betapdf {estimateW}

The four-parameter Beta probability density function

Description

A four-parameter Beta specification as the prior for the spatial autoregressive parameter \rho, as proposed by LeSage and Parent (2007) .

Usage

betapdf(rho, a = 1, b = 1, rmin = 0, rmax = 1)

Arguments

rho

The scalar value for \rho

a

The first shape parameter of the Beta distribution

b

The second shape parameter of the Beta distribution

rmin

Scalar \underline{\rho}_{min}: the minimum value of \rho

rmax

Scalar \underline{\rho}_{max}: the maximum value of \rho

Details

The prior density is given by:

p(\rho) \sim \frac{1}{Beta(a,b)} \frac{(\rho - \underline{\rho}_{min})^{(a-1)} (\underline{\rho}_{max} - \rho)^{(b-1)} }{2^{a + b - 1}}

where Beta(a, b) (a,b > 0) represents the Beta function, Beta(a, b)= \int_{0}^{1} t^{a-1} (1-t)^{b-1} dt.

Value

Density value evaluated at rho.

References

LeSage, J. P., and Parent, O. (2007) Bayesian model averaging for spatial econometric models. Geographical Analysis, 39(3), 241-267.