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Topic: Simulation for the standard deviation
Replies: 27   Last Post: Mar 1, 2013 7:30 AM

 Messages: [ Previous | Next ]
 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: Simulation for the standard deviation
Posted: Feb 22, 2013 3:06 PM

On Feb 22, 6:05 am, Cristiano <cristi...@NSgmail.com> wrote:
> On 22/02/2013 6:15, Ray Koopman wrote:
>> On Feb 20, 3:54 am, Cristiano <cristi...@NSgmail.com> wrote:
>>

>>> Short question: does anybody know how to calculate the confidence
>>> interval of the standard deviation for the uniform distribution?

>>
>> For n iid samples from a continuous uniform distribution,
>> Pr(r/R <= x) = F(x) = n*x^(n-1) - (n-1)*x^n, where
>> r is the sample range, R is the true range, and 0 <= x <= 1.
>> A 100p% confidence interval for R is R >= r/x, where F(x) = p.
>> Divide that by sqrt(12) to get a lower bound for the SD.

>
> Suppose I randomly pick 0.1, 0.4 and 0.2 (n = 3);
> what should I write to calculate a 99% confidence interval?

F(x) = 3 x^2 - 2 x^3 = p

F(.941097) = .99

SD >= (.4 - .1)/(.941097 * sqrt(12))

Date Subject Author
2/20/13 Cristiano
2/21/13 Richard Ulrich
2/21/13 Cristiano
2/21/13 Richard Ulrich
2/22/13 Cristiano
2/22/13 Richard Ulrich
2/21/13 Ray Koopman
2/22/13 Ray Koopman
2/22/13 Cristiano
2/22/13 Ray Koopman
2/23/13 Cristiano
2/23/13 Ray Koopman
2/23/13 Cristiano
2/24/13 Cristiano
2/24/13 Ray Koopman
2/24/13 Cristiano
2/25/13 Ray Koopman
2/25/13 Cristiano
2/25/13 Ray Koopman
2/25/13 David Jones
2/26/13 Cristiano
2/26/13 David Jones
2/27/13 Ray Koopman
2/27/13 Cristiano
2/28/13 Ray Koopman
2/28/13 Cristiano
2/28/13 Ray Koopman
3/1/13 Cristiano