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, log=FALSE)
    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.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### 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 0.7-9 Index]