Theoretical Mathematics & Applications

The Existence of the Moments of the Cauchy Distribution under a Simple Transformation of Dividing with a Constant

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• Abstract

  In this paper, we establish the existence of the moments of a Cauchy distribution with parameters, a and b denoted by Cauchy (a,b) , via a simple transformation of dividing with a suitable constant. As a result of this transformation every Cauchy (a,b) would be distributed on the interval [-1, 1]. The results for the first four crude moments were given in view of their importance in obtaining the very important statistical measures namely variance, skewness and kurtosis.