Simulation of random number {RFA} | R Documentation |
Generate random number of the 4 parameter Kappa distribution. This distribution encompass the Generalized Extreme Value, Generalized Pareto and Generalized Logistic distributions.
rkappa(n, loc, scale, shape1, shape2) rgpd(n, loc = 0, scale = 1, shape = 0) rgev(n, loc = 0, scale = 1, shape = 0) qgpd(p, loc = 0, scale = 1, shape = 0, lower.tail = TRUE) kappalmom(lmom)
n |
Numeric. The number of pseudo-random number to be generated. |
p |
Numeric. The probability for which the quantile has to be computed. |
loc, scale, shape, shape1, shape2 |
Numerics. The location, scale and shape parameters. |
lower.tail |
Logical. If TRUE the default, the quantile
associated to probability p of non exceedance is
computed. Otherwise, this is related to the probability of
exceedance. |
lmom |
Numeric vector of length 4. The first 4 sample L-moments, that is the sample mean, L-CV, L-Skewness and L-Kurtosis. |
The 4-parameter Kappa distribution has cumulative distribution function
F(x) = [1 - shape2{1 + shape1(x - loc) / scale }^(-1/shape1)]^(1/shape2)
For shape2
= -1, this is the Generalized Logistic distribution,
for shape2
= 0, the Generalized Extreme Value distribution and
for shape2
= 1, the Generalized Pareto distribution.
Function kappalmom
uses sample L-moments to fit the
Kappa distribution. Newtow-Raphson iteration is used to solve the
equations that express tau_3 and tau_4 as
functions of shape1
et shape2
. loc
and
scale
are calculated as functions of lambda_1, tau, shape1
and shape2
. To ensure a
1-1 relationship between parameters and L-moments, the parameter space
is restricted. See reference for more details.
The program return either a numeric vector containing estimates of the
location, scale and shape parameter of the Kappa distribution either a
fail flag informing a problem in the optimization algorithm.
'1'
L-moments invalid
'2'
(tau_3, tau_4) lies
above the generalized-logistic line (suggests that l-moments are not
consistent with any kappa distribution with shape2
> -1)
'3'
iteration failed to converge
'4'
unable to make progress from current point in iteration
'5'
iteration encountered numerical difficulties - overflow would
have been likely to occur
'6'
iteration for the shape parameters converged, but overflow
would have occurred when calculating location and scale parameters.
Ribatet Mathieu and Hosking J. R. M. for the fortran code.
Hosking, J. R. M. (1994) The four-parameter kappa distribution. IBM Journal of Research and Development, 38, 251-258