Creating a Cumulative Distribution Function (CDF) as a Plotly Object in R

In this article, we will explore how to create a cumulative distribution function (CDF) using plotly in R. We will delve into the reasons behind the disappearance of CDF endpoints when converting a ggplot object to a plotly object and provide solutions to this problem.

Introduction to Cumulative Distribution Functions

A cumulative distribution function is a mathematical function that describes the probability distribution of a random variable. It is defined as the ratio of the probability that the random variable takes on a value less than or equal to x to 1. In other words, it represents the proportion of values in a dataset that are less than or equal to a given value.

Using ggplot2 and stat_ecdf()

The stat_ecdf() function in ggplot2 is used to create a CDF plot from a dataset. This function automatically detects the minimum and maximum values in the dataset and creates a CDF curve based on these values.

However, when we convert this ggplot object to a plotly object using ggplotly(), the CDF endpoints disappear. To understand why this happens, let’s look at the code:

library(ggplot2)

new_data <- iris %>% arrange(Petal.Length)

gg <- ggplot(data = new_data, aes(x = Petal.Length, color = Species)) + stat_ecdf()

ggplotly(gg)

The Problem: Infinite X-axis Values

The problem arises from the fact that stat_ecdf() generates a CDF curve over the entire range of values in the dataset. This results in infinite x-axis values, which are then dropped when converting the ggplot object to a plotly object.

Solution: Manipulating the Data

To solve this problem, we need to manipulate the data to limit the range of values for which the CDF is calculated. One way to do this is by specifying a fixed range for the x-axis values using arrange() and then creating a new dataset that only includes these limited values.

Here’s an example:

xmin <- 0
xmax <- 7

gg2 <- new_data %>% 
  group_by(Species) %>% 
  summarise(y = sapply(seq(xmin, xmax, 0.1), function(x) ecdf(Petal.Length)(x)),
            Petal.Length = seq(xmin, xmax, 0.1)) %>%
  ggplot(aes(Petal.Length, y, color = Species)) +
  geom_step()

Creating a Custom CDF Plotly Object

With the manipulated data, we can now create a new CDF plot using geom_step():

gg2 <- new_data %>% 
  group_by(Species) %>% 
  summarise(y = sapply(seq(xmin, xmax, 0.1), function(x) ecdf(Petal.Length)(x)),
            Petal.Length = seq(xmin, xmax, 0.1)) %>%
  ggplot(aes(Petal.Length, y, color = Species)) +
  geom_step()

This creates a new CDF plot with limited x-axis values and correctly displays the CDF endpoints.

Converting to Plotly

To convert this custom CDF plot to a plotly object, we can use ggplotly():

ggplotly(gg2)

This produces a plotly object that accurately displays the CDF endpoints.

Conclusion

Creating a cumulative distribution function as a plotly object in R requires understanding of the underlying mathematics and data manipulation techniques. By limiting the range of values for which the CDF is calculated, we can ensure accurate display of CDF endpoints in both ggplot2 and plotly objects.

We have demonstrated how to create custom CDF plots using ggplot2 and then convert them to plotly objects using ggplotly(). This solution provides a reliable way to visualize cumulative distribution functions using R’s popular data visualization libraries.

Last modified on 2024-12-01