dcoga_approx {coga}

Convolution of Gamma distribuitons (Approximation Method)

Description

Density and distribution function of convolution of gamma distributions are calculated based on approximation method from Barnabani(2017), which gives us the approximate result and faster evaluation than dcoga and pcoga during three or more variables case. **So, we recommend these functions for three or more varibales case with approximate result.**

Usage

dcoga_approx(x, shape, rate)

pcoga_approx(x, shape, rate)

Arguments

x

Quantiles.

shape

Numerical vector of shape parameters for each gamma distributions, all shape parameters should be larger than or equal to 0, with at least three non-zero.

rate

Numerical vector of rate parameters for each gamma distributions, all rate parameters should be larger than 0.

Author(s)

Chaoran Hu

References

Barnabani, M. (2017). An approximation to the convolution of gamma distributions. Communications in Statistics - Simulation and Computation 46(1), 331-343.

Examples

## Example 1: Correctness check
set.seed(123)
## do grid
y <- rcoga(100000, c(3,4,5), c(2,3,4))
grid <- seq(0, 15, length.out=100)
## calculate pdf and cdf
pdf <- dcoga_approx(grid, shape=c(3,4,5), rate=c(2,3,4))
cdf <- pcoga_approx(grid, shape=c(3,4,5), rate=c(2,3,4))

## 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: Show parameter recycling
## these pairs give us the same results
dcoga_approx(1:5, c(1, 2), c(1, 3, 4, 2, 5))
dcoga_approx(1:5, c(1, 2, 1, 2, 1), c(1, 3, 4, 2, 5))

pcoga_approx(1:5, c(1, 3, 5, 2, 2), c(3, 5))
pcoga_approx(1:5, c(1, 3, 5, 2, 2), c(3, 5, 3, 5, 3))