Download the R code: https://www.data03.online/2023/09/how-i-use-ks-test-in-r.html

KS tests are statistical tests that help determine whether two datasets follow the same probability distribution. Let’s break down each part of the code step by step:

Generating a Sample from a Normal Distribution:

In this section, a random sample of 100 numbers is generated from a normal distribution with a mean of 0 and a standard deviation of 1. The set.seed(123) line is used to ensure that the random numbers generated are the same each time you run the code, making the results reproducible.

Performing a KS Test on the Normal Data:

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  x
## D = 0.093034, p-value = 0.3522
## alternative hypothesis: two-sided

This part of the code performs a KS test on the sample x to check if it follows a standard normal distribution. The ks.test function compares the sample data to the cumulative distribution function (CDF) of the standard normal distribution (pnorm). It assesses whether the data significantly deviates from this reference distribution.

Generating a Sample from an Exponential Distribution:

In this section, another sample of 100 numbers is generated, but this time from an exponential distribution with a rate parameter of 0.5. The set.seed(456) line similarly ensures reproducibility.

Estimating the Rate Parameter from the Exponential Sample:

Here, the code calculates an estimated rate parameter (lambda) for the exponential distribution. It does so by taking the reciprocal of the mean of the x sample. This estimate is used in the subsequent KS test.

Performing a KS Test on the Exponential Data:

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  x
## D = 0.071555, p-value = 0.6852
## alternative hypothesis: two-sided

This part conducts a KS test on the x sample, comparing it to the cumulative distribution function of an exponential distribution (pexp). It also includes the estimated rate parameter (lambda) as an additional argument to the test. This helps determine if the sample follows an exponential distribution with the estimated rate.

Testing Whether Two Samples Have the Same Distribution:

## 
##  Exact two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.23, p-value = 0.05551
## alternative hypothesis: two-sided

In this final example, two different samples (x and y) are generated. One follows a uniform distribution between 0 and 1, while the other follows a beta distribution with specific shape parameters. The code then performs a KS test to determine if these two samples have the same distribution.

In summary, the code provided demonstrates how to generate random samples from different probability distributions (normal, exponential, uniform, and beta) and perform KS tests to check if these samples follow specific distributional assumptions. The KS test results will indicate how closely the data matches the specified distributions.