AGHM as A Tool of Evaluating the Parameter from Observed Data Containing Itself and Random Error

Abstract

A number of methods like analytical method, stable mid-range method, and shortest interval method had been developed for determining the value of the parameter from observed data containing the parameter itself and random error. Due to (i) huge computational tasks and (ii) limitation of finite set of observed data in determining the appropriate value of the parameter involved in these methods, three more methods have recently been developed for the same purpose. These three methods are respectively based on Arithmetic-Geometric Mean (abbreviated as AGM), Arithmetic-Harmonic Mean (abbreviated as AHM), and Geometric-Harmonic Mean (abbreviated as GHM). Due to the variation occured in accuracy of values of the parameter yielded by these three methods, one more method has been developed in this study for determining the value of the said parameter with an objective of finding more accurate value of the parameter. The method is based on Arithmetic-Geometric-Harmonic Mean (abbreviated as AGHM). This paper describes the derivation of the method and one numerical application of the method in determining the central tendency, which can be represented by the said parameter, of sex ratio in the populations of the different states of India.