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Topic: A "plausible range" for a random variable
Replies: 9   Last Post: Jun 11, 2013 7:42 PM

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 Cristiano Posts: 60 Registered: 12/7/12
Re: A "plausible range" for a random variable
Posted: Jun 9, 2013 7:26 AM

On 09/06/2013 5:42, Rich Ulrich wrote:
> On Sun, 09 Jun 2013 01:10:54 +0200, Cristiano <cristiapi@NSgmail.com>
> wrote:
>

>> On 07/06/2013 19:31, Rich Ulrich wrote:
>>> Poisson consideration gives a good approximation for small
>>> proportions. This is applied for your N=2000, 2 1/2%, as follows.
>>>
>>> Rank 50 is the point estimate of L. The +/- 2SD range for Poisson
>>> can be estimated as ( Square(Sqrt(L) - 1), Square(Sqrt(L) + 1) )
>>>
>>> The square root of 50 is about 7; the square of 6 is 36, and the
>>> square of 8 is 64. That gives (approximately) the CI for L=50
>>> is (37, 65).

>>
>> When the sample is taken in N(0,1), using your limits for N= 2000 I get
>> a 73% confidence level. Is that the intended level?

>
> For a sample Xi, i=1,n (=2000) you have R1 ... Rn,
> X's sorted in rank order, so that Ri < Rj for i<j
>
> The point estimate for 5% two tailed extreme results are
> the values of (R50, R1950) where R1950 is R(2000-50),
> simply applying symmetry.
>
> The CI around the value for R50 are the values in (R37, R65) .
> Similarly, for the other end (symmetry).
>
> Where do you see a 73% confidence level?
> Do you see whatever you were doing wrong?

Now I got the point: Sergio was talking about the CI for a quantile,
while I understood that the Sergio's Y was an estimate of the population
mean.
Sorry for the inconvenience.

Cristiano