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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Finding the probability of normality via Anderson-Darling, Shapiro-Wilk , and Kolomogrov-Smirov

I have quite a few distributions that were generated by some system, and I am trying to find the probability of accordance to normality for these distributions. So, the probability of accordance to ...
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Which test is better suited to compare averaged versus single data sets

I have a light curve, that is photon count rate versus time, of an astronomical object. These data are periodic, since the source signal is periodic. I can fold the data with the period and obtain an ...
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Generalization of one-sample Kolmogorov-Smirnov test for non identically distributed data?

Is there a standard approach for testing goodness-of-fit to a probability distribution when the samples are independent but not identically distributed? In other words, given the data $\{\{x_1, y_1\}, ...
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42 views

how do normality check in ks test assess for equivalence or difference in data sets?

I have a series of data of photon counts versus time. These data are periodic, then I can fold them and obtain an average profile of the data. Nonetheless, some variations appear sometime in the ...
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Mann-Whitney U and KS tests in R are not producing significant results [duplicate]

I wish to compare two test data sets using the Mann-Whitney U and KS tests in R. As a start, I thought to compare two similar sets (an A/A test) expecting to see a highly significant indication of ...
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42 views

PIT on a sample with m bins, and KS test used to estimate a good value for m

I know about PIT, but this works only when you know the distribution, or at least have a strong hint. What I am trying to achieve is to transform a given sample into an equivalent sample with ...
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27 views

In testing random numbers, what other tests should I use to complement the Kolmogorov-Smirnov? [duplicate]

I'm using the Kolmogorov-Smirnov test to test a random number generator. I'm wondering if there are other tests that I should implement as well. So far, I've looked at the equidistribution and serial ...
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55 views

Kolmogorov-Smirnov test for large sample [duplicate]

I am investigating if an exponential distribution is a good fit for a large sample of data (200) I have. I have already looked at a histogram but was wanting to investigate further. I was going to use ...
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70 views

How to guess a curve distribution from count data

I have a sample composed by 2500 count data values. I've plotted in R the corresponding histogram and ecdf. I've run the One-Sample Kolmogorov-Smirnov test to check if the distribution is either ...
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20 views

goodness of fit for censored data

How to estimate the goodness of fit of a sample containing censored values? There is some older work on the matter (here), but i'd like to know if there is anything more modern. I think a reasonable ...
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15 views

How to test if a value is over-represented in one sample vs another

I have two multinomial data samples that both have N discrete categories. I know that a Kolmogorov-Smirnov test will let me know if the distributions of the two ...
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33 views

Kolmogorov-Smirnov with parameter estimates

Can someone explain in as clear a (formalish mathematical) way as possible why the KS test in original form with parameter estimates is unreliable?
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Test for difference between 2 empirical discrete distributions

I have test data where I have several large samples from discrete distributions which I am using as empirical distributions. I am wanting to test whether the distributions are actually different and ...
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29 views

Is it meaningful to use Kolmogorov-Smirnov test in small sub sample?

I have a data set with around 14,000 observations. This is a sample data set not the population. I have fitted a model (based on fuzzy logic) based on this data. I have 27 actual values(from 14,000 ...
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35 views

Convergence of Empirical cumulative distribution functions?

I am exploring the cumulative distribution function of two samples. I am comparing the distribution of observations in which a focal animal was disturbed with the distribution of observations in which ...
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147 views

Kolmogorov-Smirnov test?

I am studying disturbance caused by ship traffic to a small seabird. I observed focal animals for a set amount of time and record whether or not they fly from the water during the observation. This ...
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3answers
704 views

Which to believe: Kolmogorov-Smirnov test or Q-Q plot?

I'm trying to determine if my dataset of continuous data follows a gamma distribution with parameters shape $=$ 1.7 and rate $=$ 0.000063. The problem is when I use R to create a Q-Q plot of my ...
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149 views

Evaluating goodness of fit for distributions (e.g. LogNorm, Gamma, …) with estimated parameters using KS tests (and R)

Currently I am trying to find a well-known distribution that fits to my positive skewed dataset (n=70) the best. First I used the fitdistrplus R package to estimate ...
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54 views

Is it possible to calculate the probability that two samples are drawn from the same distribution?

Given $X_1$..$X_n$ and $Y_1$..$Y_n$ drawn from unknown distributions $F(x)$ and $G(x)$ respectively, statistical tests such as two-sample Kolomogorov-Smirnov, Cramer-von Mises, and Anderson-Darling ...
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65 views

Interpretation and usage of Kolmogorov-Smirnov Test in Python

I have a sample of data, and I want to know weather it is Gaussian-distributed or not. The mean of my data is not zero. To check weather I'm using the K-S test correct, I generated some ...
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27 views

Kolmogorov-Smirnov test using half the sample to estimate mean and variance and testing against the other half moments for normality

using a monte carlo simulation Im just trying to test the null hypothesis for normality in a sample that splits N values into 2, using the first N/2 values to estimate the sample mean and variance, ...
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153 views

Small sample sizes and the Kolmogorov-Smirnov test

I have split my data set into four categories but one of them only has four data points in it. I have run K-S normality tests on the other three categories which are each normal and when the data ...
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87 views

Is a p-value correction necessary for assessing pairwise location shifts on centered data?

I am currently assessing whether or not a location-shift can be assumed in non-parametric comparisons to be able to formulate the rejection of the null hypothesis in other terms than the probabilistic ...
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131 views

How to compare two samples of frequencies with categorical x values where one is subset of the other

I am trying to compare two arrays of frequencies. The second is a subset of the first. I want to know if the second is a representative of the first. The arrays are: ...
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70 views

Similarity between two sets of random values

I have two sets of random floats between [0,1], each one with a different number of elements: $$A = \{0.3637852, 0.2330702, 0.1683102, 0.2127219, 0.0152532, ..., N_A\}$$ $$B = \{0.4541056, 0.7521812, ...
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Determining which pair of empirical distributions is the most similar

I'm looking at three discrete (seven-option) survey questions that were asked on two different surveys (100 < N < 150 for each question). I've paired up the six answer distributions so that each ...
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Explain the meaning of $\alpha$ in a Kolmogorov-Smirnov two-sample test

The Wikipedia article on the two-sample Kolmogorov-Smirnov test states that: The Kolmogorov–Smirnov test may also be used to test whether two underlying one-dimensional probability distributions ...
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83 views

Calculating the Kolmogorov-Smirnov coefficient

I need to calculate the coefficient of the Kolmogorov-Smirnov test for any given null hypothesis rejection level. For example, have a look at the table in this wikipedia entry. It only gives ...
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199 views

Kolmogorov-Smirnov test strange output

I am trying to fit my data to the one of the continuous PDF (I suggest it to be gamma- or lognormal-distributed). The data consists of about 6000 positive floats. But the results of the ...
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300 views

What is the test statistic in Kolmogorov–Smirnov test?

I am reading the Wikipedia page on the Kolmogorov-Smirnov test, specifically the section titled Kolmogorov_distribution. $x$ is $D_\text{max}$ in the CDF $Pr(k\leq x)$? My question is the number of ...
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115 views

How can the Kolmogorov-Smirnov test be used/interpreted?

The test of Kolmogorov-Smirnov (K-S) is a traditional test of normality, although Shapiro-Wilk test (S-W) is applied more frequently than K-S (Arango, 2012). I am not an expert in statistics, so my ...
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How to ´check if two (ergodic) distributions statistically differ (in R)

I need to check if two ergodic distributions statistically differ. I know about the Kolmogorov - Smirnov test. However, being the ergodics computed as in Feyrer (2003), Convergence by parts, I do not ...
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132 views

How to use ks test for 2 vectors of scores in python?

I am trying to figure out how to determine whether to reject or not the null hypothesis using ks-test. In matlab there is a function named kstest2 decides if it should reject $H_0$. I want to use ...
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What is the definition of one-sample Kolmogorov–Smirnov test?

I have a time series data set of photon arrival times from a detector and need to know whether the arrival time is uniform.It is a continuous distribution? I have calculated the maximum $D$ between ...
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how to derive Kolmogorov distribution $K_\alpha$ for big n?

The Kolmogorov–Smirnov test rejects the null hypothesis at level $\alpha$ if $$\sqrt{n}D_n>K_\alpha$$ where $$D_n=\sup_x |{F}_n(x)-F(x)| $$, and $$\operatorname{Pr}(K\leq K_\alpha)=1-\alpha$$ ...
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Interpretation of Kolmogorov-Smirnov Generated Distributions [duplicate]

Note that this question is posted in Cross Validated but as of this writing have received no replies. As a non-statistician, I need help in interpreting a distribution generated from KS. A customer ...
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Interpretation of Kolmogorov-Smirnov Critical Value Generated Distributions

As a non-statistician, I need help in interpreting a customer specified two-part reliability requirement that I think involves KS. Requirement Part 1 R[4 years] must be greater than or equal to 0.95 ...
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Advice on comparing methods of generating random vectors

I'm researching a method for sampling uniformly from an $n$-dimensional shape, for which conventional rejection sampling may be too slow. I am generating 1,000 points using each method, and wish to ...
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132 views

What are some Bayesian alternatives to the Kolmogorov-Smirnov test?

What are some Bayesian ways to see if two empirical distributions come from the same data-generating process? Are any of the Bayesian alternatives implemented in Matlab/R/Python?
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193 views

Best way to test runs

I have the following sample: ...
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Kolmogorov-Smirnov test with estimated parameters

I've read through some past posts about using the KS test when the distribution parameters are estimated. This one in particular was very helpful, and I implemented Greg Snow's suggestion. However, I ...
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132 views

How can I compare two ecdfs for p-values from Kolmogorov Smirnov tests if the number of samples in the two tests are different?

The plot below shows the ecdf of the p-values from to different statistics, let us identify the blue graph as vector x and the red graph as vector y. Now I execute a ks.test for x and y compare these ...
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Assumptions of two-way ANOVA and k-fold cross validation

I want to compare 3 classifiers (kNN, SVM and CT) by using their classification accuracies on 10 folds, to highlight eventual differences between them. I think it could be done by a two-way ANOVA ...
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Test Markov Chain properties of time series

First of all, please excuse if I don't use the proper terminology for this problem. I have a markov chain composed by two states: When in state 1 the output is drawn from an exponential ...
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262 views

Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data

I need to compare whether two distributions are similar when the values are scaled by the mean of each of the distribution. One limitation of ks-test as per ...
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204 views

Implementing a Kolmogorov-Smirnov permutation test

I would like some advice on how to implement a Kolmogorov-Smirnov test. This is a condensed version of my previous question -- any further detail can be provided if needed. I have data from n ...
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Quantifying a difference in probability densities

There is a range of values (V) that I'm using to calibrate a model. I'm performing a sensitivity analysis on different calibration objectives. One calibration objective, A, selects from V such that I ...
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One-sample KS test's D-statistic peculiarity in R

First of all, let me explain what I'm after. I have a bunch of archaeological sites (point data) in GIS and a DEM-derived slope map. I classified the slope map into 1-degree interval classes and got ...
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Comparing multiple datasets from a controlled experiment

I have a system to which I make certain changes. I want to compare the impact of those changes on the system performance. For this, I record the performance as a function of a set of inputs multiple ...
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71 views

Choice of a non-parametric method

I want to compare the delays of packets belonging to some kind of traffic to the delays of packets belonging to some other (different and larger) traffic, all generated from the same machine. I would ...