Methods for identification of probability distribution of random variables from data samples with R statistical computing language

Oleksandr O. Dykhovychnyi, Nataliia V. Kruglova, Olha I. Virstiuk

Abstract


The following article discusses various methods for probability distribution fitting to simulated data by means of R statistical computing language. In particular, some graphical methods like plotting of histograms, empirical and theoretical density functions, P-P and Q-Q plots, were considered. Estimation functions for probability distribution parameters were investigated by applying method of moments, method of quantiles, method of maximum likelihood, and shortest distance method. Hypothesis about probability distribution were verifi ed with Kolmogorov–Smirnov, AIC, and BIC tests.
The corresponding data set used to illustrate the above methods was taken from probability distribution of the maximum of Chenstov field restriction to a particular curve. The distribution was simulated with the special original algorithm in R statistical software.

Keywords


R language; Chentsov field; Gaussian process; Method of moments; Method of quantiles; Maximum likelihood estimation; Minimum distance estimation; Statistical tests

References


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