VGAM: lgammaUC – R documentation

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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`.

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.

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 lgamma3 is for the three parameter (nonstandard) log-gamma distribution.

Author(s)

T. W. Yee and Kai Huang

References

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

Examples

## Not run:  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) 
## End(Not run)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13