Increase of mean and variance estimates reliability for limited data size

Abstract

The price of diagnostics technology depends on the measurements number. Due to inadequate number of measurements and statistically unjustified data, wrong results of the simulation may be received, the technology maybe ineffective. In case of both physical and mathematical identification cases it is essential to assess correctly limited size of the data. For this point theoretical technique was suggested which practical use needs additional investigation. The method is based on the assessment of normalization function H(x), through which original statistical sample can be enlarged and analyzed parameters may be corrected. The success of this methodology use depends on function H-1(yi) approximated with determine function H(y) precision and method effectiveness depends on minimal data size s0, sufficient for statistical method validity.

The problem is analyzed on the base of statistical simulation by generating random non-normal variables. It was noticed that effectiveness of the methodology depends on the order of the polynomial, which approximates normalizing function. However, due to random approximation of each sample, there is possibility, that optimal order of the polynomial will not be obtained. While comparing approximation of large and small samples it was noticed that the mentioned possibility for very small samples is larger. But the sample of more than 10 random variables is enough optimal to use the methodology and revised estimate of mean and variance can be obtained. Effectiveness of methodology does not depend on the sample variance growth; the standard deviation is more sensitive for the polynomial order than the sample mean.