%
% epage 241 
% 
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; 
clc; 

addpath('../../Code/CSTool');
load forearm; 

B = 400; 

% for the skewness: 
[bootstat,bootsam] = parm_bootstrap( B, @skewness, forearm ); 
bt_est = mean( bootstat ); 
std_err = std( bootstat ); 
fprintf( 'the estimated skewness is given by %10.5f\n', skewness(forearm) ); 
fprintf( 'the bootstrap computed standard error of the skewness is given by %10.5f\n', std_err ); 
fprintf( 'the bootstrap computed estimate of the bias of the skewness is given by %10.5f\n', bt_est - skewness(forearm) ); 

% for the kurtosis: 
[bootstat,bootsam] = parm_bootstrap( B, @kurtosis, forearm ); 
bt_est  = mean( bootstat ); % <- the bootstrap estimate of the mean ... 
std_err = std( bootstat );  % <- the bootstrap estimate of the standard error ... 
fprintf( 'the estimated kurtosis is given by %10.5f\n', kurtosis(forearm) ); 
fprintf( 'the bootstrap computed standard error of the kurtosis is given by %10.5f\n', std_err ); 
fprintf( 'the bootstrap computed estimate of the bias of the kurtosis is given by %10.5f\n', bt_est - kurtosis(forearm) ); 

% the standard percentile interval for the sample second moment: 
% technically "var" is not the sample second moment but for this exercise the approximation is OK
% the cstoolbox function "mom" didn't seem to work
B = 1500; 
[bootstat,bootsam] = parm_bootstrap( B, @var, forearm ); 
alpha = 0.1; 
qhat = quantile( bootstat, [ 0.5*alpha, 1-0.5*alpha ] ); 
fprintf( 'the bootstrap computed estimates percentile interval of the variance is given by:\n' );
fprintf( '%10.5f', qhat ); fprintf('\n');