Pyramidal Distribution and Up-Side-Down Pyramidal Distribution  
Author Zhenmin Chen




Abstract The uniformity test has its applications in various fields such as biology, astronomy and computer science. The purpose of the uniformity test is to check whether the underlying probability distribution of a population differs from the uniform distribution. This paper focuses on the two-dimensional case. Some statistical tests for bivariate uniformity can be found in the statistical literature. To compare the power of the bivariate uniformity tests, various alternative distributions must be used. In addition to the existing alternative distributions, Chen (2017) proposed a bivariate distribution named the pyramidal distribution. By moving the vertex of the pyramidal, different shapes of the alternative distributions can be obtained for the power study purpose. It was found in Chen and Ye (2009) that the power comparison results might be different when some up-side-down distributions are used. The discussion of that paper was merely on univariate case. It is reasonable to believe that the same situation may happen in multivariate case. Because of that, an up-side-down bivariate distribution, named the up-side-down pyramidal distribution is proposed in this paper. The proposed distribution can be used as an alternative distribution in power comparison for bivariate uniformity tests.


Keywords Pyramidal Distribution, Up-Side-Down Pyramidal Distribution, Bivariate Uniformity, Power Comparison
    Article #:  RQD25-263
Proceedings of 25th ISSAT International Conference on Reliability & Quality in Design
August 1-3, 2019 - Las Vegas, NV, U.S.A.