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    filename: spm_invPcdf.m
    path of file: ./repos/spm
    
    the code of the file until where you have to start completion: function x = spm_invPcdf(F,l)
% Inverse Cumulative Distribution Function (CDF) of Poisson distribution

    
function x = spm_invPcdf(F,l)
% Inverse Cumulative Distribution Function (CDF) of Poisson distribution
% FORMAT x = spm_invPcdf(F,l)
%
% F - CDF (lower tail p-value)
% x - ordinates
% l - Poisson mean parameter (lambda l>0) [Defaults to 1]
%__________________________________________________________________________
%
% spm_invPcdf returns the inverse Cumulative Distribution Function for
% the Poisson family of distributions.
%
% Definition:
%--------------------------------------------------------------------------
% The Poisson Po(l) distribution is the distribution of the number of
% events in unit time for a stationary Poisson process with mean
% parameter lambda=1, or equivalently rate 1/l. If random variable X is
% the number of such events, then X~Po(l), and the CDF F(x) is
% Pr({X<=x}.
%
% The Poisson distribution is discrete, defined for l in [0,Inf) and x
% in {0,1,...}, so F(x) is a discrete function. This inverse CDF
% function returns the smallest Whole x such that the F(x) equals or
% exceeds the given CDF probability F. I.e. F(x) is treated as a step
% function.
%
% Algorithm:
%--------------------------------------------------------------------------
% x is found by direct summation of the Poisson PDFs until F is exceeded.
%
% References:
%--------------------------------------------------------------------------
% Evans M, Hastings N, Peacock B (1993)
%       "Statistical Distributions"
%        2nd Ed. Wiley, New York
%
% Abramowitz M, Stegun IA, (1964)
%       "Handbook of Mathematical Functions"
%        US Government Printing Office
%
% Press WH, Teukolsky SA, Vetterling AT, Flannery BP (1992)
%       "Numerical Recipes in C"
%        Cambridge
%
%__________________________________________________________________________

% Andrew Holmes
% Copyright (C) 1996-2022 Wellcome Centre for Human Neuroimaging



%-Format arguments, note & check sizes
%--------------------------------------------------------------------------
if nargin<2, l=1; end