dcoga2dim {coga}

Convolution of Two Gamma Distributions (Exact Method).

Description

Density, and distribution function of convolution of *two* gamma distributions. These two functions still give us the exact density and distribution function value, but which are much faster than dcoga and pcoga. **So, we recommend these two functions for two variables case.** The algorithm of these two functions comes from Mathai, A.M. (1982).

Usage

dcoga2dim(x, shape1, shape2, rate1, rate2)

pcoga2dim(x, shape1, shape2, rate1, rate2)

Arguments

x

Quantiles.

shape1, shape2

Shape parameters for the first and second gamma distributions, both shape parameters should be larger than or equal to 0, with at least one non-zero.

rate1, rate2

Rate parameters for the first and second gamma distributions, both rate parameters should be larger than 0.

Author(s)

Chaoran Hu

References

Mathai, A.M.: Storage capacity of a dam with gamma type inputs. Ann. Inst. Statist.Math. 34, 591-597 (1982)

Examples

## Example 1: Correctness check
set.seed(123)
## do grid
y <- rcoga(100000, c(3,4), c(2,3))
grid <- seq(0, 15, length.out=100)
## calculate pdf and cdf
pdf <- dcoga2dim(grid, 3, 4, 2, 3)
cdf <- pcoga2dim(grid, 3, 4, 2, 3)

## plot pdf
plot(density(y), col="blue")
lines(grid, pdf, col="red")

## plot cdf
plot(ecdf(y), col="blue")
lines(grid, cdf, col="red")

## Example 2: Comparison with `dcoga` and `pcoga`
## these pairs give us the same results
dcoga(1:5, c(1, 2), c(3, 4))
dcoga2dim(1:5, 1, 2, 3, 4)

pcoga(1:5, c(1, 3), c(3, 5))
pcoga2dim(1:5, 1, 3, 3, 5)