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Function Reference: gampdf

statistics: y = gampdf (x, a, b)

Gamma probability density function (PDF).

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

OCTAVE/MATLAB use the alternative parameterization given by the pair α, β, i.e. shape a and scale b. In Wikipedia, the two common parameterizations use the pairs k, θ, as shape and scale, and α, β, as shape and rate, respectively. The parameter names a and b used here (for MATLAB compatibility) correspond to the parameter notation k, θ instead of the α, β as reported in Wikipedia.

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, β = 2", "α = 2, β = 2", "α = 3, β = 2", ...
          "α = 5, β = 1", "α = 9, β = 0.5", "α = 7.5, β = 1", ...
          "α = 0.5, β = 1"}, "location", "northeast")
 title ("Gamma PDF")
 xlabel ("values in x")
 ylabel ("density")
plotted figure