Effective Measyrand Estimators for Samples of Trapezoidal PDF-s

This paper is final overview of investigations on the accuracy of basic estimators of trapezoidal probability distribution samples of the measured data. For symmetrical trapezoidal PDF of straight as well concaved sides, using Monte-Carlo method of simulation, the standard deviation (SD) of linear 1- and 2-component estimators are evaluated. Approaches for theirs evaluation are proposed. It is established that in the ratio of upper and bottom bases of trapezoidal PDF in the range from 1 to 0,35 the mid-range value has smaller standard deviation (SD) than the mean value and median. It is find then for the whole family of the symmetric linear trapezoidal PDF more accurate than above single element estimators are two-component (2C) estimators as the linear form of the mean and mid-range values of the sample. Their coefficients are found, properties discussed and formulas of SD are given. The new simplified 2C-estimator of equal coefficients is also proposed. These estimators successfully extend estimation of the measurand value as the sample mean and description of its accuracy by the uncertainty type A recommended by the international guides of uncertainty evaluation in measurement GUM-2008 [1], EA-4/02 [2] and by Handbook NASA [3]. Approaches of described below investigations could be effectively applied also for other models of convoluted PDF-s.