- #1
Deimantas
- 41
- 0
Homework Statement
We are given a sample of size 100. After some tests (histogram, Kolmogorov) we deduce the sample X is distributed uniformly. The next task is to presume the parameters are equal to values of your choice, and test if such hypothesis is true.
Homework Equations
The Attempt at a Solution
Uniform distribution has two parameters, a and b. My estimated parameters are a=1.01 (minimum value in the sample) and b=3 (max value in the sample).
I'm testing null hypothesis: b=3. The value of parameter a is known (1.01).
Mn= ((Xmax-b)*100)/(b-a) = 0
The percentiles are calculated using this formula:
hp=ln(p). So
h0.025=ln(0.025)=-3.6888794541139363
h0.975=ln(0.975)=-0.0253178079842899
The value of Mn should fall in the interval between h0.975 and h0.025 for the hypothesis to be accepted as correct.
This must be wrong, because I chose b value that is equal to the max value of the sample X, which should be a good estimate, and so the hypothesis should be accepted. What am I missing?