# dist-gld: Generalized Lambda Distribution In fBasics: Rmetrics - Markets and Basic Statistics

## Description

Density, distribution function, quantile function and random generation for the generalized lambda distribution.

## Usage

 ```1 2 3 4``` ```dgld(x, lambda1 = 0, lambda2 = -1, lambda3 = -1/8, lambda4 = -1/8, log = FALSE) pgld(q, lambda1 = 0, lambda2 = -1, lambda3 = -1/8, lambda4 = -1/8) qgld(p, lambda1 = 0, lambda2 = -1, lambda3 = -1/8, lambda4 = -1/8) rgld(n, lambda1 = 0, lambda2 = -1, lambda3 = -1/8, lambda4 = -1/8) ```

## Arguments

 `lambda1, lambda2, lambda3, lambda4` are numeric values where `lambda1` is the location parameter, `lambda2` is the location parameter, `lambda3` is the first shape parameter, and `lambda4` is the second shape parameter. `n` number of observations. `p` a numeric vector of probabilities. `x, q` a numeric vector of quantiles. `log` a logical, if TRUE, probabilities `p` are given as `log(p)`.

## Value

All values for the `*gld` functions are numeric vectors: `d*` returns the density, `p*` returns the distribution function, `q*` returns the quantile function, and `r*` generates random deviates.

All values have attributes named `"param"` listing the values of the distributional parameters.

## Author(s)

Chong Gu for code implemented from R's contributed package `gld`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ``` ## rgld - set.seed(1953) r = rgld(500, lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8) plot(r, type = "l", col = "steelblue", main = "gld: lambda1=0 lambda2=-1 lambda3/4=-1/8") ## dgld - # Plot empirical density and compare with true density: hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue") x = seq(-5, 5, 0.25) lines(x, dgld(x, lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8)) ## pgld - # Plot df and compare with true df: plot(sort(r), ((1:500)-0.5)/500, main = "Probability", col = "steelblue") lines(x, pgld(x, lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8)) ## qgld - # Compute Quantiles: qgld(pgld(seq(-5, 5, 1), lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8), lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8) ```

fBasics documentation built on Nov. 17, 2017, 2:14 p.m.