.025 0.975],0,1) x = -1.9600 1.9600
Note that the interval
x is not the only
such interval, but it is the shortest.
xl = norminv([0.01 0.96],0,1) xl = -2.3263 1.7507
xl also contains 95% of the
probability, but it is longer than