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

Some studies have already been made on method of determining the value of parameter from observed data containing the parameter itself and random error due to the reason that the existing statistical methods of estimation in such situation fail in finding out the appropriate value of the parameter. The methods, so developed, suffer from two limitations which are: (i) the methods involve huge computational tasks and (ii) 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, based on arithmetic-geometric mean, for the same has recently been developed which involves lesser computational tasks than those involved in the methods developed earlier and which can be applicable in the case of finite set of data. In this paper, another method has been developed for the same which is based on arithmetic-harmonic mean. 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.