CDF of gamma distribution

Question

RNTL 2012-6-24

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https://ww2.mathworks.cn/matlabcentral/answers/41918-cdf-of-gamma-distribution

assuming X~Gamma(k,theta) where k and theta are shape and scale parameters, the CDF Fx(x) should be

Fx(x) = 1/Gamma(k)*gamma(k,x/theta) where Gamma is the gamma function and gamma is the lower incomplete gamma function

however, trying to use gammainc for the incomplete gamma function I get a monotonic decreasing result, instead of the expected increasing to 1 CDF. instead I am using gamcdf which seems reasonable, but I don't understand the nature of the difference.

help ? anyone?

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Answer 1

Wayne King 2012-6-24

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I'm not sure how you are calling it, but you should get the same result with gamcdf and gammainc, provided you scale the x vector by the value of your theta parameter prior to calling gammainc

   x = 0:0.01:20;
   k = 2;  % shape parameter
   theta = 3; % scale parameter
   F = gamcdf(x,k,theta);
   plot(x,F,'b');
   hold on;
   x1 = x./theta;  %scale x axis by theta
   Z = gammainc(x1,k);
   plot(x,Z,'k')
   max(abs(Z-F))