% BINCOMP file bincomp.m  Approx of binomial by Poisson and gaussian
% Version of 5/24/96
% Gaussian adjusted for "continuity correction"
% Plots distribution functions for specified parameters n, p
n = input('Enter the parameter n  ');
p = input('Enter the parameter p  ');
a = floor(n*p-2*sqrt(n*p));
a = max(a,1);                         % Prevents zero or negative indices
b = floor(n*p+2*sqrt(n*p));
k = a:b; 
Fb = cumsum(ibinom(n,p,0:n));         % Binomial distribution function
Fp = cumsum(ipoisson(n*p,0:n));       % Poisson distribution function
Fg = gaussian(n*p,n*p*(1 - p),k+0.5); % Gaussian distribution function
stairs(k,Fb(k+1))                     % Plotting details
hold on
plot(k,Fp(k+1),'-.',k,Fg,'o') 
hold off
xlabel('t values')                    % Graph labeling details
ylabel('Distribution function')
title('Approximation of Binomial by Poisson and Gaussian')
grid 
legend('Binomial','Poisson','Adjusted Gaussian')
disp('See Figure for results')