Functions for Statistical Distributions

R has functions available for most of the famous statistical distributions. Prefix the name as follows:

With d for the density or probability mass function (pmf)
With p for the cumulative distribution function (cdf)
With q for quantiles
With r for random number generation

The rest of the name indicates the distribution. Table 8-1 lists some common statistical distribution functions.

Table 8-1. Common R Statistical Distribution Functions

Distribution	Density/pmf	cdf	Quantiles	Random Numbers
Normal	`dnorm()`	`pnorm()`	`qnorm()`	`rnorm()`
Chi square	`dchisq()`	`pchisq()`	`qchisq()`	`rchisq()`
Binomial	`dbinom()`	`pbinom()`	`qbinom()`	`rbinom()`

As an example, let’s simulate 1,000 chi-square variates with 2 degrees of freedom and find their mean.

> mean(rchisq(1000,df=2))
[1] 1.938179

The r in rchisq specifies that we wish to generate random numbers—in this case, from the chi-square distribution. As seen in this example, the first argument in the r-series functions is the number of random variates to generate.

These functions also have arguments specific to the given distribution families. In our example, we use the df argument for the chi-square family, indicating the number of degrees of freedom.

Note

Consult R’s online help for details on the arguments for the statistical distribution functions. For instance, to find our more about the chi-square function for quantiles, type ?qchisq at the command prompt.

Let’s also compute the 95^th percentile of the chi-square distribution with two degrees of freedom:

> qchisq(0.95,2)
[1] 5.991465

Here, we used q to indicate quantile—in this case, the 0.95 quantile, or the 95^th percentile.

The first argument in the d, p, and q series is actually a vector so that we can evaluate the density/pmf, cdf, or quantile function at multiple points. Let’s find both the 50^th and 95^th percentiles of the chi-square distribution with 2 degrees of freedom.

qchisq(c(0.5,0.95),df=2)
[1] 1.386294 5.991465