I have an array of values, with those values I plotted the histogram, calculated mean and variance. I want to know the corresponding distribution from the histogram obtained. How is it possible? Could you please explain the steps in obtaining appropriate probability distribution from histograms?
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1$\begingroup$ What do you mean by "obtaining distribution from histogram"? $\endgroup$– TimCommented Jun 30, 2016 at 13:09
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2 Answers
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Not sure I fully understand the question. If you are interested to know which distribution best fits your data then I would direct you to this QnA which gives a very good detailed answer (How to determine which distribution fits my data best?)
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To find candidates for the distribution by histogram, you will need to know the look of a range of distributions in their respective histogram. If there is a bunch of data points in the middle and decreasing to the right and the left of that in a symmetric way, than normal Distribution is a good candidate. If it has a big bunch of data in one place and less to both sides but with a long tail to the right, then lognormal distribution is a candidate. If there is a distinct window of values with a limit to the right and a limit to the left, then beta distributions should be considered:
Take some time with the Wikipedia and study the probabily distribution of a number of distributions: https://en.wikipedia.org/wiki/Beta_distribution https://en.wikipedia.org/wiki/Exponential_distribution https://en.wikipedia.org/wiki/F-distribution https://en.wikipedia.org/wiki/Log-normal_distribution https://en.wikipedia.org/wiki/Student%27s_t-distribution https://en.wikipedia.org/wiki/Weibull_distribution https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
Once you have identified a candidate then quantile-quantile plots are often advantageous over histograms to check the fit: https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot They just need more getting used to.
