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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Plot Pareto tails in QQ-plot for log-normal distributions

I'm working on samples that I'm trying to fit into log-normal distributions. In some cases, Kolmogorov-Smirnov test statistics is something like D = 0.0056 with an associated p-value of 0. Hence, my ...
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19 views

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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102 views

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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1answer
45 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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15 views

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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1answer
43 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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1answer
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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72 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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21 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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1answer
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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1answer
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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2answers
60 views

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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0answers
30 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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1answer
152 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
716 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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157 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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1answer
68 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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156 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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1answer
90 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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73 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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1answer
70 views

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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86 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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1answer
201 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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1answer
312 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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1answer
116 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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61 views

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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1answer
141 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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290 views

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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29 views

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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367 views

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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63 views

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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1answer
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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209 views

Best way to test runs

I have the following sample: ...
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137 views

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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68 views

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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266 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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206 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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26 views

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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396 views

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 ...