To plot the probability density function for a Weibull distribution in R, we can use the following functions:

**dweibull(x, shape, scale = 1)**to create the probability density function.**curve(function, from = NULL, to = NULL)**to plot the probability density function.

To plot the probability density function, we need to specify the value for the **shape** and **scale** parameter in the **dweibull **function along with the **from **and **to **values in the **curve() **function.

For example, the following code illustrates how to plot a probability density function for a Weibull distribution with parameters shape = 2 and scale = 1 where the x-axis of the plot ranges from 0 to 4:

curve(dweibull(x, shape=2, scale = 1), from=0, to=4)

We can add a title, change the y-axis label, increase the line width, and even change the line color to make the plot more aesthetically pleasing:

curve(dweibull(x, shape=2, scale = 1), from=0, to=4, main = 'Weibull Distribution (shape = 2, scale = 1)', #add title ylab = 'Density', #change y-axis label lwd = 2, #increase line width to 2 col = 'steelblue') #change line color to steelblue

We can also add more than one curve to the graph to compare Weibull distributions with different shape and scale parameters:

curve(dweibull(x, shape=2, scale = 1), from=0, to=4, col='red') curve(dweibull(x, shape=1.5, scale = 1), from=0, to=4, col='blue', add=TRUE)

We can add a legend to the plot by using the **legend() **function, which takes on the following syntax:

**legend(x, y=NULL, legend, fill, col, bg, lty, cex)**

where:

**x, y:**the x and y coordinates used to position the legend**legend:**the text to go in the legend**fill:**fill color inside the legend**col:**the list of colors to be used for the lines inside the legend**bg:**the background color for the legend**lty:**line style**cex:**text size in the legend

In our example we will use the following syntax to create a legend:

#create density plots curve(dweibull(x, shape=2, scale = 1), from=0, to=4, col='red') curve(dweibull(x, shape=1.5, scale = 1), from=0, to=4, col='blue', add=TRUE) #add legend legend(2, .7, legend=c("shape=2, scale=1", "shape=1.5, scale=1"), col=c("red", "blue"), lty=1, cex=1.2)