R Tutorial: Gaussian distribution

Want to learn more? Take the full course at https://learn.datacamp.com/courses/mixture-models-in-r at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- In the last lesson, we actually fit a mixture of two Gaussian, or normal, distributions. Here are the real gender labels of each observation and also the areas depicted by the ellipses, which represent where the most probable zones are to find each subpopulation according to the fitting. Since mixture models are based on probability distributions, in this lesson we'll start by studying one of the most famous, the Gaussian, before diving back into the structure of a mixture model in Chapter 2. It is worth saying that this lesson is not an exhaustive cover of the Gaussian distribution, but rather a reference for the Mixture Models. First, though, let's comment on the packages to fit mixture models in R. Currently, there are many packages on Cran that can fit mixture models, the most popular ones are: Mixtools, which is a great library, but the Poisson distribution is not implemented so far and we'll need it later in the course. bayesmix, which uses Bayesian inference, and is outside of the scope of this course. EMCluster, which is really easy to implement but only works with Gaussian distributions. Flexmix, which is the one you will learn because not only have plenty of probability distributions been implemented but it also gives you the possibility of going deeper with mixture models if you choose. Gaussian distributions are characterized by two measures; the mean and the standard deviation. The mean represents the central point where the values tend to fall. And the standard deviation is the measure that determines the degree to which the values differ from the mean. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out. The range formed by four