How to detect data that does not follow a bell curve?

Question

Miguel 2023-9-14

1
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https://ww2.mathworks.cn/matlabcentral/answers/2020746-how-to-detect-data-that-does-not-follow-a-bell-curve

评论： Miguel 2023-9-14

Hello everyone!

I have significantly large dataset and I need to detect which data does not follow a gaussian distribution or bell curve (see screenshots). I have tried using several tests such as kstest, lillietest, etc but for some reason, these tests do not work for me. I have tried using the histcounts function for visualizing the data distribution that you see in the screenshots. Any insights would be appreciated.

[N1,edges1,bin1] = histcounts(normal);
plot(N1)
[N2,edges2,bin2] = histcounts(abnormal);
plot(N2)

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Answer 1

Sam Chak 2023-9-14

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https://ww2.mathworks.cn/matlabcentral/answers/2020746-how-to-detect-data-that-does-not-follow-a-bell-curve#answer_1309696

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Hi @Miguel

Not sure if you can try it this way to compare the R-square value. Data that follows the bell curve tends to have a high R-squared value close to 1. Data that does not follow the bell curve usually have relatively low R-squared values.

load('normal.mat');

[N1,edges1,bin1] = histcounts(normal);

x1 = 1:length(N1);

[fitobject1, gof1] = fit(x1', N1', 'gauss1')

fitobject1 =

General model Gauss1: fitobject1(x) = a1*exp(-((x-b1)/c1)^2) Coefficients (with 95% confidence bounds): a1 = 3609 (3563, 3654) b1 = 45.27 (45.16, 45.38) c1 = 10.65 (10.5, 10.81)

gof1 = struct with fields:

sse: 8.9523e+05 rsquare: 0.9939 dfe: 189 adjrsquare: 0.9939 rmse: 68.8235

load('abnormal.mat');

[N2,edges2,bin2] = histcounts(abnormal);

x2 = 1:length(N2);

[fitobject2, gof2] = fit(x2', N2', 'gauss1')

fitobject2 =

General model Gauss1: fitobject2(x) = a1*exp(-((x-b1)/c1)^2) Coefficients (with 95% confidence bounds): a1 = 1862 (1450, 2274) b1 = 11.65 (-3.404, 26.7) c1 = 33.07 (15.12, 51.03)

gof2 = struct with fields:

sse: 9.6821e+07 rsquare: 0.3657 dfe: 99 adjrsquare: 0.3529 rmse: 988.9337

subplot(211)

plot(N1), grid on, title('N_{1} follows Bell curve')

subplot(212)

plot(N2), grid on, title('N_{2} does not follows Bell curve')