VGAM (version 0.7-5)

lgammaUC: 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 $k$.

Value

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

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.

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

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)