Generalized Lambda Distribution

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

Usage

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

location parameter.

lambda2

scale parameter.

lambda3

first shape parameter.

lambda4

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).

Details

dgld gives the density, pgld gives the distribution function, qgld gives the quantile function, and rgld generates random deviates.

Value

numeric vector

Author

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

Examples

## 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) 
#>  [1] -5 -4 -3 -2 -1  0  1  2  3  4  5