Arithmetic-Geometric Mean: Evaluation of Parameter from Observed Data Containing Itself and Random Error

Abstract

Recently some methods have been developed for determining the value of parameter from observed data containing a single parameter and random error since the existing statistical methods of estimation in such situation fail in finding out the appropriate value of the parameter. The methods, so developed, involve huge computational tasks. Moreover, a finite set of observed data may not yield the appropriate value of the parameter in many situations while the number of observations required in the methods may be too large for obtaining the appropriate value of the parameter. For these two limitations, one method for the same has been developed here which involves lesser computational tasks than those involved in the methods developed so far. Moreover, the method described here can be applicable in the case of finite set of data. This paper describes the derivation of the method and one numerical application of the method in determining the central tendency of each of annual maximum and annual minimum of surface air temperature at Guwahati.