% Assume that corneoretinal potential is a random variable  X = Y + 0.35  [mV]
% where Y is gamma distributed with shape parameter 3 and rate parameter 20   [1/mV]
% (or equivalently, scale parameter 1/20=0.05  [mV]).
% 
% (a) What is the probability to observe corneoretinal potential X exceeding 0.5  [mV].
% 
% (b) If an observed corneoretinal potential exceeds  x*  it is recorded
% as significant. If, in the long run, we wish to label 1% largest
% potentials as significant, how the threshold  x*  should be set?
% 
% Hint.  This is a simple  gamcdf-gaminv-type of problem, but you need to be careful.
%  Y, not X, is gamma distributed and in calculations the constant 0.35 needs to be properly handled.

%(a) P(X > 0.5)=P(Y+0.35 > 0.5)=P(Y > 0.15)
1-gamcdf(0.15, 3, 1/20)  %0.5768
%(b) 0.01=P(X > x*)=P(Y-0.35 > x*)=P(Y>x*-0.35).
% x*-35 is 0.99-quantile of gamma distribution with shape=3 and rate=20.
xstar = 0.35 + gaminv(0.99, 3, 1/20)    %0.7703
