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))