I run the code below and expect to get a uniform histogram. It's not. I don't understand why not.

% I have a two column array, the first column is time and the second column is state. I ran interp1 to observe my data at uniform time points. The results were unexpected. In trying to identify the problem, I have run this simpler code expecting the deterministic uniformly spaced points to be uniformly distributed. They are not. Can anyone explain why not? Thanks.

% Parameters
thismesh = 100; % Number of bins 
deltat = 1 / thismesh;
lasttime = 1000; % Example last time

% Generate uniform time steps
xx = 0:deltat:lasttime;

% Calculate fractional times
fractime = (xx - floor(xx)).';

% Plot histogram to check uniformity
figure;
histogram(fractime, thismesh);
title('Histogram of fractional times');
xlabel('Fractional time');
ylabel('Count');

% Display counts in each bin
[counts, edges] = histcounts(fractime, thismesh);
disp('Counts per bin:');

Counts per bin:

disp(counts);

  Columns 1 through 15

        1907         918         680        1172         884         936        1313         903         562        1095         753         894        1937         793         806

  Columns 16 through 30

        1141         578         918        1300         794         863        1110         819         957         968        1906         918         680        1172         882

  Columns 31 through 45

         938        1313         903         562        1093         755         894        1937         793         806        1141         578         918        1300         794

  Columns 46 through 60

         862        1111         815         961         968        1906         918         680        1172         882         938        1313         903         562        1093

  Columns 61 through 75

         754         895        1937         793         806        1140         579         918        1299         793         857        1117         816         960         969

  Columns 76 through 90

        1906         917         681        1172         882         938        1313         903         562        1093         754         894        1938         793         806

  Columns 91 through 100

        1140         579         917        1300         793         857        1116         817         960         969

% Expected count per bin
expected_count = length(fractime) / thismesh;
disp('Expected count per bin:');

Expected count per bin:

disp(expected_count);

   1.0000e+03

% Plot actual counts vs expected uniform count
figure;
bar(counts);
hold on;
yline(expected_count, 'r', 'LineWidth', 2);
hold off;
title('Actual counts vs Expected uniform count');
xlabel('Bin');
ylabel('Count');
legend('Actual counts', 'Expected count');

[SL: formatted code as code and ran that code]

Answer 1

[the cyclist]

It's because of your choice of 100 bins is tuned to the periodicity of your function in a way that makes it the counts chaotic near the bin edges. Here is a better choice for binning, that gives what you expect.

% Parameters
thismesh = 100; % Number of bins 
deltat = 1 / thismesh;
lasttime = 1000; % Example last time

% Generate uniform time steps
xx = 0:deltat:lasttime;

% Calculate fractional times
fractime = (xx - floor(xx)).';
%%
% Plot histogram to check uniformity
figure;
histogram(fractime, -0.005 : 0.01 : 1.005);
title('Histogram of fractional times');
xlabel('Fractional time');
ylabel('Count');

Answer 2

[Barbara Margolius]

in answer to my own question, I can define

bin_edges=-0.005:.01:.995;

and then

hh=histogram(fractime, bin_edges);

Unrecognized function or variable 'fractime'.

and the result is uniform. This feels very jerry-rigged. I guess when I run my code (kept as text here because the rest of the code is not provided):

lasttime = cumRV(end,1);

deltat = 1/thismesh;

xx = 0:deltat:lasttime;

ph = interp1(cumRV(:,1),cumRV(:,2),xx,'previous').';

I could change the definition of xx so that the interpolation points are in the center of the bars. This seems awkward, and I would appreciate other thoughts on how better to do this. Thanks.

% Parameters
thismesh = 100; % Number of bins 
deltat = 1 / thismesh;
lasttime = 1000; % Example last time
% Generate uniform time steps
xx = 0:deltat:lasttime;
% Calculate fractional times
fractime = (xx - floor(xx)).';
% Plot histogram to check uniformity
figure;
histogram(fractime, thismesh);
title('Histogram of fractional times');
xlabel('Fractional time');
ylabel('Count');
% Display counts in each bin
[counts, edges] = histcounts(fractime, thismesh);
disp('Counts per bin:');
disp(counts);
% Expected count per bin
expected_count = length(fractime) / thismesh;
disp('Expected count per bin:');
disp(expected_count);
% Plot actual counts vs expected uniform count
figure;
bar(counts);
hold on;
yline(expected_count, 'r', 'LineWidth', 2);
hold off;
title('Actual counts vs Expected uniform count');
xlabel('Bin');
ylabel('Count');
legend('Actual counts', 'Expected count');

% corrections below here
bin_edges=-0.005:.01:.995;
hh=histogram(fractime, bin_edges);