In Julia, there are multiple ways to create a histogram such that the sum of bar heights is 1. In this article, we will explore three different approaches to achieve this.
Approach 1: Using the `normalize` parameter
The `Plots` package in Julia provides a convenient way to create histograms. By default, the `histogram` function normalizes the bar heights such that the area under the histogram is equal to 1. We can use this feature to ensure that the sum of bar heights is 1.
using Plots
data = randn(1000) # Sample data
histogram(data, normalize=true)
This code snippet generates a histogram of the `data` array with normalized bar heights. The resulting histogram will have a sum of bar heights equal to 1.
Approach 2: Manually normalizing the bar heights
If you prefer more control over the normalization process, you can manually normalize the bar heights using the `normalize` function from the `Statistics` module.
using Plots
using Statistics
data = randn(1000) # Sample data
hist = histogram(data, normalize=false) # Create histogram without normalization
bar_heights = hist.weights # Get the bar heights
normalized_heights = normalize(bar_heights, 1) # Normalize the bar heights to sum up to 1
hist.weights = normalized_heights # Update the histogram with the normalized heights
plot(hist)
In this code snippet, we first create a histogram without normalization using the `normalize=false` parameter. Then, we extract the bar heights using the `weights` property of the histogram object. Next, we normalize the bar heights using the `normalize` function, specifying the desired sum of 1. Finally, we update the histogram object with the normalized heights and plot it.
Approach 3: Scaling the bar heights
Another approach to achieve a sum of bar heights equal to 1 is by scaling the bar heights. We can divide each bar height by the sum of all bar heights and multiply by 1.
using Plots
data = randn(1000) # Sample data
hist = histogram(data, normalize=false) # Create histogram without normalization
bar_heights = hist.weights # Get the bar heights
scaled_heights = bar_heights ./ sum(bar_heights) * 1 # Scale the bar heights
hist.weights = scaled_heights # Update the histogram with the scaled heights
plot(hist)
In this code snippet, we follow a similar approach as in Approach 2. After obtaining the bar heights, we divide each bar height by the sum of all bar heights and multiply by 1 to scale the heights. Finally, we update the histogram object with the scaled heights and plot it.
Among the three options, Approach 1 using the `normalize` parameter is the simplest and most straightforward. It allows us to create a histogram with normalized bar heights and a sum of 1 in a single line of code. Therefore, Approach 1 is the recommended option for creating a histogram with a sum of bar heights equal to 1 in Julia.
