The Kolmogorov-Smirnov test is a test for goodness of fit of data to a distribution. It is often used to test whether a variable is normally distributed.

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Comparing accuracy of two non-parametric predictors

I have a quantity x_i that I have n measurements for. I also have for every point two separate non-parametric and non-symmetric distributions A_i and B_i that are supposed to predict the quantity ...
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Estimation of scale parameter and shape parameter of using 'maxLik' package [on hold]

I want to test the closeness of my sample data with the Generalized Exponential (GE) distribution. For that, I am using ks test in R. In the documentation of ...
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Gibbs Sampling Parallel convergence

I have a Gibbs Sampler. I am running 1000 parallel walks of the sampler. For any given walk I use the 2 value Kolmogorov Smirnov test to determine if convergence is reached within that instance. I ...
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compare multiple size frequency distributions

I have a dataframe with annual size frequency distributions: ...
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Help me understand a step of the procedure for KS test with estimated parameters

I read the following procedure to perform KS test with estimated parameters Testing whether data follows T-Distribution At first I couldn't make head or tails of it, partly because I mistaked the ...
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Kolmogorov-Smirnov vs. Kuiper test

I would like to compare two 2D distributions with quantitative variables, illustrated here: For each "x", they are several measures "y". I can't assume these distributions are parametric. A ...
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1answer
68 views

Anderson-Darling test for normality with estimated parameters

I have a set of measurements coming from a manufacturing processes. I want to test if the measurements come from a normal distribution. If I understadn correctly, it's wrong to use K-S test or A-D ...
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2answers
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Is it valid to rank goodness-of-fit based on the value of the Kolmogorov-Smirnov or Anderson-Darling test statistics?

When using Kolmogorov-Smirnov or Anderson-Darling goodness-of-fit tests, is it valid to claim that, because distribution X has a lower test statistic than distribution Y, distribution X is a better ...
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1answer
15 views

KS test for normality on residuals from OLS vs. MLE

This is a conceptual issue. Suppose, one wants to test the residuals $e_t$ from the regression for normality. So, he runs the regression, obtains the estimates of error variance $\sigma^2$, and forms ...
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Distribution analysis “too uniform” - need help understanding my result

I have $n>1000$ vectors of size $k=20$, sampled from an unknown source that I would like to find their distribution. They appear uniform, so I run the KS test with $\alpha=0.1$ to check. If this ...
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49 views

Two sample one-sided Kuiper Test and KS-statistic

With the KS-Test it is possible to conduct a two sample one-sided test between two different random samples $A$ and $B$ to test whether one CDF is larger or smaller than the other, i.e. is $CDF_A$ ...
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How can I test variance explained by the factor group if each subject in the group comprises a different number of measurements?

The data structure I have 2 groups with 30 subjects each. Each subject has a different number of fibers (approximately 46000 +/- 3000) of different length (see histogram). My goal is to determine how ...
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Splitting dataset at intersection of 2 ECDF before ks.boot analyses

This is my follow-up to an earlier post Help with understanding the ks.boot test results. I have an example pair of datasets: http://pastebin.com/s6ATRLDC and http://pastebin.com/hEc7Mqhp. I want to ...
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2answers
49 views

Help with understanding the ks.boot test results

I am trying to perform the ks.boot analysis to compare two numerical dstributions for 2 different phenomena. Those 2 numerical lists are at http://pastebin.com/s6ATRLDC and ...
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1answer
44 views

What is the best way to find change points in empirical power law distributions?

I'm looking at some data that conform reasonably well to a continuous power law distribution, according to a Kolmogorov-Smirnov test that compares the estimated power-law fit to the data (per Clauset, ...
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1answer
78 views

Goodness of fit in R

I need to check for goodness of fit using K-S test in R. I have a dataset (containing 50 data points) and a non-standard continuous probability distribution. Should I peform a one-sample or two-sample ...
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1answer
61 views

Difference between the two way of performing Kolmogorov-Smirnov normality test [duplicate]

There are 2 ways to perform Kolmogorov-Smirnov test in SPSS: Analyze; Nonparametric Tests; 1-Sample K-S Analyze; Descriptive Statistics; Explore; Plots; Normality plots with tests What is the ...
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generating discrete distribution comparison score

I have constructed a distribution of some data that I am analyzing, so it is discrete, and I would like to be able to compare it to other distributions in order to generate a score or rank so that I ...
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1answer
44 views

Similarity between two small datasets

I have gone through several test's (Kolmogorov-Smirnov, t-test, u-test etc..) but I am not sure which one to use when it comes to comparing two small data sets, lets say of size 10 each. ...
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48 views

Comparing two estimated distributions

I estimated the density function (adaptive kde) from two samples and the cdf using approxfun() and integrate(). Now, I would implement a ks test to know if the two distributions are similar. I guess I ...
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1answer
82 views

KS Test and Wilcoxon Rank Sum Test, large differences in p values

I am relatively new to non-parametric tests. I wrote the following R code to test 2 sample tests using the KS test and the Wilcoxon Rank Sum test. Drawing 2 samples of various sizes from unit Normal ...
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28 views

Adapt Kolmogorov-Smirnov Test to Lilliefors Test

I'm using EasyFit to fit distributions to a sample of data and test with the Kolmogorov-Smirnov test whether the null hypothesis may be rejected or not. But as this test estimates the parameters from ...
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42 views

Fitting Data with Ties Using unique() Walk-Around and ks.test

I'm looking for a distribution that best fits my data. Looking at the frequency plot, seems like the distribution could follow a Gamma or Weibull distribution. With that in mind, I use the ...
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58 views

KS, RMSE tests in R

I have a set of yearly peak river flows and I am trying to use the KS test to conclude if the data is coming from a generalized extreme value (GEV) distribution. I am also trying to calculate a root ...
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Using KS test to evaluate differences

There are two different empirical CDFs which I have and I would like to evaluate how different they are. The place at which I started was Kolmogorov-Smirnov test - the result in my case looks like ...
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50 views

Efficient statistical test to compare two multivariate distributions

I am looking for a test to assert the "equality" of two multivariate discrete distributions, $\mathbf{A}=\{A_1,\dots,A_k\}$ and $\mathbf{B}=\{B_1,\dots,B_k\}$ for which I do observe two samples ...
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1answer
40 views

Test to compare distributions using the intersection area of the densities

I have to compare several distributions, but I don't want to use Kolmogorov-Smirnov test, since I'm dealing with big data ($N > 10^{6}$) and traditional hypothesis tests end up with detecting the ...
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57 views

Two dimensional Kolmogorov-Smirnov test

For a one dimensional Kolmogorov-Smirnov test there is a theoretical result, one can compare his or her test results directly by theoretical one, which is infinite sum (notice this formula is for big ...
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1answer
194 views

KS-test - how is the p-value calculated?

How is the p-value calculated in Kolmogorov-Smirnov test? What's the formula for it? I suspect it's derived based on the definition of p-value. The value of test statistic is the largest differnece ...
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9 views

Distribution testing in presence of variable noise

I have a number of integer data points $x_1, ..., x_n \in \{0, 1, \dots\}$ and would like to test whether they belong to a certain distribution discrete distribution. For this purpose, it seems that ...
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45 views

Statistically compare differences between output probabilities of two trained models

I'm using two classification models that compute output probabilistic for my out-of-sample data (MLP and SVM). I want test that ...
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20 views

How can I express $D_{m,n}$ as a distribution free statistic in terms of $d_l$

Consider 2-sample problem with m and n observations from the mutually independent, absolutely continuous populations $F_X$ and $F_Y$, respectively, define 2-sided kolmogorov-smirnov statistics ...
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Do Dvoretzky–Kiefer–Wolfowitz bounds and Kolmogorov-Smirnov test different hypotheses?

This question is related to my previous question that was answered excellently by Matt Krause. I am trying to compare two data vectors to find out if they come from the same distribution. I computed ...
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73 views

Computing Dvoretzky–Kiefer–Wolfowitz bounds in MATLAB

When I run the Kolmogorov-Smirnov test (kstest2 function in MATLAB) on two given data vectors, I get the value of KS Statistic. How should I compute Dvoretzky–Kiefer–Wolfowitz (DKW) bound using this ...
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Statistical test to check if mean of two groups are “significantly” same [duplicate]

Is there a statistical test, to check mean of two group is "sigificantly" same. Something opposite to Wilcoxon test. I was thinking may be running Wilcox test and if it not significant, then check the ...
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Reference request: Using randomized interpolation to apply KS-Test to discrete distributions

I'm dealing with $n$ samples $X_1,\ldots,X_n$ from $n$ different (but related) distributions with CDFs $F_n$. If all the distributions were continuous, I could use the transformation $U_i := ...
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Comparing distributions from a factorial design

I have the following experimental design: I have six animals, where three received treatment and the other three were used as control (so treatment and control animals are not paired). From each of ...
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353 views

Can you calculate the power of a Kolmogorov-Smirnov test in R?

Is it possible to do a power analysis for a 2-sided Kolmogorov Smirnov test in R? I am testing whether two empirical distributions differ using ks.test(), and am looking to add a power analysis. I ...
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Proof of Kolmogorov-Smirnov test

Could someone provide me a reference, preferably a book, where I can find detailed proofs and explanations of the Kolmogorov-Smirnov test (including the two-sample variant) and the derivation of the ...
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1answer
474 views

Can I use Kolmogorov Smirnov test to check if my data are uniformly distributed?

I'd like to check if distribution of my data is significantly different from a uniform distribution. I know that the K-S test is used for checking the normality of data, but I wonder if it can be ...
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2answers
171 views

Interpretation P value one sample KS test

I have some difficulties with understanding the output of the KS test in R. Suppose I want to test whether my data follows a exponential distribution with rate 1/117.5 with a significance level ...
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Comparing two distribution known by their deciles

I am trying to compare a travel time measuring device with a reference device. The assessed device only provide the decile (+min and max values) and not all the measured individual travel time. I am ...
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72 views

Does the position at which maximum distance occurs in a KS test make a difference?

From my understanding of the KS test, fromt the CDF of two datasets, it measures the distance between the two distributions at various points and and compares the 'maximum distance' to a predefined ...
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468 views

How do you interpret Kolmogorov-Smirnov Test results in R?

I'm using 50,000 values of data. I can't perform a K.Wallis test in R because my data amount is bigger than 5000. Therefore I considered to use Kolmogorov-Smirnov test. I guess that my data follows a ...
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2answers
112 views

Meaning of significance level and critical values for kolmogorov smirnov goodness of fit test

I'm new to using goodness of fit tests and am encountering what I guess is a beginners misunderstanding of how the tables for critical values and different significance levels have to be read. I have ...
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2answers
127 views

Low p-value in test of uniformity of uniformly distributed data?

First we generated 10 numbers from a $U(0,1)$ then performed a Kolmogorov Smirnov test for q uniform distribution. Why is the p-value small? ...
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When KL Divergence and KS test will show inconsistent results?

I know that Kullback–Leibler divergence and Kolmogorov–Smirnov test are differnt and should be used in different scenarios. But they are similar in many ways and given two distributions, we could ...
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270 views

Reproducibility of the two-sample Kolmogorov–Smirnov test

I am using the two-sample Kolmogorov–Smirnov test to check if two datasets have the same underlying distribution. I can regenerate those two datasets as many times as I want. When I apply the test, ...
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Kolmogorov-Smirnov test: horizontal variant?

The Kolmogorov Smirnov test is based on the maximum vertical distance between the ECDFs of two provided samples. Is there a variant that checks the maximum horizontal distance?
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39 views

Compare cumulative distribution functions of several function point counters

Function point counters are used to measure the size of software. However, they are believed not to deliver exact results. Different measurements sometimes produce different results. The performance ...