Standard Uniform Distribution

• Jul 2nd 2009, 03:02 PM
Standard Uniform Distribution
Never really did much stats so this is probably an easy question.

What values can the standard uniform distribution take? Is it just any value between 0 and 1? Is each value chosen with equal probability?

So for example, if I'm to asked the question...

Calculate \$\displaystyle t_1\$ ~ \$\displaystyle U(0,1)\$ where U is the uniform distribution and t is a random variable. Is that even a properly written out question? Does it just mean t will take a random value between 0 and 1?

As I say I've not done much stats and not entirely sure what the notation stands for.
• Jul 2nd 2009, 03:31 PM
Plato
Quote:

Calculate \$\displaystyle t_1\$ ~ \$\displaystyle U(0,1)\$ where U is the uniform distribution and t is a random variable. Is that even a properly written out question? Does it just mean t will take a random value between 0 and 1?

I would say that is a good guess.
Only your textbook can say for sure.
• Jul 2nd 2009, 05:54 PM
matheagle
Quote:

Never really did much stats so this is probably an easy question.

What values can the standard uniform distribution take? Is it just any value between 0 and 1? Is each value chosen with equal probability?

So for example, if I'm to asked the question...

Calculate \$\displaystyle t_1\$ ~ \$\displaystyle U(0,1)\$ where U is the uniform distribution and t is a random variable. Is that even a properly written out question? Does it just mean t will take a random value between 0 and 1?

As I say I've not done much stats and not entirely sure what the notation stands for.

\$\displaystyle t\$ ~ \$\displaystyle U(0,1)\$ means that t has a density that is 1 on (0,1) and 0 otherwise.
• Jul 3rd 2009, 02:53 AM
Hmm I'm still not totally clear on this... Let me put down whats in the textbook. Its to do with the Kolmogorov-Smirnov distribution.

I'm testing the hypothesis that a sample of n independent observations comes from a specified continuous distribution.
...Let \$\displaystyle F_0(x)\$ be the distribution function from which, according to the hypothesis to be tested, the sample has been taken. We let \$\displaystyle x_1, x_2, \ldots , x_n\$ denote the order statistics of the sample, and define \$\displaystyle t_j = F_0(x_j)\$ for \$\displaystyle j = 1,2, \ldots , n\$.
Then I have a formula to use.
If the null hypothesis holds \$\displaystyle t_1, t_2, \ldots t_n\$ are the order statistics of a random sample size n from the uniform distribution on (0,1).

And the first thing I have written down to do (written by my prof)...
Set n to be a fixed amount
Calculate \$\displaystyle t_1, t_2, \ldots , t_n \$ ~ U(0,1)

note, \$\displaystyle F_0(x)\$ is not given but i assume thats the empirical distribution function?

So, given this info, how would you calculate the t's for say, n=4?

As I say im quite new to stats and this is all the info I have. If I can calculate the t's I'm sorted for the rest of it.