How to measure mean and standard deviation according to bin size?

I have 1 to 144 columns.

I want to know the standard deviation and mean value according to the bin size when performing Gaussian fitting for 144 columns.

I want to measure the value when 'bin size=50'.

Answer 1

[MULI]

You can follow these steps to know the mean value and standard deviation according to bin size.

1. Take each of the 144 columns of data individually.
2. Create a histogram of data in each column using a bin size of 50.
3. Fit a Gaussian distribution to each histogram.
4. Extract the mean and standard deviation from each fitted Gaussian distribution.

clc;
clear all;
close all;

% Define the URL of the data file
url = 'https://in.mathworks.com/matlabcentral/answers/uploaded_files/833625/1to10_30s_15mm_diff_pivoted.txt';

% Download the data file
filename = websave('localdata.txt', url);

% Load the data into MATLAB using readmatrix
data = readmatrix(filename);

% Define the number of columns and bin size
nColumns = 144;
binSize = 50;

% Preallocate arrays for means and standard deviations
means = zeros(1, nColumns);
stdDevs = zeros(1, nColumns);

% Loop through each column to perform Gaussian fitting
for col = 1:nColumns
    columnData = data(:, col); % Extract data for the current column
    
    % Create histogram bins with the specified bin size
    binEdges = min(columnData):binSize:max(columnData);
    binCenters = binEdges(1:end-1) + binSize/2;
    binCounts = histcounts(columnData, binEdges);
    
    % Fit a Gaussian distribution to the binned data
    % Define Gaussian function (normal distribution)
    gaussEqn = 'a*exp(-((x-b)/c)^2)';
    startPoints = [max(binCounts), mean(columnData), std(columnData)]; % Initial guess
    
    % Perform the fit
    fitObject = fit(binCenters(:), binCounts(:), gaussEqn, 'Start', startPoints);
    % Extract the mean and standard deviation from the fit parameters
    means(col) = fitObject.b;
    stdDevs(col) = abs(fitObject.c); % Ensure standard deviation is positive
end

% Display the results
disp('Means of Gaussian fits for each column:');
disp(means);
disp('Standard deviations of Gaussian fits for each column:');
disp(stdDevs);