Lognormal inverse cumulative distribution function
The function logninv
uses the inverse complementary error
function erfcinv
. The relationship between
logninv
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 logninv
function computes confidence bounds for
x
by using the delta method.
log(logninv(p,mu,sigma))
is equivalent to
mu + sigma*log(logninv(p,0,1))
. Therefore, the
logninv
function estimates the variance of
mu + sigma*log(logninv(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.
logninv
is a function specific to lognormal distribution.
Statistics and Machine Learning Toolbox™ also offers the generic function icdf
, which supports various probability distributions. To use
icdf
, create a LognormalDistribution
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 logninv
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. Hoboken, NJ: Wiley-Interscience, 2000. pp. 102–105.
erfcinv
| icdf
| logncdf
| lognfit
| lognlike
| LognormalDistribution
| lognpdf
| lognrnd
| lognstat