# How to use rt() in R to generate values for Student’s t distribution

The student’s t distribution, also simply known as t distribution, is remarkably easy to work with in the R programming language. In fact, you can implement it in your R code with a single function – rt. However, there’s still more to using rt() in R than simply calling the function and applying the results within your code. But you’re about to discover how to use rt in R and how to apply it to misclassification rates in machine learning.

## Starting Out With the Foundational Concepts

Before working with actual code it’s best to define a few concepts. Most importantly, the student’s t distribution itself. The distribution is a method to determine probabilities based on smaller sample sizes with unknown standard deviations. In other words, it’s an extremely useful method of probability distribution to help you get the most out of limited resources.

It’s also extremely easy to use in R. Take a look at the following code.

ourTval <- rt(50, df = 5)
print(ourTval)

As you can see, this complex student t-distribution calculation is done with just a single call to rt. Following that, it prints the result to the screen. But take note of the arguments passed in rt. We have three main arguments when calling the rt function. The first is n, which is the number of observations. In this case we’re going with an n-value of 50. Next is degrees of freedom. This defines the shape of our distribution. We move closer to a bell curve as the df increases.

Degrees of freedom is as discussion unto itself. But in this example, we’re going with a value of 5 simply to illustrate the use of rt. In real-world situations the df value will be largely determined by the context of your usage scenario. For example, in a one-sample t-test you’d typically want to set the df at your sample size minus one. This is because the sample mean is excluded from the data.

Finally, rt also accepts an optional non-centrality parameter. As the name suggests it’s primarily used when working with a non-central t-distribution. The ncp value doesn’t need to be supplied for a standard t-distribution. As such we just pass the 50 and 5. Keep in mind that this is a simple example, but it can operate as a foundation for more complex operations. For example, working with misclassification rates.

Misclassification rates, or error rates, measure the proportion of false predictions within the full pool of generated values. This helps to act as a metric for classification model evaluation and identification. For example, when calculating a t-distribution you might have two models and want to compare their performance. You can perform this process in different ways to generate usable values based on your own predefined metrics. You can then run a trial on different implementations.

In doing so you’ll be able to judge the overall efficiency of different approaches. This is especially useful in the context of machine learning since results aren’t always going to be self-apparent at first glance. You can easily judge the results of a simple calculation within a function. But it’s a different thing entirely when you’re trying to judge a model’s work on datasets that are far too massive for any human to wrap his mind around. This is why automated testing is so important. You can calculate misclassification rates using those same tools and techniques. This can point out where you might have made an error, where code can be tweaked, or just which implementation is inherently superior for any given task.

## Tying It All Together

The concept of misclassification rates in machine learning might seem intimidatingly complex at first glance. And it’s true that misclassification rates are a large subject with many, many, different permutations. But creating a simple implementation of misclassification testing into the context of t-distribution in R is surprisingly easy. For example, consider a situation where you’ve generated data and want to test it against student’s t distribution to measure the misclassification rate. Take a look at the following code to see just how simple the process can be.

ourTrialVal <- 50
ourDegreesOfFreedom <- 5
ourTval <- rt(ourTrialVal, df = ourDegreesOfFreedom)
normalizedTvalues <- (ourTval – min(ourTval)) / (max(ourTval) – min(ourTval))
hist(normalizedTvalues, main = “Our Misclassification Readout”, xlab = “Rate”, ylab = “Frequency”)

We begin by setting a few parameters. We retain 50 as the observation n-value. And the same goes for the degrees of freedom with ourDegreesOfFreedom. Next, we keep to the previous order of logic in running rt against those two variables. As in the previous example, we once again assign the result to ourTval. But things differ when we get to the next line. We normalize the t-value in order to create a simulated misclassification rate. This would of course be a naturally derived value in real-world situations. But for the purpose of creating an example, we’ll simply run our data through this sequence. Finally, we create a histogram from the results.

Again though, it’s important to keep in mind that both t-distribution and misclassification rates are significant topics with an equally varied range of applications within the R programming language. The prior examples highlight the foundational elements of both. But R can leverage them with a wide variety of other concepts and tools to open up a treasure trove of advanced data analysis techniques.

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