CODEWITHSUNDEEP
rplotdistributionprobability-distribution
BLP92
BLP92

Reputation: 301

Plotting the area under the curve of various distributions in R

Suppose I'm trying to find the area below a certain value for a student t distribution. I calculate my t test statistic to be t=1.78 with 23 degrees of freedom, for example. I know how to get the area under the curve above t=1.78 with the pt() function. How can I get a plot of the student distribution with 23 degrees of freedom and the area under the curve above 1.78 shaded in. That is, I want the curve for pt(1.78,23,lower.tail=FALSE) plotted with the appropriate area shaded. Is there a way to do this?

Upvotes: 0

Views: 2448

Answers (2)

Jrakru56
Jrakru56

Reputation: 1321

ggplot version: 

ggplot(data.frame(x = c(-4, 4)), aes(x)) +
  stat_function(fun = dt, args =list(df =23)) +
  stat_function(fun = dt,   args =list(df =23),
                xlim = c(1.78,4),
                geom = "area")

enter image description here

Upvotes: 5

Milan Valášek
Milan Valášek

Reputation: 611

This should work:

x_coord <- seq(-5, 5, length.out = 200) # x-coordinates
plot(x_coord, dt(x_coord, 23), type = "l",
     xlab = expression(italic(t)), ylab = "Density", bty = "l") # plot PDF
polygon(c(1.78, seq(1.78, 5, by = .3), 5, 5), # polygon for area under curve
        c(0, dt(c(seq(1.78, 5, by = .3), 5), 23), 0),
        col = "red", border = NA)

Regarding arguments to polygon():

  • your first and last points should be [1.78, 0] and [5, 0] (5 only in case the plot goes to 5) - these basically devine the bottom edge of the red polygon
  • 2nd and penultimate points are [1.78, dt(1.78, 23)] and [5, dt(5, 23)] - these define the end points of the upper edge
  • the stuff in between is just X and Y coordinates of an arbitrary number of points along the curve [x, dt(x, 23)] - the more points, the smoother the polygon

Hope this helps

Upvotes: 1

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