Date: Feb 22, 2013 3:06 PM
Author: Ray Koopman
Subject: Re: Simulation for the standard deviation
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))