cdfln3 {lmomco} | R Documentation |
Cumulative Distribution Function of the 3-Parameter Log-Normal Distribution
Description
This function computes the cumulative probability or nonexceedance probability of the Log-Normal3 distribution given parameters (, lower bounds;
, location; and
, scale) computed by
parln3
. The cumulative distribution function (same as Generalized Normal distribution, cdfgno
) is
where is the cumulative ditribution function of the
Standard Normal distribution and
is
where is the lower bounds (real space) for which
(checked in
are.parln3.valid
), be the mean in natural logarithmic space, and
be the standard deviation in natural logarithm space for which
(checked in
are.parln3.valid
) is obvious because this parameter has an analogy to the second product moment. Letting , the parameters of the Generalized Normal are
,
, and
. At this point, the algorithms (
cdfgno
) for the Generalized Normal provide the functional core.
Usage
cdfln3(x, para)
Arguments
x |
A real value vector. |
para |
Value
Nonexceedance probability () for
.
Note
The parameterization of the Log-Normal3 results in ready support for either a known or unknown lower bounds. Details regarding the parameter fitting and control of the parameter can be seen under the Details section in
parln3
.
Author(s)
W.H. Asquith
References
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.
See Also
pdfln3
, qualn3
, lmomln3
, parln3
, cdfgno
Examples
lmr <- lmoms(c(123,34,4,654,37,78))
cdfln3(50,parln3(lmr))