Gamma CDF
p = distfun_gamcdf ( x , a , b ) p = distfun_gamcdf ( x , a , b , lowertail )
a matrix of doubles, the outcome, x>=0
a matrix of doubles, the shape parameter, a>0.
a matrix of doubles, the scale parameter, b>0.
a 1-by-1 matrix of booleans, the tail (default lowertail=%t). If lowertail is true (the default), then considers P(X<=x) otherwise P(X>x).
a matrix of doubles, the probability
Computes the Gamma cumulated probability distribution function.
Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.
// Test x scalar, a scalar, b expanded b = 1:5; computed = distfun_gamcdf(1,1,b) expected = [ .. 6.321205588285576660D-01 .. 3.934693402873664647D-01 .. 2.834686894262107293D-01 .. 2.211992169285951215D-01 .. 1.812692469220181790D-01 .. ] // Plot the function shape = [1 2 3 5 9]; scale = [2 2 2 1 0.5]; cols = [1 2 3 4 5]; nf = size(cols,"*"); lgd = []; scf(); for k = 1 : nf x = linspace(0,20,1000); y = distfun_gamcdf ( x , shape(k) , scale(k) ); plot(x,y) str = msprintf("shape=%s, scale=%s",.. string(shape(k)),string(scale(k))); lgd($+1) = str; end h = gcf(); for k = 1 : nf hk = h.children.children.children(nf - k + 1); hk.foreground = cols(k); end xtitle("Gamma CDF","x","$P(X\leq x)$") legend(lgd); // See upper tail p = distfun_gamcdf(1,3,5) q = distfun_gamcdf(1,3,5,%f) p+q // See an extreme case p = distfun_gamcdf(300,3,5,%f) | ![]() | ![]() |