Determining the 95% Confidence Interval of Arbitrary Non-gaussian Probability Distributions

− Measurements are nowadays permanent attendants of scientific research, health, medical care and treatment, industrial development, safety and even global economy. All of them depend on accurate measurements and tests, and many of these fields are under the legal metrology because of their severity. How the measurement is accurate, is expressed by uncertainty, which is obtained by multiplication of standard deviations by coverage factors to increase trustfulness in the measured results. These coverage factors depend on degree of freedom, which is the function of the number of implied repetitions of measurements, and therefore the reliability of the results is increased. The standard coverage factor is 1.96 for normal (Gaussian) distributions or near-Gaussian distributions, and the obtained expanded uncertainty has the 95% statistical probability. In general, it is not possible to achieve the 95% confidence interval by using the standard coverage factor 1.96, nevertheless of the degree of freedom. The present paper describes the method of estimating the expanded uncertainty by an algorithm of this model based on the 95% confidence interval of any probability distribution of any shape, dealing with the A-type or the B-type uncertainty. Furthermore the coverage factor is determined due to the 95% confidence interval of the actual probability distribution. The algorithm successfully copes with adding two or more uncertainties with mathematical properties of sums, and is established in accordance with the standards and guides. The model is introduced in procedures carried out in the calibration laboratory.