function [X, P1] = MEBPinit(samplingftn, weightsftn)

% function [X, P1] = MEBPinit(samplingftn, weightsftn)
%
% returns a randomly chosen initial state for an MEBP process
%
% samplingftn is a function handle for a function that samples from 
%   the offspring sampling distribution n*p(n)/mu
% weightsftn is a function handle for a function that samples from 
%   the weights distribution, given the number of offspring
%
% X = (kappa(0,0,1), S(0,0,1), Z(0,1,1), alpha(0,0,1), P(0,1,1))
%
% types are 0+ 0- 1+ 1- -1+ -1-, labelled 1 2 3 4 5 6
%
% P1 is the weight of the first crossing at level 0
%
% Owen Jones 6 July 2003, 17 January 2007

X = {{1, 0, 0, 0, []}};
X{1}{3} = feval(samplingftn, []);
X{1}{2} = ceil(rand*X{1}{3});
X{1}{5} = feval(weightsftn, X{1}{3});
if X{1}{2} == X{1}{3}
    if rand < 0.5, X{1}{4} = 3; else X{1}{4} = 6; end
elseif mod(X{1}{2},2) == 1
    if rand < 0.5, X{1}{4} = 1; else X{1}{4} = 2; end
else
    if rand < 0.5, X{1}{4} = 4; else X{1}{4} = 5; end
end
P1 = X{1}{5}(1);