| cdfgno {lmom} | R Documentation |
Generalized normal distribution
Description
Distribution function and quantile function of the generalized normal distribution.
Usage
cdfgno(x, para = c(0, 1, 0))
quagno(f, para = c(0, 1, 0))
Arguments
x |
Vector of quantiles. |
f |
Vector of probabilities. |
para |
Numeric vector containing the parameters of the distribution,
in the order |
Details
The generalized normal distribution with
location parameter \xi,
scale parameter \alpha and
shape parameter k has distribution function
F(x)=\Phi(y)
where
y=-k^{-1}\log\lbrace1-k(x-\xi)/\alpha\rbrace
and \Phi(y) is the distribution function of the standard normal distribution,
with x bounded by \xi+\alpha/k
from below if k<0 and from above if k>0.
The generalized normal distribution contains as special cases the usual
three-parameter lognormal distribution, corresponding to k<0,
with a finite lower bound and positive skewness;
the normal distribution, corresponding to k=0;
and the reverse lognormal distribution, corresponding to k>0,
with a finite upper bound and negative skewness.
The two-parameter lognormal distribution,
with a lower bound of zero and positive skewness,
is obtained when k<0 and \xi+\alpha/k=0.
Value
cdfgno gives the distribution function;
quagno gives the quantile function.
Note
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
See Also
cdfln3 for the lmom package's version of the three-parameter
lognormal distribution.
cdfnor for the lmom package's version of the normal distribution.
pnorm for the standard R version of the normal distribution.
plnorm for the standard R version of the two-parameter lognormal distribution.
Examples
# Random sample from the generalized normal distribution
# with parameters xi=0, alpha=1, k=-0.5.
quagno(runif(100), c(0,1,-0.5))
# The generalized normal distribution with parameters xi=1, alpha=1, k=-1,
# is the standard lognormal distribution. An illustration:
fval<-seq(0.1,0.9,by=0.1)
cbind(fval, lognormal=qlnorm(fval), g.normal=quagno(fval, c(1,1,-1)))