dBED {MDBED}

Joint density function of the bivariate exponential distribution (BED) based on the Moran-Downton model

Description

Given the values of the parameters, this function provides the joint density value of the BED for a positive pair or pairs (x,y). The required inputs are the correlation coefficient, the scale parameters of the marginal distributions, and the pair/s (x,y).

Usage

dBED(rho,Betax,Betay,x,y)

Arguments

rho

Correlation coefficient between the marginal distributions of x and y.

Betax

Scale parameter of the marginal distribution of x.

Betay

Scale parameter of the marginal distribution of y.

x

A value or set of values (vector) of the marginal distribution of x. It must be the same size of y.

y

A value or set of values (vector) of the marginal distribution of y. It must be the same size of x.

Details

The values of the joint density function are computed based on Eq.18 described in Nagao and Kadoya (1971).

Value

The value of the joint PDF of the pair/s (x,y).

Note

The equation of the PDF is based on the Bessel function. Therefore, for very extreme values this function may reaches infinity. It might generate NA values.

Author(s)

Luis F. Duque <[e-mail]> <[e-mail]>

References

Nagao M, Kadoya M (1971). “Two-variate Exponential Distribution and Its Numerical Table for Engineering Application.” Bulletin of the Disaster Prevention Research Institute, 20(3), 34.

Examples

dBED(rho=0.85,Betax=1,Betay=1,x=0.6,y=0.8)