Re: Mean of truncated Gaussian

john wrote: 
Anon. wrote:

frisbieinstein@xxxxxxxxx wrote:
 > Is there an easy way to estimate the mean of a truncated Gaussian?
 > That is, with X a standard Gaussian,
 >
 > E[ X | X>1 ]
 >
Yes, it's one of those results kicking around the literature.  Google
"truncated normal", and you'll get a lot of hits, for example this one:
<http://www.biostat.wustl.edu/archives/html/s-news/2002-09/msg00173.html>

Or, Lynch & Walsh (a book on quantitative genetics) give this:

mu_T = mu + (sigma p_T)/Phi_T

where T is the truncation point
mu_T is the mean of the truncated distribution,
mu is the mean of the un-truncated distribution,
sigma is the standard deviation of the un-truncated distribution,
p_T is the probability density at the truncation point, and
Phi_T is 1- the  cumulative density at the truncation point, i.e. Pr(z>T)

This is for left truncation, i.e. where values below the truncation point are removed. Right truncation is easy to work out from this.

Bob


So would something similar work in two dimensions for a bivariate pdf ?

Errr... The simple answer is I don't know, but someone has probably worked it out.

Bob

--
Bob O'Hara

Dept. of Mathematics and Statistics
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Relevant Pages

  • Re: Mean of truncated Gaussian
    ... > Is there an easy way to estimate the mean of a truncated Gaussian? ... > That is, with X a standard Gaussian,> ... where T is the truncation point ... sigma is the standard deviation of the un-truncated distribution, ...
    (sci.stat.math)
  • Re: Mean of truncated Gaussian
    ... >> Is there an easy way to estimate the mean of a truncated Gaussian? ... >> That is, with X a standard Gaussian, ... > where T is the truncation point ... > sigma is the standard deviation of the un-truncated distribution, ...
    (sci.stat.math)
  • Re: Mean of truncated Gaussian
    ... >> Is there an easy way to estimate the mean of a truncated Gaussian? ... > where T is the truncation point ... > sigma is the standard deviation of the un-truncated distribution, ... > Bob O'Hara ...
    (sci.stat.math)
  • Re: Mean of truncated Gaussian
    ... > Is there an easy way to estimate the mean of a truncated Gaussian? ... > That is, with X a standard Gaussian,> ... where T is the truncation point ... sigma is the standard deviation of the un-truncated distribution, ...
    (sci.stat.math)
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