Verification of the Hypothesis of Compliance of the Errors of the Results of Analyses of Oil Products to the Normal Distribution Law for a Random Variable

Abstract

We test the normality of the distribution of united samples of errors of the results of analysis of various types and brands of oil products obtained in the course of interlaboratory comparative tests in different fuel laboratories of the Russian Ministry of Defense in 1997–2017. The data of more than 8000 analyses of 20 physicochemical quality indices are investigated. The homogeneity of individual samples of errors included in the united sample is proved with the help of three criteria: a criterion of homogeneity of the mean values (the multisample Kruskal–Wallis criterion and its more accurate Iman–Davenport approximation), a criterion of homogeneity of distributions (the multisample Anderson–Darling criterion), and criteria of homogeneity of the variances (the Cochran and Bartlett criteria). The deviations of the law of distribution of the input data from the normal distribution is estimated by means of 11 parametric (two-sided David– Hartley–Pearson, D’Agostino, and Giry criteria, one-sided Hegazy–Green criterion, directed tests for the asymmetry |√b1| and curvature b2, and a multidirectional test based on the joint statistics of |√b1| and b2) and nonparametric (Kolmogorov–Smirnov, Cramer–Mises–Smirnov, Anderson–Darling, and χ2 Pearson criteria) criteria. It is shown that the actual plot of the distribution density of measurement errors is a unimodal asymmetric curve with positive excess and heavy tails. The main difference between the actual distribution of the errors of measurements of the properties of oil products and the normal distribution is a higher concentration of the results in the interval [–1σ; +1σ]. It is suggested to use algorithms of the robust statistics that are insensitive to the deviations from the theoretical distribution law and give more reliable results.