Here I've got such a problem.
I was given $n = 20$ values for time of good functioning of a robot between two consecutive defects.
1200, 1432, 1502, 1100, 3286, 4235, 1149, 5236, 2234, 2115, 2025
I have to determine if these values fits in an exponential distribution using chi-squared test.
What I've done is:
- I've created an interval large enough to comprise all these values;
- I've divided this interval and then counted the frequency of appearance of values from the above sample between two consecutive limits. For example, taken an interval $[1000, 1500]$, the frequency of occurrences of the values from the sample in this interval, choosing 1200,1432,1100,1149 is 4.
- I calculated $$\sum_{i = 1}\frac{(f_i - np_{i})^2}{np_{i}}$$ formula(1)
!!! I used for calculating probability the punctual estimator for parameter of exponential distribution, using the formula: $$\alpha = \frac{1}{\bar X}$$, where $\alpha$ is the parameter estimator and $$\bar X = \frac{X_1 + ... + X_n}{n}$$
The problem is: I've got a totally different value for formula (1) in comparison with the value of Hi-squared with n - 1 freedom grades and $\alpha = 0.1$, where n is the number of sub-intervals I divided the interval. I suppose it's too big.
It's obvious that the selection does not fit in exponential distribution The idea also is, I'm confused about how I should properly solve this exercise. Can you, please, show me some kind of example of how can I exactly determine this ? Thanks in advance.