R: The Log-Gamma Distribution

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, 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.

### See Also

`lgamma1`, `prentice74`.

### 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)

[Package VGAM version 1.0-3 Index]