There are many distributions that are available within the base R Statistical System and it is possibly to use these functions to visualise the density or cumulative density functions for a distribution with a given set of parameters.

To illustrate this we could the standard normal distribution which has zero mean and variance of one and the cumulative density function has the familiar S-shape. To plot the distribution on a graph we first create a variable to store the values for the distribution, which we set to be a sequence ranging from -4 to +4 and save the data to a variable **tempX** so that it can be used in the **plot** function:

tempX = seq(-4, 4, 0.1) |

The next step is to call the plot function and we provide a list of X and Y values that we want to plot against each other. In this case we have already defined the X values so we use the **pnorm** function to calculate the cumulative values at each of the X values that we have specified. We also set the text for the title and the two axis using the arguments **main**, **xlab** and **ylab**. We use the **expression** function to create a text string with Mathematical characters in it. The **mu** and **sigma** are converted to the corresponding greek letters. Lastly the option **type = “l”** is used to get the **plot** function to draw lines rather than symbols. Our final function call is:

plot(tempX, pnorm(tempX, mean=0, sd=1), xlab="X Values", ylab="Cumulative Probability", main = expression(paste("Normal Distribution: ", mu, " = 0, ", sigma, " = 1")), type="l") |

We add a horizontal grey line at the bottom of the graph using the **abline** function:

abline(h=0, col="gray") |

The graph that is produced looks like this:

We can use this approach to visualise the density or cumulative density functions of any distribution that is available in **R**.