VGAM (version 1.0-1)

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, shape = 1, log = FALSE)
plgamma(q, location = 0, scale = 1, shape = 1,
        lower.tail = TRUE, log.p = FALSE)
qlgamma(p, location = 0, scale = 1, shape = 1,
        lower.tail = TRUE, log.p = FALSE)
rlgamma(n, location = 0, scale = 1, shape = 1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Same as runif.

location

the location parameter $a$.

scale

the (positive) scale parameter $b$.

shape

the (positive) shape parameter $k$.

log

Logical. If log = TRUE then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Value

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

Details

See lgamma1, 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

lgamma1, prentice74.

Examples

loc <- 1; Scale <- 1.5; shape <- 1.4
x <- seq(-3.2, 5, by = 0.01)
plot(x, dlgamma(x, loc = loc, Scale, shape = shape), type = "l",
     col = "blue", ylim = 0:1,
     main = "Blue is density, orange 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 = loc, Scale, shape = shape),
      dlgamma(qlgamma(seq(0.05, 0.95, by = 0.05), loc = loc, scale = Scale,
                      shape = shape),
      loc = loc, Scale, shape = shape), col = "purple", lty = 3, type = "h")
lines(x, plgamma(x, loc = loc, Scale, shape = shape), col = "orange")
abline(h = 0, lty = 2)