beta.laplace {EbayesThresh}

Function beta for the Laplace prior

Description

Given a single value or a vector of x and s, find the value(s) of the function \beta(x;s,a)=g(x;s,a)/fn(x;0,s) - 1, where fn(x;0,s) is the normal density with mean 0 and standard deviation s, and g is the convolution of the Laplace density with scale parameter a, \gamma_a(\mu), with the normal density fn(x;\mu,s) with mean mu and standard deviation s.

Usage

beta.laplace(x, s = 1, a = 0.5)

Arguments

x

the value or vector of data values

s

the value or vector of standard deviations; if vector, must have the same length as x

a

the scale parameter of the Laplace distribution

Value

A vector of the same length as x is returned, containing the value(s) beta(x).

Note

The Laplace density is given by \gamma(u;a) = \frac{1}{2} a e^{-a|u|} and is also known as the double exponential density.

Author(s)

Bernard Silverman

References

See ebayesthresh and http://www.bernardsilverman.com

See Also

beta.cauchy

Examples

beta.laplace(c(-2,1,0,-4,8,50), s=1)
beta.laplace(c(-2,1,0,-4,8,50), s=1:6, a=1)