coga (version 1.2.2)

pcoga2dim_diff_shape: Recurrence Identity of Shape Parameter for pcoga2dim

Description

The difference of distribution functions of convolution of two gamma distributions between consecutive neighbors of shape parameter. This function evaluate the value of 'pcoga2dim(x, shape1, shape2, rate1, rate2) - pcoga2dim(x, shape1 + 1, shape2, rate1, rate2)' with higher efficiency (this function is much more faster than call pcoga2dim two-times).

Usage

pcoga2dim_diff_shape(x, shape1, shape2, rate1, rate2)

Arguments

x

Quantiles.

shape1, shape2

Shape parameters of the first and second gamma distributions, both shape parameters should be larger than or equal to 0.

rate1, rate2

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

Author

Chaoran Hu

Examples

## these pairs give us the same results
pcoga2dim_diff_shape(3,2,4,5,4)
pcoga2dim(3,2,4,5,4) - pcoga2dim(3,3,4,5,4)

pcoga2dim_diff_shape(3,0,4,3,5)
pgamma(3,4,5) - pcoga2dim(3,1,4,3,5)

pcoga2dim_diff_shape(3,6,0,5,4)
pgamma(3,6,5) - pgamma(3,7,5)

pcoga2dim_diff_shape(3,0,0,4,5)
1 - pgamma(3,1,4)