Is it possible to write the function (mathematical formula) of a custom probability distribution from data?

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Is it possible to write the function (mathematical formula) of a custom probability distribution from data?
in the case of the existing probability distributions are not fit to the data.

Risposte (1)

dpb
dpb il 27 Lug 2020
Modificato: dpb il 27 Lug 2020
To generate a functional form totally independently from only a dataset is pretty much not feasible.
There are a number of general distribution families; the Johnson and Pearson are two of the more commonly used.
Selection of one of the candidate families begins by computing (commonly "beta1" and "beta2") measures of skewness and kurtosis and seeing where on a generalized chart of b1,b2 the particular data sample lies and using that to select a potential candidate distribution family.
It must be noted, however, this is no magic panacea that can be applied blindfolded...
Hahn & Shapiro, Statstical Models in Engineering, Wiley, Chapters 6,7 is a good introductory text.

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