`vignettes/webs/statistical_methods.rmd`

`statistical_methods.rmd`

In the previous tutorial we constructed a Normal distribution and accessed and updated its parameters for a variety of parameterisations. In this tutorial we cover how to access mathematical and statistical methods of the Normal distribution including the `dnorm/pnorm/qnorm/rnorm`

equivalents in distr6.

The advantage of distr6 over R stats is that once a distribution is constructed, it’s very easy to find properties and results from the distribution by changing very little. For simple distributions like the Normal distribution, this may not seem like a big difference, but for more complicated ones with multiple parameters, you’ll find yourself saving a lot of time!

Once again we start with constructing the Standard Normal distribution

N <- Normal$new()

For simplicity, we refer to both the probability density functions of continuous distributions and probability mass functions of discrete distributions, as the “pdf” function. This is in line with R stats using “d” for “density”. The other statistical methods from R stats are referred to as “cdf”, “quantile” and “rand”, the same as in R stats:

N$pdf(1:2) # Density evaluated at points '1' and '2' #> [1] 0.24197072 0.05399097 N$cdf(1:2) # Distribution function evaluated at points '1' and '2' #> [1] 0.8413447 0.9772499 N$quantile(0.975) # Quantile function evaluated at 0.975 #> [1] 1.959964 N$rand(5) # 5 samples from the Normal distribution #> [1] 1.3709584 -0.5646982 0.3631284 0.6328626 0.4042683

We have seen in the first tutorial how the `summary`

method can be used to view quick statistics about a probability distribution, i.e.

summary(N) #> Normal Probability Distribution. Parameterised with: #> c("mean", "var", "sd", "prec") = list(0, 1, 1, 1) #> #> Quick Statistics #> Mean: 0 #> Variance: 1 #> Skewness: 0 #> Ex. Kurtosis: 0 #> #> Support: ℝ Scientific Type: ℝ #> #> Traits: continuous; univariate #> Properties: symmetric; mesokurtic; no skew

But all these statistics can be accessed individually as well. To see the full list of available methods view the ‘Statistical Methods’ section of the distribution help page, `?Normal`

. All probability distributions have the same methods available if possible, i.e. If there is an analytic expression for a statistical result, then we provide it! Below are just a few examples

In this tutorial we looked at using the d/p/q/r functions in distr6 and accessing other statistical results. In the next tutorial we take a quick look at distribution properties and traits, whilst trying not to get into too big a discussion about object-oriented programming!