gconv {sensitivity2x2xk}

Convolution of Two Probability Generating Functions

Description

Computes the convolution of two probability generating functions using the convolve function in the stats package. The convolve function uses the fast fourier transform.

Usage

gconv(g1,g2)

Arguments

g1

A probability generating function. A vector g1 for a random variable X taking values 0, 1, 2, ..., length(g1)-1, where g1[i] = Pr(X=i-1)For example, g1 = c(2/3, 1/3) is the generating function of a binary random variable X with Pr(X=0)=2/3, Pr(X=1)=1/3. The random variable that is 0 with probability 1 has g1=1.

g2

Another probability generating function for a random variable Y. For a fair die, g2 = c(0, 1/6, 1/6, 1/6, 1/6, 1/6, 1/6).

Value

The probability generating function of X+Y when X and Y are independent.

References

Pagano, M. and Tritchler, D. (1983). On obtaining permutation distributions in polynomial time. Journal of the American Statistical Association, 78, 435-440.

Rosenbaum, P. R. (2010). Design of Observational Studies. New York: Springer. Section 3.9: Appendix Exact Computations for Sensitivity Analysis.

Examples

gconv(c(2/3,1/3),c(2/3,1/3))

gconv(1,c(2/3,1/3))

gconv(c(0, 1/6, 1/6, 1/6, 1/6, 1/6, 1/6),
     c(0, 1/6, 1/6, 1/6, 1/6, 1/6, 1/6))