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I know what is Probability Density Function and its application in Machine Learning and Statistics. The problem I faced is that how does it being calculated? For a specific example like the probability of amount of rain in a rainy day, the researchers measure the rain amount for specific period of time and they make a function for that (frequentist approach)?

More specifically, The question is about how the following diagram is obtained?

pdf

PS It's not related to this question, because I asked how to create a diagram like the following diagram!

Amir Hooshang
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  • I marked it as a duplicate of a thread that gives detailed answer to your question. – Tim Oct 06 '20 at 12:38
  • Hi @Tim, It's not related to the question you have marked. As I have explained the question is about the creation of this diagram, not about the normalization or other things! – Amir Hooshang Oct 06 '20 at 12:39
  • The phrase "make a function of that" is called *inference* in statistics. It comprises a huge part of statistical theory and procedure and therefore is not readily answered in a forum like this. – whuber Oct 06 '20 at 12:52
  • If the plot you show has rainfall along $x$-axis and shows the empirical amount of rain then it is usually called a density plot. If that is what you want then perhaps if you read up about such plots it might help you to focus your question more. – mdewey Oct 06 '20 at 13:44
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    @AmirHooshang but we *don't know* how the plot was generated, since you gave us no details about it. It could be as well drawn by someone in MS Paint! We can *guess* that it is a kernel density plot, but it's not a place for a guessing game. Maybe edit your question to make it more precise (that you ask specifically about the plot) and tell us more about the plot, i.e. what does it show, how did you get it, etc. – Tim Oct 06 '20 at 13:49
  • @Tim Yeah, you are right. The question was the one you explained. The plot was just an example. How do we create such plots? with collecting datas like frequentist approach or the other methods? I have edited my answer. – Amir Hooshang Oct 06 '20 at 16:14
  • @mdewey Thank you for your guidance. Would you please give me some useful links to read? – Amir Hooshang Oct 06 '20 at 16:15
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    We do have a tag [tag:density-estimation] on this site or you could try https://en.wikipedia.org/wiki/Kernel_density_estimation and see if that fits what your problem is. If it does not then you can edit your question to say why and move forward. – mdewey Oct 06 '20 at 16:31
  • @AmirHooshang does this help https://stats.stackexchange.com/a/244023/35989 ? – Tim Oct 06 '20 at 17:22
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    One reason I characterized this problem as inference (or, perhaps even better, *estimation*) is that the plot could have been produced by fitting a mixture model to a sample of univariate data. It's not necessarily a kernel density estimate. – whuber Oct 06 '20 at 17:38
  • @Tim Yeah you are right man. Thanks for your help – Amir Hooshang Oct 06 '20 at 18:47
  • @whuber thank you very very much! – Amir Hooshang Oct 06 '20 at 18:48

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