Observed Data Containing One Parameter and Chance Error: Probabilistic Evaluation of Parameter by Pythagorean Mean

Abstract

Recently some methods have been developed for determining the appropriate value of the parameter from observed data containing the parameter itself and chance error since the existing statistical methods of estimation in such situation fail in finding out the appropriate value of the parameter. However, the methods are based on some probabilistic assumptions. Accordingly, the value of the parameter obtained by the methods is not deterministic but probabilistic i.e. one cannot be fully certain that the value of the parameter obtained is identical with its actual value. This paper is based on the evaluation of the probability that the value obtained is the actual value of the parameter and on one numerical application of the method in determining the central tendency of each of annual maximum and annual minimum of ambient air temperature at Guwahati.