Normal inverse cumulative distribution function
The norminv
function uses the inverse complementary
error function erfcinv
. The relationship
between norminv
and erfcinv
is
The inverse complementary error function
erfcinv(x)
is defined as
erfcinv(erfc(x))=x
, and the complementary error
function erfc(x)
is defined as
The norminv
function computes confidence bounds for
x
by using the delta method.
norminv(p,mu,sigma)
is equivalent to
mu + sigma*norminv(p,0,1)
. Therefore, the
norminv
function estimates the variance of
mu + sigma*norminv(p,0,1)
using the
covariance matrix of mu
and sigma
by the delta method, and finds the confidence bounds using the estimates of
this variance. The computed bounds give approximately the desired confidence
level when you estimate mu
, sigma
, and
pCov
from large samples.
norminv
is a function specific to normal
distribution. Statistics and Machine Learning Toolbox™ also offers the generic function icdf
, which supports various
probability distributions. To use icdf
, create a NormalDistribution
probability
distribution object and pass the object as an input argument or specify the
probability distribution name and its parameters. Note that the
distribution-specific function norminv
is faster than
the generic function icdf
.
[1] Abramowitz, M., and I. A. Stegun. Handbook of Mathematical Functions. New York: Dover, 1964.
[2] Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc., 1993.