--- title: "Week 3 R lecture" subtitle: "Statistics and statistical programming \nNorthwestern University \nMTS 525" author: "Aaron Shaw" date: "April 18, 2019" output: html_document --- ```{r setup, include=FALSE} knitr::opts_chunk\$set(echo = TRUE) ``` This week, we'll focus on one more way to manage date-time objects and some ways to generate distributions. ## as.Date First, something I meant to include in last week's materials. The `as.Date()` function provides an alternative to `as.POSIX()` that is far more memorable and readable, but far less precise. Note that it truncates the time of day and the timezone from the ouput ```{r} m <- "2019-02-21 04:35:00" class(m) a.good.time <- as.Date(m, format="%Y-%m-%d %H:%M:%S", tz="CDT") class(a.good.time) a.good.time ``` ## Distribution functions distribution functions: lets focus on *unif(): the key is on page 222 of Verzani The “d” functions return the p.d.f. of the distribution dunif(x=1, min=0, max=3) # 1/3 of the area is the to the left 1 The “p” functions return the c.d.f. of the distribution. dunif(q=2, min=0, max=3) #1/(b-a) is 2/3 The “q” functions return the quantiles. qunif(p=0.5, min=0, max=3) # half way between 0 and 3 The “r” functions return random samples from a distribution. runif(n=1, min=0, max=3) # a random value in [0,3] ## Doing simple simulations with random data runif() rnorm() ## A quick simulation In case you don't believe the central limit theorem, let's put together a quick simulation to illustrate it in R. Write a function to repeatedly take the mean of a sample. Experiment by changing the size of the sample ## Quantile quantile plots ## Binomial and factorial functions Choose, factorial