Improving the Accuracy of the Probability Density Function Estimation

Abstract

The paper considers the new approach to the reconstruction of the probability density function similarly the averaged shifted histogram method. An algorithm is used Richardson's extrapolation for increasing accuracy. We prove the estimates of the accuracy of the probability density function and its second derivative to choose the optimal settings for smoothing the histogram and kernel estimators and to consider the optimal choice problem of the bandwidth parameter. Presented the results of numerical experiments.

The Reliability of Numerical Modeling in Remote Sensing Data Analysis

“…We also have proposed the arithmetic operations on probability density functions and procedures for constructing probabilistic extensions as the basis of computational probabilistic analysis [3][4][5][6][7][8][9].…”

“…Accordingly, the total number of calculations will be equal to Cnm 2 . Thus, the article [7] compares the number of generate random variables of Monte Carlo methods and numerical operations using probabilistic arithmetic to achieve the same accuracy. Thus, the accuracy of addition of n uniform random variables (m = 10) is achieved by Monte Carlo methods with the number of generate uniform random variables equal to n · 10 6 .…”