Testing normality based on new entropy estimators

Abstract

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Classifying distributions via symbolic entropy estimation

“…Vasicek's work also forms the basis of the estimators by Correa [9] and Wieczorkowski and Grzegorzewsky [10]. More recent estimator proposals by Noughabi [13] and Zamandande and Arghami [15] similarly follow Vasicek's principle of Shannon entropy estimation over a sample window. In recent years, Vasicek's technique and its derivatives have also been investigated in conjunction with ranked set sampling (see, e.g., [16]) . We note here that Shannon entropy forms a common basis for these estimators and observe that the individual sample values are sorted by size before estimation -which destroys any information about the sequence in which these samples occurred, i.e., it does not capture information such as whether the samples were i.i.d.…”

Performances of Shannon’s Entropy Statistic in Assessment of Distribution of Data

“…Different approaches were applied to estimate entropy and based on the new introduced estimators (e.g. modified Vasicek's estimator [37,38], Noughabi's entropy estimator [39]) new goodness-of-fit tests were developed and performances in testing the normal [40][41][42], lognormal [43], uniform [44][45][46], exponential [47], beta [47,48], Poisson [49], Weibull [43], Gamma [43], Pareto [50,51], Student and exponential distribution [52] were studied.…”

“…The scientific community shows attention not just to the assessment of the existing tests but also to development and validation of new tests. New approaches are reported to test certain distributions of measured/observed data, such as mean and quantile statistics based on the posterior predictive distribution [27], quantile-mean covariance [28], empirical distribution function [29], maximum entropy [30], Kullback-Leibler measure [31], sums of squares in decomposition of the Shapiro-Wilk-type statistic [32], Euclidean distance between sample elements for assessment of multivariate normality [33], or entropy estimators [34].…”

Computation of Probability Associated with Anderson–Darling Statistic

“…The goodness-of-fit tests use different procedures (see Table 1). Alongside the well-known goodness-of-fit test, other methods based for example on entropy estimator [17][18][19], jackknife empirical likelihood [20], on the prediction of residuals [21], or for testing multilevel survival data [22] or multilevel models with binary outcomes [23] have been reported in the scientific literature. Tests used to assess the distribution of a dataset received attention from many researchers (for testing normal or other distributions) [24][25][26][27].…”