The Correlation between Variate-Values and Ranks in Samples from Complete Fourth Power Exponential Distribution

Tahani A. Maturi, Anga Elsayigh

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.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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