R help - Sep 2009 - Best Way to Compute/Approximate(?) Probabilty of a Point in a Given Distribution

AFAIK, R only has "pnorm" which computes the probability of getting a
value smaller or equal to "x" from
a normal distribution N[mean,stdev]. For example:

R> pnorm(0, 4, 10)
[1] 0.3446

means there is  34.46% chance of getting a value equal to or smaller
than 0 from a N(4, 10) distribution.


What I intend to get is: given the observed value "x", mean, and stdev
of normal distribution,
find the probabiltiy of "x" falls into that distribution.

Is there any reasonable way to obtain that?

- G.V.

Gundala Viswanath wrote:
> 
> AFAIK, R only has "pnorm" which computes the probability of
getting a
> value smaller or equal to "x" from
> a normal distribution N[mean,stdev]. For example:
> 
> R> pnorm(0, 4, 10)
> [1] 0.3446
> 
> means there is  34.46% chance of getting a value equal to or smaller
> than 0 from a N(4, 10) distribution.
> 
> 
> What I intend to get is: given the observed value "x", mean, and
stdev
> of normal distribution,
> find the probabiltiy of "x" falls into that distribution.
> 
> Is there any reasonable way to obtain that?
> 
> - G.V.
> 
Your question isn't entirely clear.
We could interpret it as 

1. "what is the probability (density) of x being drawn
from a normal distribution with a specified mean and sd?" in which case the
answer is dnorm(x,mean,sd)

or

2. "what is the probability that x is drawn from N(mean,sd)
[vs. some unspecified alternative distribution]?" in which case the problem
is underspecified.  If you wanted the probability that x was drawn
from D1 as opposed to D2 (where D1 and D2 are two different specified
probability
of density functions) then the Bayesian answer (assuming an equal
prior probability on the two distributions) is D1/(D1+D2).


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