lgammaUC {VGAM}R Documentation

The Log-Gamma Distribution

Description

Density, distribution function, quantile function and random generation for the log-gamma distribution with location parameter location, scale parameter scale and shape parameter k.

Usage

dlgamma(x, location=0, scale=1, k=1)
plgamma(q, location=0, scale=1, k=1)
qlgamma(p, location=0, scale=1, k=1)
rlgamma(n, location=0, scale=1, k=1)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations. Positive integer of length 1.
location the location parameter a.
scale the (positive) scale parameter b.
k the (positive) shape parameter k.

Details

See lgammaff, the VGAM family function for estimating the one parameter standard log-gamma distribution by maximum likelihood estimation, for formulae and other details. Apart from n, all the above arguments may be vectors and are recyled to the appropriate length if necessary.

Value

dlgamma gives the density, plgamma gives the distribution function, qlgamma gives the quantile function, and rlgamma generates random deviates.

Note

The VGAM family function lgamma3ff is for the three parameter (nonstandard) log-gamma distribution.

Author(s)

T. W. Yee

References

Kotz, S. and Nadarajah, S. (2000) Extreme Value Distributions: Theory and Applications, pages 48–49, London: Imperial College Press.

See Also

lgammaff, prentice74.

Examples

## Not run: 
x = seq(-3.2, 5, by=0.01)
loc = 1
Scale = 1.5
k = 1.4
plot(x, dlgamma(x, loc, Scale, k), type="l", col="blue", ylim=c(0,1),
     main="Blue is density, red is cumulative distribution function",
     sub="Purple are 5,10,...,95 percentiles", las=1, ylab="")
abline(h=0, col="blue", lty=2)
lines(qlgamma(seq(0.05,0.95,by=0.05), loc, Scale, k), 
      dlgamma(qlgamma(seq(0.05,0.95,by=0.05), loc, Scale, k), loc, Scale, k),
      col="purple", lty=3, type="h")
lines(x, plgamma(x, loc, Scale, k), type="l", col="red")
abline(h=0, lty=2)
## End(Not run)

[Package VGAM version 0.7-7 Index]