Finding the probability that a roughly normal distributed will have the highest value among multiple curves

I have 30 roughly normal probability curves, the x-axis being points, the Y-Axis being Probability Density. I am trying to find the underlying probabilty for each curve of having the highest amount of points in a random trial. Whether there is a simulation system that can simulate the scenario many times to give a close estimate of the true probability of having the highest value in a random trial or if there is a statistical formula that can be used to find the probability.

  • Your question is a little vague. So you want to find the probability that the data from the random trial is from one of those Normal distributions and decide which normal distribution is more likely to produce the random points?

  • No sorry theres 30 different values generated each according to a roughly normal distribution, and i need to find the probability of each being the highest scoring

  • I think the best way to go about it would be using something like python to make a simulation but I don’t know how to use python

  • What do you mean by " being the highest scoring"?

  • The highest x-value

  • I see. This is more involved than I thought. You may want to raise the offer, hopefully another user may be able to help.

Answer

unless i am confused on the question, you want to perform an ANOVA. 

perform these steps:

-ANOVA (very common analysis)
-post hoc test: tukey kramer test (compares confidence intervals which are means and distributions). this tells you which are significantly and insignificantly different from eachother along with how much the confidence intervals overlap. its best to include a plot for this for easier interpretation.

- retest for HOV
- restest for normal distribution.

this isnt the most robust way to perform this analysis, but it essentially forms confidence intervals for the distribution of these normally distributed data points and compares the means. those with the best overlap are considered the best fit. it should also be taken into consideration that with normally distributed data, there is a range of values that may deviate from a perfect distribution due to random affects. these can generally be ignored. youa re essentially comparing distribution of data and variation from the mean. 

The answer is accepted.