On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown

By Hubert W. Lilliefors. 1967

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Citations in the corpus

Deep Learning Stock Volatility with Google Domestic Trends (2015, background): “However, this residual fails the one-sample Kolmogorov-Smirnov test [25] with a p-value ≪ 1% for the null hypothesis that the residual is normally distributed.”
Estimating field‐saturated soil hydraulic conductivity by a simplified Beerkan infiltration experiment (2014, background): “28, 1095–1103 (2014) to the test by Lilliefors (1967) at P= 0.05 for most considered scenarios.”
Skimming Digits: Neuromorphic Classification of Spike-Encoded Images (2016, methodology): “Furthermore, applying the Lilliefor’s composite goodness-of-ﬁt test of composite normality (Lilliefors, 1967) (which itself is a specialized version of the Kolmogorov-Smirnov test) also retained the null hypothesis that the data are normally distributed ( p > 0.5) for both patterns.”
Density, size and distribution of stomata in 35 rainforest tree species in Central Amazonia (2011, unknown): “As data had a normal distribution (Lilliefors 1967) no transformation was used before conducting analysis of variance.”
Convolution-Weight-Distribution Assumption: Rethinking the Criteria of Channel Pruning (2020, methodology): “) In ith layer, we use KolmogorovSmirnov (KS) test (Lilliefors, 1967) to check if all the weights in the same layer follow a normal distribution (3)(1) In Table 3, we perform a lot of experiments on various situations; (2) In Section 4, we make further discussion and Analysis on the conditions for C”
Group-Wise Learning for Aurora Image Classification With Multiple Representations (2019, unknown): “In the literature, there are several ways to measure the distance between a pair of samples represented by histogram-based features, for example, Chi-square distance [55], histogram intersection [56], and log-likelihood statistic.”
Assessment of modified Anderson–Darling test statistics for the generalized extreme value and generalized logistic distributions (2011, methodology): “Lilliefors (1967, 1969) presented a table for testing normality using the KS test statistic when the mean and variance of the population were unknown.”
Correlating viral phenotypes with phylogeny: accounting for phylogenetic uncertainty. (2008, methodology): “Using a two-sample Kolmogorov–Smirnov test (see Lilliefors, 1967), we found that the CDFs of the AI and PS statistics did not depart from the theoretically expected unit uniform distribution; the MC statistic, however, did.”
Testing for differences between two distributions in the presence of serial correlation using the Kolmogorov–Smirnov and Kuiper's tests (2021, methodology): “In such instances, another approach, such as the Lilliefors test (Lilliefors, 1967) or Monte Carlo simulation are required.”
A de novo paradigm for mental retardation (2010, methodology): “The assumption of normality in the data required for the model was determined using Lilliefors (Kolmogorov-Smirnov) normality testin”
A characteristic oxygen abundance gradient in galaxy disks unveiled with CALIFA (2013, methodology): “The probability of being compatible with a Gaussian distribution is 98%, based on a Lilliefors test (Lilliefors 1967) (compared with 77% derived for the distribution of zero points).”
Shapiro–Francia test compared to other normality test using expected p-value (2015, methodology): “The LF test for normality [8] modifies the KS goodness-of-fit test by assuming that the parameters from the tested model are not known and are estimated from the sample data.”