R: The Log-Laplace Distribution

loglapUC {VGAM} | R Documentation

## The Log-Laplace Distribution

### Description

Density, distribution function, quantile function and random generation for the 3-parameter log-Laplace distribution with location parameter `location.ald`, scale parameter `scale.ald` (on the log scale), and asymmetry parameter `kappa`.

### Usage

    dloglap(x, location.ald = 0, scale.ald = 1,
            tau = 0.5, kappa = sqrt(tau/(1-tau)), log = FALSE)
    ploglap(q, location.ald = 0, scale.ald = 1,
            tau = 0.5, kappa = sqrt(tau/(1-tau)), lower.tail = TRUE, log.p = FALSE)
    qloglap(p, location.ald = 0, scale.ald = 1,
            tau = 0.5, kappa = sqrt(tau/(1-tau)), lower.tail = TRUE, log.p = FALSE)
    rloglap(n, location.ald = 0, scale.ald = 1,
            tau = 0.5, kappa = sqrt(tau/(1-tau)))

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. If `length(n) > 1` then the length is taken to be the number required.
`location.ald, scale.ald` | the location parameter xi and the (positive) scale parameter sigma, on the log scale.
`tau` | the quantile parameter tau. Must consist of values in (0,1). This argument is used to specify `kappa` and is ignored if `kappa` is assigned.
`kappa` | the asymmetry parameter kappa. Must consist of positive values.
`log` | if `TRUE`, probabilities `p` are given as `log(p)`.
`lower.tail, log.p` | Same meaning as in `pnorm` or `qnorm`.

### Details

A positive random variable Y is said to have a log-Laplace distribution if \log(Y) has an asymmetric Laplace distribution (ALD). There are many variants of ALDs and the one used here is described in `alaplace3`.

### Value

`dloglap` gives the density, `ploglap` gives the distribution function, `qloglap` gives the quantile function, and `rloglap` generates random deviates.

### Author(s)

T. W. Yee and Kai Huang

### References

Kozubowski, T. J. and Podgorski, K. (2003) Log-Laplace distributions. International Mathematical Journal, 3, 467–495.

### See Also

`dalap`, `alaplace3`, `loglaplace1`.

### Examples

    loc <- 0; sigma <- exp(0.5); kappa <- 1
    x <- seq(-0.2, 5, by = 0.01)
    ## Not run:
    plot(x, dloglap(x, loc, sigma, kappa = kappa), type = "l", col = "blue",
         main = "Blue is density, red is cumulative distribution function",
         ylim = c(0,1), sub = "Purple are 5,10,...,95 percentiles", las = 1, ylab = "")
    abline(h = 0, col = "blue", lty = 2)
    lines(qloglap(seq(0.05,0.95,by = 0.05), loc, sigma, kappa = kappa),
          dloglap(qloglap(seq(0.05,0.95,by = 0.05), loc, sigma, kappa = kappa),
                    loc, sigma, kappa = kappa), col = "purple", lty = 3, type = "h")
    lines(x, ploglap(x, loc, sigma, kappa = kappa), type = "l", col = "red")
    abline(h = 0, lty = 2)

    ## End(Not run)
    ploglap(qloglap(seq(0.05,0.95,by = 0.05), loc, sigma, kappa = kappa),
              loc, sigma, kappa = kappa)

[Package VGAM version 1.0-3 Index]