# Articles by LeaRning Stats

### Laguerre-Samuelson Inequality

September 12, 2019 |

Chebychev’s Theorem gives bounds on how spread out a probability distribution can be from the mean, in terms of the standard deviation. More precisely, if $$X$$ is a random variable with mean $$\mu$$ and standard deviation $$\sigma$$, then $P(|X - ... [Read more...] ### Advent of Code Day 14 December 24, 2018 | Introduction Advent of code 2018, day 14, was a tough one to do in R. Here is a link. I did this problem a lot of different ways, trying to find a nice way to do it. In the end, I did it using vectors in base R, data.table and finally ... [Read more...] ### On power and effect size November 8, 2018 | Introduction I have seen a lot of tweets on my feed about power and effect size. I wanted to think about those things carefully, so I did some reading and am writing down some thoughts. An interesting paper that I read on this is here The takeaway is that studies ... [Read more...] ### Copula Sampling October 31, 2018 | Introduction I was reading about different ways to sample from distributions, and one that caught my eye was based on copulas. There is an answer here, but there seemed to be enough details left to the reader that I wanted to just do it. One variable example To start, let’... [Read more...] ### Prediction Bands April 6, 2018 | Introduction In this post, we study a seemingly easy question; what is a 95% prediction interval in simple linear regression? We assume that our data comes from \[ y_i = 1 + 2x_i + \epsilon_i$ where $$\epsilon_i$$ are iid normal with mean 0 and standard deviation 3. R Code for Prediction We can build ... 