Using Generalized Multinomial Distribution To Estimate The Correlation Coefficient Of Discrete Data

Based on the model proposed by Tallis in1962, we develop a extended method make it is commonly applicable in estimating the correlation coefficient of discrete data.In this paper, by introducing an multi-state random variable, we first presents a joint distribution of n identically distributed multinomial random variables. Next, we give the numerical characters of the joint distribution and sum distribution of the n identically distributed random variables. Although the maximum likelihood estimation proposed by Fisher is widely used on parameter estimation, it is not an ideal choice of the case that the expression of the logarithm likelihood function is quite complex. Therefore. In order to simplify the process of estimating the unknown parameters, we put forward the EM algorithm to give the estimators of the parameters. At last, we discuss the asymptotic property of the parameters estimators.