Updated some files
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@ -1,23 +1,24 @@
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nsamples = 1000
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resample = 500
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x = randn( nsamples, 1 );
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sem = std(x)/sqrt(nsamples);
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mu = zeros( resample, 1 );
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for i = 1:resample
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% resample:
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xr = x(randi(nsamples, nsamples, 1));
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% compute statistics on sample:
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mu(i) = mean(xr);
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end
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bootsem = std( mu );
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hold on
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hist( x, 20 );
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hist( mu, 20 );
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hold off
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disp(['bootstrap standard error: ', num2str(bootsem)]);
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disp(['standard error: ', num2str(sem)]);
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nsamples = 100;
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nresamples = 1000;
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% draw a SRS (simple random sample, "Stichprobe") from the population:
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x = randn( 1, nsamples );
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fprintf('%-30s %-5s %-5s %-5s\n', '', 'mean', 'stdev', 'sem' )
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fprintf('%30s %5.2f %5.2f %5.2f\n', 'single SRS', mean( x ), std( x ), std( x )/sqrt(nsamples) )
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% bootstrap the mean:
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mus = zeros(nresamples,1); % vector for storing the means
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for i = 1:nresamples % loop for generating the bootstraps
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inx = randi(nsamples, 1, nsamples); % range, 1D-vector, number
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xr = x(inx); % resample the original SRS
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mus(i) = mean(xr); % compute statistic of the resampled SRS
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end
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fprintf('%30s %5.2f %5.2f -\n', 'bootstrapped distribution', mean( mus ), std( mus ) )
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% many SRS (we can do that with the random number generator, but not in real life!):
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musrs = zeros(nresamples,1); % vector for the means of each SRS
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for i = 1:nresamples
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x = randn( 1, nsamples ); % draw a new SRS
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musrs(i) = mean( x ); % compute its mean
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end
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fprintf('%30s %5.2f %5.2f -\n', 'sampling distribution', mean( musrs ), std( musrs ) )
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@ -1,18 +1,26 @@
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x = randn( 100, 1 ); % generate some data
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bins1 = -4:2:4; % large bins
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bins2 = -4:0.5:4; % small bins
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db1=2;
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db2 = 0.5;
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bins1 = -4:db1:4; % large bins
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bins2 = -4:db2:4; % small bins
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[h1,b1] = hist(x,bins1);
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[h2,b2] = hist(x,bins2);
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subplot( 1, 2, 1 );
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hold on;
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hist( x, bins1 );
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hist( x, bins2 );
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bar(b1,hn1)
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hold on
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bar(b2,hn2, 'facecolor', 'r' )
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xlabel('x')
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ylabel('Frequeny')
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hold off;
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subplot( 1, 2, 2 );
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hold on;
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% normalize to the rigtht bin size:
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hist( x, bins1, 1.0/(bins1(2)-bins1(1)) );
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hist( x, bins2, 1.0/(bins2(2)-bins2(1)) );
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ylabel('Frequency')
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hold off
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% normalize:
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hn1 = h1/sum(h1)/db1;
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hn2 = h2/sum(h2)/db2;
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subplot( 1, 2, 2 )
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bar(b1,hn1)
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hold on
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bar(b2,hn2, 'facecolor', 'r' )
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xlabel('x')
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ylabel('Probability density')
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hold off;
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hold off
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48
statistics/code/sprintfexamples.m
Normal file
48
statistics/code/sprintfexamples.m
Normal file
@ -0,0 +1,48 @@
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% sprintf returns a string.
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% This string can be used to annotate plots using the text() function.
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s = sprintf( 'x=%f', pi )
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% fprintf writes directly to console (or into files).
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% for fprintf you usually want to add the line break '\n':
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% '%f' formats floating point numbers:
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fprintf( 'x=%f\n', pi )
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% The '%f' formatting string can be anywhere in the string:
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fprintf( 'x=%fms\n', pi )
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% There can be arbitrary many '%' formatting strings:
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fprintf( 'x=%fms, y=%fkHz\n', pi, 2*pi )
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% The '%' itself is generated by '%%':
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fprintf( 'x=%f%%\n', pi )
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% A point followed by a number sets the number of digits after the point:
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fprintf( 'x=%.2fms\n', pi )
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% The numbers are appropriately rounded:
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fprintf( 'x=%.3fms\n', pi )
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% A number right before the point sets the width of the generated output:
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fprintf( 'x=%10.3fms\n', pi )
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% '%e' also formats floating point numbers but forces to write in
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% exponential style:
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fprintf( 'x=%e\n', pi )
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% again, a point and number set the number of digits after the point.
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fprintf( 'x=%.1e\n', pi )
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% '%g% formats the floating point number to a given number of valid digits
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% (default is 5):
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fprintf( 'x=%g\n', pi )
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% The number of valid digits is not the number of digits after the point:
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fprintf( 'x=%.2g\n', pi )
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fprintf( 'x=%.2g\n', 10.123 )
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fprintf( 'x=%.2g\n', 18765.123 )
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fprintf( 'x=%.5g\n', 18765.123 )
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% '%d' formats integers:
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fprintf( 'x=%d\n', 5 )
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% the number defines the width of the output:
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fprintf( 'x=%3d\n', 5 )
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% precedig the width with a '0' fills up the space with leading zeros:
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fprintf( 'x=%03d\n', 5 )
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% '%s' formats a string:
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fprintf( 'x=%s\n', 'hallo' )
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% ... aligned to the right:
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fprintf( 'x=%10s\n', 'hallo' )
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% ... unless the width is negative:
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fprintf( 'x=%-10s!\n', 'hallo' )
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