R help - Sep 2008 - help on sampling from the truncated normal/gamma distribution on the far end (probability is very low)

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.

Also, pls help me on the similar situation on gamma dist'n.


Thanks,
Sonia

	[[alternative HTML version deleted]]

Hi Sonia,

If I did not make a mistake, the conditional distribution of X given that X >
0 is very close to exponential distribution with parameter lambda = 40, so you
can sample from this distribution.


--- On Mon, 15/9/08, Daniel Davis <paperprint at gmail.com> wrote:
> From: Daniel Davis <paperprint at gmail.com>
> Subject: [R] help on sampling from the truncated normal/gamma distribution
on the far end (probability is very low)
> To: r-help at r-project.org
> Received: Monday, 15 September, 2008, 2:28 PM
> 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.
> 
> Also, pls help me on the similar situation on gamma
> dist'n.
> 
> 
> Thanks,
> Sonia
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.

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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