Function beta for the Laplace prior

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Description

Given a value or vector x of values, find the value(s) of the function beta(x) = g(x)/phi(x) - 1 , where g is the convolution of the Laplace density with scale parameter a with with the normal density phi(x).

Usage

1
beta.laplace(x, a = 0.5)

Arguments

x

the value or vector of data values

a

the scale parameter of the Laplace distribution

Value

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

Note

The Laplace density is given by gamma(u)= (a/2) exp ( - 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

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