# Wilcoxonank Sum Statistic Distribution in R (4 Examples) | dwilcox, pwilcox, qwilcox & rwilcox Functions

This article illustrates how to **apply the Wilcoxonank Sum Statistic functions** in the R programming language.

The table of content is structured as follows:

- Example 1: Wilcoxonank Sum Statistic Probability Density Function (dwilcox Function)
- Example 2: Wilcoxonank Sum Statistic Cumulative Distribution Function (pwilcox Function)
- Example 3: Wilcoxonank Sum Statistic Quantile Function (qwilcox Function)
- Example 4: Generating Random Numbers (rwilcox Function)
- Video & Further Resources

Let’s dive into it.

## Example 1: Wilcoxonank Sum Statistic Probability Density Function (dwilcox Function)

The following R code shows how to draw a graph illustrating the probability density function (PDF) of the Wilcoxonank Sum Statistic:

x_dwilcox <- seq(0, 100, by = 1) # Specify x-values for dwilcox function y_dwilcox <- dwilcox(x_dwilcox, m = 50, n = 20) # Apply dwilcox function plot(y_dwilcox, type = "o") # Plot dwilcox values |

x_dwilcox <- seq(0, 100, by = 1) # Specify x-values for dwilcox function y_dwilcox <- dwilcox(x_dwilcox, m = 50, n = 20) # Apply dwilcox function plot(y_dwilcox, type = "o") # Plot dwilcox values

**Figure 1: PDF of Wilcoxonank Sum Statistic.**

## Example 2: Wilcoxonank Sum Statistic Cumulative Distribution Function (pwilcox Function)

This example explains how to draw a graphic of the cumulative distribution function (CDF) of the Wilcoxonank Sum Statistic:

x_pwilcox <- seq(0, 100, by = 1) # Specify x-values for pwilcox function y_pwilcox <- pwilcox(x_pwilcox, m = 50, n = 20) # Apply pwilcox function plot(y_pwilcox, type = "o") # Plot pwilcox values |

x_pwilcox <- seq(0, 100, by = 1) # Specify x-values for pwilcox function y_pwilcox <- pwilcox(x_pwilcox, m = 50, n = 20) # Apply pwilcox function plot(y_pwilcox, type = "o") # Plot pwilcox values

**Figure 2: CDF of Wilcoxonank Sum Statistic.**

## Example 3: Wilcoxonank Sum Statistic Quantile Function (qwilcox Function)

This example shows how to create a graphic of the quantile function of the Wilcoxonank Sum Statistic:

x_qwilcox <- seq(0, 1, by = 0.01) # Specify x-values for qwilcox function y_qwilcox <- qwilcox(x_qwilcox, m = 50, n = 20) # Apply qwilcox function plot(y_qwilcox, type = "o") # Plot qwilcox values |

x_qwilcox <- seq(0, 1, by = 0.01) # Specify x-values for qwilcox function y_qwilcox <- qwilcox(x_qwilcox, m = 50, n = 20) # Apply qwilcox function plot(y_qwilcox, type = "o") # Plot qwilcox values

**Figure 3: Quantile Function of Wilcoxonank Sum Statistic.**

## Example 4: Generating Random Numbers (rwilcox Function)

The last example illustrates how to generate random numbers according to the Wilcoxonank Sum Statistic:

set.seed(98989) # Set seed for reproducibility N <- 100000 # Specify sample size y_rwilcox <- rwilcox(N, m = 50, n = 20) # Draw N random values y_rwilcox # Print values to RStudio console hist(y_rwilcox, # Plot of randomly drawn density breaks = 50, main = "") |

set.seed(98989) # Set seed for reproducibility N <- 100000 # Specify sample size y_rwilcox <- rwilcox(N, m = 50, n = 20) # Draw N random values y_rwilcox # Print values to RStudio console hist(y_rwilcox, # Plot of randomly drawn density breaks = 50, main = "")

**Figure 4: Random Number According to Wilcoxonank Sum Statistic.**

## Video & Further Resources

I have recently released a video instruction on my YouTube channel, which shows the R codes of this tutorial. You can find the video below:

*The YouTube video will be added soon.*

You might also have a look at the other tutorials on distributions and the simulation of random numbers in R:

- Bernoulli Distribution in R
- Beta Distribution in R
- Binomial Distribution in R
- Bivariate & Multivariate Distributions in R
- Cauchy Distribution in R
- Chi-Squred Distribution in R
- Exponential Distribution in R
- F Distribution in R
- Gamma Distribution in R
- Geometric Distribution in R
- Hypergeometric Distribution in R
- Log Normal Distribution in R
- Logistic Distribution in R
- Negative Binomial Distribution in R
- Normal Distribution in R
- Poisson Distribution in R
- Student t Distribution in R
- Studentized Range Distribution in R
- Uniform Distribution in R
- Weibull Distribution in R
- Wilcoxon Signedank Statistic Distribution in R
- Wilcoxonank Sum Statistic Distribution in R

Additionally, you may want to read the related tutorials of my website:

This article explained how to **use the dwilcox, pwilcox, qwilcox, and rwilcox functions** in the R programming language. Don’t hesitate to tell me about it in the comments, in case you have further questions.

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