# Distribution of the Affinity Coefficient between Variables based on the Monte Carlo Simulation Method

## Keywords:

Affinity coefficient, Pearson's correlation coefficient, Monte Carlo simulation method, probability laws## Abstract

*The affinity coefficient and its extensions have both been used in hierarchical and non-hierarchical Cluster Analysis. **The purpose of the present **empirical study **on the distribution of the basic and the generalized affinity coefficients** **and on the distribution of the** standardized **affinity coefficient, by the method of Wald and **Wolfowitz, **under different assumptions, is to assess the effect of the **statistical probability distributions **of the variables (columns) of the initial data matrix, and of the respective parameters, in the distribution of the values of these coefficients.** **We present some results concerning the asymptotic distribution of the referred coefficients **under the assumption that the variables (for which the values of these coefficients â€‹â€‹are calculated) are independent and have statistical probability distributions specified apriori**. **In this distributional study, based on the Monte Carlo simulation method, we considered ten well-known statistical probability distributions with different variations of the respective parameters.** The simulation studies lead to the conclusion that the coefficientsâ€™ convergence for the normal distribution is quite fast and, in general, a good approximation is obtained for small sample sizes, that is for**sample sizes above 20 and in many cases for sample sizes above 10.*

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