Approaching normality

qqnorm(rt(10000, df=1), xlab="Gaussian(0,1) quantiles", ylab="t_1 quantiles", main="t_1 v. Gaussian QQ-Plot")


qqnorm(rt(10000, df=10), xlab="Gaussian(0,1) quantiles", ylab="t_10 quantiles", main="t_10 v. Gaussian QQ-Plot")
abline(0, 1)


qqnorm(rt(10000, df=100), xlab="Gaussian(0,1) quantiles", ylab="t_100 quantiles", main="t_100 v. Gaussian QQ-Plot")
abline(0, 1)


y <- sqrt(rnorm(10000, mean=1)^2 + rnorm(10000)^2)
qqnorm(y, xlab="Gaussian(0,1) quantiles", ylab="Rice(1,1) quantiles", main="Rice(1,1) v. Gaussian QQ-Plot")
qqline(y)


y <- sqrt(rnorm(10000, mean=1, sd=10)^2 + rnorm(10000, sd=10)^2)
qqnorm(y, xlab="Gaussian(0,1) quantiles", ylab="Rice(1,100) quantiles", main="Rice(1,100) v. Gaussian QQ-Plot")
qqline(y)

Oh, I've got this backwards. Duh.


y <- sqrt(rnorm(10000, mean=100, sd=10)^2 + rnorm(10000, sd=10)^2)
qqnorm(y, xlab="Gaussian(0,1) quantiles", ylab="Rice(100,100) quantiles", main="Rice(100,100) v. Gaussian QQ-Plot")
qqline(y)

But there's more to it than signal-to-noise ratio, it seems. At least the relation between the quantiles doesn't look nearly so linear for Rice(1,1) as it does for Rice(100,100). It doesn't seem surprising that the distance of mu from the origin would play a role, however. This would probably be a good time to break out some math. But it's past my bed time.