rald {bsamGP} R Documentation

## The asymmetric Laplace distribution

### Description

Density for and random values from a three-parameter asymmetric Laplace distribution.

### Usage

  rald(n, location=0, scale=1, p=0.5)


### Arguments

 n Number of random values to be generated. location Location parameter. scale Scale parameter. p Skewness parameter.

### Details

This generic function generates a random variable from an asymmetric Laplace distribution (ALD). The ALD has the following probability density function:

ALD_p(x ; μ, σ) = \frac{p(1-p)}{σ}\exp\Big(-\frac{(x-μ)[p-I(x≤μ)]}{σ}\Big),

where 0 < p < 1 is the skew parameter, σ > 0 is the scale parameter, -∞ < μ < ∞ is the location parameter, and I(\cdot) is the indication function. The range of x is (-∞, ∞).

### Value

rald gives out a vector of random numbers generated by the asymmetric Laplace distribution.

### References

Koenker, R. and Machado, J. (1999). Goodness of fit and related inference processes for quantile regression. Journal of the American Statistical Association, 94(3), 1296-1309.

Yu, K. and Zhang, J. (2005). A Three-parameter asymmetric Laplace distribution and its extension. Communications in Statistics - Theory and Methods, 34, 1867-1879.

[Package bsamGP version 1.2.3 Index]