dgam: Density of bivariate gamma

In gbasulto/mvdeconvolution: Multivariate kernel deconvolution

Description

The correlated gammas where generated from a bivariate normal whose variance matrix has 1 in the diagonal and r otherwise, then each coordinate was used to generate a gamma distribution.

Usage

dgam(val, shape1, rate1, shape2, rate2, r)

Arguments

val	2-columns matrix with the values to evaluate the density
shape1	Shape parameter for the first coordinate.
rate1	Rate parameter for the first coordinate.
shape2	Shape parameter for the second coordinate.
rate2	Rate parameter for the second coordinate.
r	correlation of the normal entries.

Value

A nx2 matrix with the samples.

See Also

rgam

Examples

library(mvdeconvolution)

###################################
##  Test relationship between input and output correlations
###################################
#
r1 <- seq(-1, 1, length.out= 20)
ff <- function(r) cor(rgam(2e4, .5, .5, 9, 2, r))[1, 2]
##ff <- function(r) rgam(1e5, .5, 5, .5, 5, r)$correl ## Interesting case
r2 <- sapply(r1, ff)
plot(r2 ~ r1, type = "l", main = "r2 (sample correl. gammas) vs. \n r1 (correl. normal)")
abline(0, 1, col = 2)
legend("topleft", legend = c("Correlations", "Identity"), 
       col = c(1:2), pch = 20)

###################################
## Observe how a biv. gamma looks like
###################################
##
n <- 1e3
shape1 <- 20
rate1 <-  2
shape2 <- 5
rate2 <-  1
r <- -.6

sam <- rgam(n, shape1, rate1, shape2, rate2, r)
colnames(sam) <- c("x", "y")

ran1 <- range(sam[, 1])
ran2 <- range(sam[, 2])
x <- seq(ran1[1], ran1[2], length.out= 100)
y <- seq(ran2[1], ran2[2], length.out= 90)
z <- apply(matrix(y), 1, function(a)
  dgam(cbind(x, a), shape1, rate1, shape2, rate2, r))


plot(y ~ x, data = sam, col = "gray",
     main = "Sample with true density overlaid")
contour(x, y, z, add = TRUE)

gbasulto/mvdeconvolution documentation built on May 16, 2019, 10:11 p.m.