Random Signals for Engineers using MATLAB and Mathcad
Copyright  1999 Springer Verlag NY
Example 4.1 Two Dimensional Discrete Distributions
In this example we will show how we may plot the two dimensional cumulative distribution
functions. We define a set of discrete probabilities by a matrix and tabulate the random variables x i
and yj.
P=[1/8 0 0 0;0 3/8 0 0;0 1/8 2/8 0;0 0 0 1/8]
P =
0.1250
0
0
0
x0=0:3
y0=0:3;
x0 =
0
0
0.3750
0.1250
0
1
2
0
0
0.2500
0
0
0
0
0.1250
3
The cumulative distribution function is now plotted. This operation requires a lengthy computation
by Matlab because of the number of points involved and, if desired, the computation can be
suppressed until the final output is required.
xp= -.5:.2:4;
yp=-.5:.2:4;
r=F2D(xp,yp,x0,y0,P);
view([20 -20]); axis('ij');mesh(r)
The marginal functions can also be plotted and it may be verified that these correspond to the surface
plot at (x,3.5) for the x marginal and (3.5, y) for the y marginal distribution functions. The marginals
are plotted
plot(xp,FX(xp,x0,P),yp,FX(yp,y0,P'))
1
0.8
0.6
0.4
0.2
0
-1
0
1
2
3
4
The functions required by the plots are listed below.
function y=F2Ds(xp,yp,x0,y0,p)
% 2D cumulative probability function
n=length(x0);
y=0;
for j=1:n
for i=1:n
y=p(i,j)*stepfun(xp,x0(i))*stepfun(yp,y0(j)) + y;
end
end
function y=F2D(xp,yp,x0,y0,p)
% 2D cumulative probability function
np=length(xp);
y=zeros(np,np);
for i=1:np
for j=1:np
y(i,j)=F2Ds(xp(i),yp(j),x0,y0,p);
end
end
function y=FX(xp,x0,p)
% 2D cumulative probability function
n=length(x0);
np=length(xp);
y=zeros(1,np);
for j=1:n
for i=1:n
y=p(i,j)*stepfun(xp,x0(i)) + y;
end
end
function y=stepfun(t,t0)
%stepfun
for i=1:length(t)
y(i)=t(i)>t0;
end
