The correlation between variate-values and ranks in samples from Complete Fourth Power Exponential distribution.

Abstract

In this paper, we derive the correlation between variate-values and ranks in a sample from the Complete Fourth Power Exponential (CFPE) distribution. A sample from the CFPE distribution could be misclassified as if it is drawn from the normal distribution due to some similarities between the two distributions. In practice, ranks are used instead of real values (variate-values) when there is hardly any knowledge about the underlying distribution. This may lead to loss of some of the information contained in the actual values. In this paper we found that the amount of information loss, by using ranks instead of real data, is larger when the sample is from the CFPE distribution than if it is from the normal distribution. However, there is still a relatively high correlation between variate-values and the corresponding ranks. Comparisons between the correlation between variate-values and ranks for the CFPE distribution and some other distributions are provided.