rho_Z(z) = integral rho_X(x) rho_Y(z - x) dx, trapezoid on the x
grid with rho_Y linearly interpolated and zero outside its grid.
Usage
SumDens(grid_x, density_x, grid_y, density_y, z)
Arguments
- grid_x, density_x
the density of X.
- grid_y, density_y
the density of Y.
- z
evaluation point.
References
Morin, D. J. (2016). Probability: For the Enthusiastic
Beginner. Createspace. Eq (6.65).
Examples
g <- seq(-8, 8, length.out = 1601); SumDens(g, stats::dnorm(g), g, stats::dnorm(g), 1)$density
#> [1] 0.2196956
