Function Reference: gampdf

statistics: y = gampdf (x, k, theta)

Gamma probability density function (PDF).

For each element of x, compute the probability density function (PDF) of the Gamma distribution with shape parameter k and scale parameter theta. The size of y is the common size of x, k and theta. A scalar input functions as a constant matrix of the same size as the other inputs.

There are two equivalent parameterizations in common use:

  1. With a shape parameter k and a scale parameter θ, which is used by gampdf.
  2. With a shape parameter α = k and an inverse scale parameter β = 1 / θ, called a rate parameter.

Further information about the Gamma distribution can be found at https://en.wikipedia.org/wiki/Gamma_distribution

See also: gamcdf, gaminv, gamrnd, gamfit, gamlike, gamstat

Source Code: gampdf

Example: 1

 

 ## Plot various PDFs from the Gamma distribution
 x = 0:0.01:20;
 y1 = gampdf (x, 1, 2);
 y2 = gampdf (x, 2, 2);
 y3 = gampdf (x, 3, 2);
 y4 = gampdf (x, 5, 1);
 y5 = gampdf (x, 9, 0.5);
 y6 = gampdf (x, 7.5, 1);
 y7 = gampdf (x, 0.5, 1);
 plot (x, y1, "-r", x, y2, "-g", x, y3, "-y", x, y4, "-m", ...
       x, y5, "-k", x, y6, "-b", x, y7, "-c")
 grid on
 ylim ([0,0.5])
 legend ({"α = 1, θ = 2", "α = 2, θ = 2", "α = 3, θ = 2", ...
          "α = 5, θ = 1", "α = 9, θ = 0.5", "α = 7.5, θ = 1", ...
          "α = 0.5, θ = 1"}, "location", "northeast")
 title ("Gamma PDF")
 xlabel ("values in x")
 ylabel ("density")

                    
plotted figure