What is Kolmogorov-Smirnov Test?

What is Kolmogorov-Smirnov Test?

Kolmogorov–Smirnov Test is a completely efficient manner to determine if two samples are significantly one of a kind from each other. It is normally used to check the uniformity of random numbers. Uniformity is one of the maximum important properties of any random number generator and the Kolmogorov–Smirnov check can be used to check it....

Kolmogorov Distribution

The Kolmogorov distribution, often denoted as D, represents the cumulative distribution function (CDF) of the maximum difference between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution....

How does Kolmogorov-Smirnov Test work?

Below are the steps for how the Kolmogorov-Smirnov test works:...

When use Kolmogorov-Smirnov Test?

The main idea behind using this Kolmogorov-Smirnov Test is to check whether the two samples that we are dealing with follow the same type of distribution or if the shape of the distribution is the same or not....

One Sample Kolmogorov-Smirnov Test

The one-sample Kolmogorov-Smirnov (KS) test is used to determine whether a sample comes from a specific distribution. It is particularly useful when the assumption of normality is in question or when dealing with small sample sizes....

Kolmogorov-Smirnov Test Python One-Sample

Python3 import numpy as npfrom scipy.stats import norm, kstest # Step 1: Generate a sample from a normal distributionnp.random.seed(42)sample_size = 100mean = 0std_dev = 1sample = np.random.normal(mean, std_dev, sample_size) # Step 2: Compute the Empirical Distribution Function (EDF)def empirical_distribution_function(x, data):    return np.sum(data <= x) / len(data)edf_values = [empirical_distribution_function(x, sample) for x in sample] # Step 3: Define the Reference Distributionreference_cdf = norm.cdf(sample) # Step 4: Calculate the Kolmogorov–Smirnov Statisticks_statistic, ks_p_value = kstest(sample, 'norm') # Step 5: Comparingalpha = 0.05critical_value = 1.36  # This value can be obtained from the Kolmogorov-Smirnov table for a specific significance level print(f"Kolmogorov-Smirnov Statistic: {ks_statistic}")print(f"P-value: {ks_p_value}") if ks_statistic > critical_value or ks_p_value < alpha:    print("Reject the null hypothesis. The sample does not come from the specified distribution.")else:    print("Fail to reject the null hypothesis. The sample comes from the specified distribution.")...

Two-Sample Kolmogorov–Smirnov Test

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Kolmogorov-Smirnov Test Python Two-Sample

The two-sample Kolmogorov-Smirnov (KS) test is used to compare two independent samples to assess whether they come from the same distribution. It’s a distribution-free test that evaluates the maximum vertical difference between the empirical distribution functions (EDFs) of the two samples....

One-Sample KS Test vs Two-Sample KS Test

The null hypothesis assumes that the two samples come from the same distribution.The decision is based on comparing the p-value with a chosen significance level (e.g., 0.05). If the p-value is less than the significance level, reject the null hypothesis, indicating that the two samples come from different distributions....

Multidimensional Kolmogorov-Smirnov Testing

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Conclusion

One-Sample KS Test Two-Sample KS Test Employed to assess whether a single sample of data conforms to a specific theoretical distribution. Utilized to evaluate whether two independent samples originate from the same underlying distribution. Compares the (EDF) of the sample with the (CDF) of the theoretical distribution. It compares the EDF of one sample with the EDF of the other sample. Null hypothesis assumes that the sample is drawn from the specified distribution. Null hypothesis posits that the two samples are drawn from identical distributions. Test statistic, represents the maximum vertical deviation between the EDF and CDF. The test statistic, reflects the maximum difference between the two EDFs....

Kolmogorov-Smirnov test- FAQs

The Kolmogorov-Smirnov (KS) test, in its traditional form, is designed for one-dimensional data, where it assesses the similarity between the empirical distribution function (EDF) and a theoretical or another empirical distribution along a single axis. However, when dealing with data in more than one dimension, the extension of the KS test becomes more complex....