Identification of the Probability Density Distribution of a Random Value

The dependence of the identification accuracy of the probability density distribution of a random variable on the number of digits (intervals) of the histogram and the size of the sample used is investigated. The bias and standard deviation of the error are estimated using simulation modeling. Quantitative results are obtained for the uniform probability distribution and the Simpson distribution. It is shown that with an increase in the histogram interval, the bias error monotonically increases, and the RMS deviation of the error has an extremum.