Bootstrap Kuiper Testing of the Identity of 1D Continuous Distributions using Fuzzy Samples

Abstract

This paper aims to statistically test the null hypothesis H 0 for identity of the probability distribution of onedimensional (1D) continuous parameters in two different populations, presented by fuzzy samples of i.i.d. observations. A degree of membership to the corresponding population is assigned to any of the observations in the fuzzy sample. The test statistic is the Kuiper's statistic, which measures the identity between the two sample cumulative distribution functions (CDF) of the parameter. A Bootstrap algorithm is developed for simulation-based approximation for the CDF of the Kuiper statistic, provided that H 0 is true. The p value of the statistical test is derived using the constructed conditional distribution of the test statistic. The main idea of the proposed Bootstrap test is that, if H 0 is true, then the two available fuzzy samples can be merged into a unified fuzzy sample. The latter is summarized into a conditional sample distribution of the 1D continuous parameter used for generation of synthetic pairs of fuzzy samples in different pseudo realities. The proposed algorithm has four modifications, which differ by the method to generate the synthetic fuzzy sample and by the type of the conditional sample distribution derived from the unified fuzzy sample used in the generation process. Initial numerical experiments are presented which tend to claim that the four modifications produce similar results.

Neutrophil extracellular traps in thrombi retrieved during interventional treatment of ischemic arterial diseases

“…A Kuiper statistical test for equality of distribution [5] and a one-tail statistical test for median equality [1] were used to identify differences in the characteristics of two one-dimensional continuous populations. Each of the populations was represented by independent and identically distributed samples of observations which could be either crisp or fuzzy.…”

“…Regression analysis and statistical hypothesis testing were performed on an array of thrombus composition and routine clinical data of each patient. Previously described algorithms were used (Kuiper statistical test for equality of distribution [28], one-tail statistical test for median equality [25], linear regression models with response variable described as quadratic function of one or two explanatory variables [25]) with modifications detailed in the Online Resource.…”

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Cryopreservation moderates the thrombogenicity of arterial allografts during storage

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Using Fuzzy Sets in Surgical Treatment Selection and Homogenizing Stratification of Patients with Significant Chronic Ischemic Mitral Regurgitation

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