Probability distributions have a central role in Statistics and the **R** software has functions to work with a large range of distributions – the syntax has been selected to provide some consistency based on the type of information required about a distribution.

There are four functions that are defined for each distribution that is available within **R**. These functions are:

- The density function – name starts with a d.
- The cumulative density function – name starts with a p.
- The quantile function – name starts with a q.
- Random number generation – name starts with a r.

Both discrete and continuous distributions are available in **R**. Distributions that we can access include: Beta, Binomial, Chi-squared, F, Logistic, Normal, Poisson, Student’s t and Weibull.

There is a *base* name for each of the distributions and we use the suffix letter mentioned above to access the requisite information. If we consider the Normal distribution as an example then **dnorm** is the function that will provide the density:

> dnorm(1.96, mean = 0, sd = 1) [1] 0.05844094 |

The **mean** and **sd** arguments are used to specify a particular pair of parameters for the Normal distribution. The cumulative distribution function is **pnorm** and the syntax is very similar to the **dnorm** function:

> pnorm(1.96, mean = 0, sd = 1) [1] 0.9750021 |

The default option is for the function to return the cumulative probability for values less than the specified figure. The quantile function, **qnorm**, allows us to work back from probabilities to values on the original data scale:

> qnorm(0.95, mean = 0, sd = 1) [1] 1.644854 |

As with the previous functions we can definition the parameters of the distribution where required. The last option of interest is the function that allows us to generate random samples for a particular distribution, which in the case of the Normal distribution is **rnorm**. Here we specify the number of samples to be drawn from the distribution along with the parameters of the distribution:

> rnorm(n = 20, mean = 0, sd = 1) [1] -1.1322606 -2.8320170 -0.5768220 1.0569513 1.0824524 1.4925396 -0.3010086 -0.4345893 2.6813322 [10] 0.3774106 1.7226911 0.5922038 0.0770510 1.4015955 -0.9998051 0.1924921 0.7181194 1.0107967 [19] 1.3224979 -0.1511634 |

The previous command samples twenty observations from the standard Normal distribution.