%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Let's try the lognormal distribution
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%The normal and lognormal distributions are closely related. 
%If X is distributed lognormal with parameters µ and sigma, 
% then ln(X) is distributed normal with parameters µ and sigma. 

%The lognormal distribution is often applicable 
%  *when something multiplicative causes the distribution
%  *the quantity of interest must be positive,
%     since ln(X) exists only when X is positive. 
%Economists often model the distribution of income 
%   using a lognormal distribution.
%Cumulative population size is distributed this way.
%   (something multiplicative causes the distribution...)


help lognpdf %for more details

%which parameters do you need to set?
clear all
close all


mu=40000;                      % set the mean
sigma=1.25;                    % set the standard deviation
x = (10:1000:125010)';      % set the range of x

figure(20)
y = lognpdf(x,log(mu),sigma);
plot(x,y);
text(mu,.1E-5,['\downarrowmean = ' num2str(mu)],'FontSize',16)
set(gca,'xtick',[0 30000 60000 90000 120000])
set(gca,'xticklabel',str2mat('0','30,000','60,000',...
                             '90,000','120,000'))
title(['Lognormal Distribution, \mu =' num2str(mu) ', \sigma = ' num2str(sigma)])
xlabel('outcome')
ylabel('probability density')