[R] help on sampling from the truncated normal/gamma distribution on the far end (probability is very low)

[Peter Dalgaard]

Daniel Davis wrote:
> Hi, guys,
>
> I am trying to sample from a truncated normal/gamma distribution.
> But only the far end of the distribution (where the probability is very low)
> is left. e.g.
>
> mu = - 4;
> sigma = 0.1;
> The distribution is Normal(mu,sigma^2) truncated on [0,+Inf];
>
> How can I get a sample? I tried to use inverse CDF method, but got Inf as
> answers. Please help me out.
>
>   
You were on track, but you need more awareness of the cancellation 
issues. Two hints: Use logarithms and look at the correct tail.  So:

T <- pnorm(0, -4, .1, lower=F, log=T)
z <- qnorm(T-rexp(1000), -4, .1, lower=F, log=T)
hist(z)

> Also, pls help me on the similar situation on gamma dist'n.
>
>   
Exercise for the reader....

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