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

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)

Answer 1

[Sam Chak]

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')

[Miguel]

Hi Sam,

Thank you so much for your reply. I highly appreciate your help. This worked perfectly for my dataset. Have a nice day!