60 lines
1.3 KiB
Matlab
60 lines
1.3 KiB
Matlab
function cumulants = computeCumulants(x, maxOrder)
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%% computeCumulants
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% Author: Karthik
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% Date: 2025-09-12
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% Version: 1.0
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%
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% Description:
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% Compute cumulants up to specified order from data vector x.
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%
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% Inputs:
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% x - 1D numeric vector (may contain NaNs)
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% maxOrder - maximum order of cumulants to compute (default: 6)
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%
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% Output:
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% cumulants - vector [kappa_1, ..., kappa_maxOrder]
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%
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% Notes:
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% Syntax- cumulants = computeCumulants(x, maxOrder).
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if nargin < 2
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maxOrder = 6;
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end
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x = x(:);
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x = x(~isnan(x)); % Remove NaNs
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if isempty(x)
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cumulants = NaN(1, maxOrder);
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return;
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end
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mu1 = mean(x, 'omitnan');
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x_centered = x - mu1;
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cumulants = zeros(1, maxOrder);
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cumulants(1) = mu1;
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mu = zeros(1, maxOrder);
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for k = 2:maxOrder
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mu(k) = mean(x_centered.^k, 'omitnan');
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end
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if maxOrder >= 2
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cumulants(2) = mu(2);
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end
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if maxOrder >= 3
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cumulants(3) = mu(3);
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end
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if maxOrder >= 4
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cumulants(4) = mu(4) - 3 * mu(2)^2;
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end
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if maxOrder >= 5
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cumulants(5) = mu(5) - 10 * mu(3) * mu(2);
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end
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if maxOrder >= 6
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cumulants(6) = mu(6) - 15 * mu(4) * mu(2) - 10 * mu(3)^2 + 30 * mu(2)^3;
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end
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end
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