Stats Cheat Sheet: Normal Distributions
If you’ve ever taken a stats/econ/math class, the phrase “normal distribution” probably rings a bell for you (pun definitely intended). Also known as the bell curve, the probably density function of the normal distribution occurs often in society/nature/the world. There are about a million different defintions to describe this distribution on the world wide web but my favorite is a stats definition that describes the normal distribution as “a probability function that describes how the values of a variable are distributed. It is a symmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions” (https://statisticsbyjim.com/basics/normal-distribution/). This definition highlights that the function centers around the mean/average of the values and hence the highest point in the graph is the mean.
I’m not going to dive into the mathemtical functions and reasoning behind the normal distribution or probably density functions in this post. If you’re interested in that I recommend reviewing the Wolfram Alpha page (or just google normal distribution there is so much information you can dive into) https://mathworld.wolfram.com/NormalDistribution.html.
In R, the stats package contains four functions for the Normal Distribution. For the complete documentation, just type “?rnorm” into your R console. R has four functions pertaining to the normal distribution and each return a different aspect of a distribution:
| Function | Description |
|---|---|
| dnorm(x, mean = 0, sd = 1, log = FALSE) | Returns the density |
| rnorm(n, mean = 0, sd =1) | Returns random deviates |
| pnrom(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) | Returns the distribution function |
| qnorm(p, mean=0,sd=1, lower.tail = TRUE, log.p = FALSE) | Returns the quantile function |
The length of an rnorm function is determined by n and for the other three functions is the maximum of the lengths of their numeric arguments.
