Arbitrary Precision<i>Mathematica</i>Functions to Evaluate the One-Sided One Sample K-S Cumulative Sampling Distribution

Brown, James R.; Harvey, Milton E.

doi:10.18637/jss.v026.i03

Cited by 5 publications

(4 citation statements)

References 15 publications

(27 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to determine the normality interval we use the Kolmogorov-Smirnov normality test [ 31 , 32 ], which is the most usual empirical distribution function test for normality.…”

Section: Methodsmentioning

confidence: 99%

Fractal Analysis of Laplacian Pyramidal Filters Applied to Segmentation of Soil Images

Castro

Ballesteros

Méndez

et al. 2014

The Scientific World Journal

View full text Add to dashboard Cite

The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter a. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results.

show abstract

“…In order to determine the normality interval we use the Kolmogorov-Smirnov normality test [ 31 , 32 ], which is the most usual empirical distribution function test for normality.…”

Section: Methodsmentioning

confidence: 99%

Fractal Analysis of Laplacian Pyramidal Filters Applied to Segmentation of Soil Images

Castro

Ballesteros

Méndez

et al. 2014

The Scientific World Journal

View full text Add to dashboard Cite

show abstract

“…several opportunities to lose accuracy: in the addition/subtraction, the exponentiation, and the multiplication, before considering the summation. Brown and Harvey [17] go into quite some detail on the precision required for internal computations in order to achieve a desired accuracy in the final result. The magnitude of the terms in Eq.…”

Section: Controlling Accuracy Lossmentioning

confidence: 99%

“…Computing S n ( k n ) in this manner loses about 1.6 * (k− 1) bits. Brown and Harvey [17] analyzed the extra internal digits of precision needed to compute using Formula 31. They found that the number of extra digits needed grows like O( √ n) (keeping the p SF fixed and evaluating at x n = S −1 n (p SF )).…”

Section: Evaluation Near X=0mentioning

confidence: 99%

Computing the Cumulative Distribution Function and Quantiles of the One-sided Kolmogorov-Smirnov Statistic

Mulbregt¹

2018

Preprint

View full text Add to dashboard Cite

The cumulative distribution and quantile functions for the one-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. While the Smirnov-Birnbaum-Tingey formula for the CDF appears straight forward, its numerical evaluation generates intermediate results spanning many hundreds of orders of magnitude and at times requires very precise accurate representations. Computing the quantile function for any specific probability may require evaluating both the CDF and its derivative, both computationally expensive. To work around avoid these issues, different algorithms can be used across different parts of the domain, and approximations can be used to reduce the computational requirements. We show here that straight forward implementation incurs accuracy loss for sample sizes of well under 1000. Further the approximations in use inside the open source SciPy python software often result in increased computation, not just reduced accuracy, and at times suffer catastrophic loss of accuracy for any sample size. Then we provide alternate algorithms which restore accuracy and efficiency across the whole domain.

show abstract

“…Drew Glen & Leemis [14] generated the collection of polynomial splines for n <= 30. Brown and Harvey [15,16,17] implemented several algorithms in both rational arithmetic and arbitrary precision arithmetic. Simard and L'Ecuyer [18] analyzed all the known algorithms for numerical stability and sped.…”

Section: Review Of Kolmogorov-smirnov Statisticsmentioning

confidence: 99%

Computing the Cumulative Distribution Function and Quantiles of the limit of the Two-sided Kolmogorov-Smirnov Statistic

van Mulbregt

2018

Preprint

View full text Add to dashboard Cite

The cumulative distribution and quantile functions for the two-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. The CDF is notoriously difficult to explicitly describe and to compute, and for large sample size use of the limiting distribution is an attractive alternative, with its lower computational requirements. No closed form solution for the computation of the quantiles is known. Computing the quantile function by a numeric root-finder for any specific probability may require multiple evaluations of both the CDF and its derivative. Approximations to both the CDF and its derivative can be used to reduce the computational demands. We show that the approximations in use inside the open source SciPy python software result in increased computation, not just reduced accuracy, and cause convergence failures in the root-finding. Then we provide alternate algorithms which restore accuracy and efficiency across the whole domain.

show abstract

Arbitrary PrecisionMathematicaFunctions to Evaluate the One-Sided One Sample K-S Cumulative Sampling Distribution

Cited by 5 publications

References 15 publications

Fractal Analysis of Laplacian Pyramidal Filters Applied to Segmentation of Soil Images

Fractal Analysis of Laplacian Pyramidal Filters Applied to Segmentation of Soil Images

Computing the Cumulative Distribution Function and Quantiles of the One-sided Kolmogorov-Smirnov Statistic

Computing the Cumulative Distribution Function and Quantiles of the limit of the Two-sided Kolmogorov-Smirnov Statistic

Contact Info

Product

Resources

About