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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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 Richard Ulrich Posts: 2,961 Registered: 12/13/04
Re: A "plausible range" for a random variable
Posted: Jun 8, 2013 11:42 PM

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?

>
>That CI doesn't seem good for other distributions (uniform, exponential,
>log-normal and weibull), because I get 0 or 100%. Am I wrong?

This non-parametric approach is sound. Whatever you were
doing was not what I *intended* to prescribe. My apologizies,
if I previously was too terse. I've give a *bit* more detail this
time.

--
Rich Ulrich