# What are alternatives to uniform distribution when trying to fit observed data distribution?

I have a dataset of 500 observations and I have to find the best fitting distribution. If I look at the histogram of the data and the QQ plot my data seems to follow an uniform distribution. But a chi-square test rejects the corresponding null hypothesis, and I can't use Kolmogorov-Smirnov test (which doesn't reject null hypothesis) because parameters are estimated from the data. What other distributions could I try to fit?

• You need to provide more information about your data if you want this question answered. A plot, such as a histogram, can be helpful. It would also help (a lot) to state why you are fitting a distribution, for otherwise "best" is too ambiguous to be an effective criterion. – whuber Mar 14 '12 at 19:06
• I would like to post the histogram but i'm not allowed because i'm new here and i need at 10 reputation points to post images. The data are processing time of a machine and i want to fit them to use them in a simulation program – francesca Mar 14 '12 at 19:16
• If you really want to fit a uniform to your data, it should be on $(\min(x_i),\max(x_i))$ to maximise the likelihood. If you have no constraint on the family of distributions, the sky's the limit! – Xi'an Mar 14 '12 at 20:28
• Arguably, Xi'an, likelihood maximization is not a good approach. The solution lies along a corner of the parameter space, suggesting that many of the "nice" properties enjoyed by ML estimators might not hold. Intuitively, the true endpoints ought to lie slightly beyond the observed extrema of the data. – whuber Mar 15 '12 at 15:47
• I'm voting to close this question as off-topic because it really needs more information for a useful answer, and the OP is long gone – kjetil b halvorsen May 8 at 12:33