Generalized Lambda Distribution

Description

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

Usage

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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

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## 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) 

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