%% Graphs of the beta density
% Here are graphs of the beta density for different values of the
% parameters. From the graphs you can imagine how changing the parameters
% would allow you to fit a beta density to a wide variety of data sets. In 
% fact, MATLAB has a command *betafit* designed to do that.
%%
% I begin by creating a vector of $X$ values to plot, with 1000 equally
% spaced points in [0,1].
X = linspace(0,1,1000);
%%
% The command *betapdf(X,a,b)* computes the values of the beta density with
% parameters $a$ and $b$ at the points of $X$. I'll use that to plot.
% After each plot I give two commands to change the tick marks on the $x$
% axis to go from 0 to 1 instead of 0 to 1000 (the values of $X$).

%% a=b=1.5
plot(betapdf(X,1.5,1.5))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=b=0.5
plot(betapdf(X,0.5,0.5))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=b=0.75
plot(betapdf(X,0.75,0.75))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=b=2.5
plot(betapdf(X,2.5,2.5))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=0.5, b=2.5
plot(betapdf(X,0.5,2.5))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=2.5, b=0.5
plot(betapdf(X,2.5,0.5))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=0.75, b=0.5
plot(betapdf(X,0.75,0.5))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=b=3.5
plot(betapdf(X,3,5));
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=b=5
plot(betapdf(X,5,5));
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=5, b=3
plot(betapdf(X,5,3))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=5, b=1.5
plot(betapdf(X,5,1.5))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=7, b=2
plot(betapdf(X,7,2))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};
%% a=2, b=7.5
plot(betapdf(X,2,7))
ax=gca;
ax.XTickLabel = {'0','0.2','0.4','0.6','0.8','1'};