Uncertainties of the estimators and parameters of distribution in measurements with multiply observations

Abstract

The article shows that the commonly used method of estimating the Type A uncertainty of measurements based on the standard deviation of estimators of population parameters does not meet the definition of uncertainty. For correct determination of the standard uncertainty, it is necessary to use the distribution of the corresponding population parameter at the values of population estimators determined from the experiment but not the probability distribution of the estimator. The joint probability distribution of population parameters can be derived by transforming the joint distribution of estimators using a Jacobian equal to the ratio of the scale parameter estimator to the population scale parameter itself. Independently on population distribution, the standard uncertainties of the location and scale parameters of the population depend on the number of observation n as a function of 1 3 n - , i.e. can be determined when n ≥ 4. When the number of observations is small then the uncertainty value calculated by the usual method may differ significantly from the correct value. The given numerical example confirms this statement. Key words:Measurement; Observation; Estimator; Uncertainty; Probability distribution.