Why, when I calculate the skewness of a series with constants, do I not get NaN?

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Angelavtc 2021-10-11

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评论： Cris LaPierre 2021-10-11

Dear Matlab community,

I have a simulation of normally distributed numbers with a mean of 76 and a standard deviation of 0, which describes a series of constant numbers with the value 76. To this simulation, I apply a function that also yields constants and, therefore, its skewness should be also NaN. Why, when I calculate their skewness, do I not get NaN but 1? How do I correct this error?

Thanks in advance!

Np=20; 
cb=2; 
ab = 30*(Np/100)^(cb-1); 
n=100;
Qd = normrnd(76,0,n,1);
Pw=ab*((Qd/Np).^(cb-1)); 
skewness(Pw)
skewness(Qd)
var(Qd)

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Answer 1

Cris LaPierre 2021-10-11

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I suspect this has to do with how floating point numbers are stored in a computer. 76 can be stored exactly as is, but 22.8000 is not exactly 22.8 in your computer. If you round Pw, you will see the skewness is also NaN.

format long
Np=20; 
cb=2; 
ab = 30*(Np/100)^(cb-1); 
Qd = normrnd(76,0,100,1);
Pw=ab*((Qd/Np).^(cb-1));
Pw(1)
ans = 
  22.799999999999997
skewness(Pw)
ans = 
    -1
var(Pw)
ans = 
     1.274926715508706e-29
skewness(round(Pw))
ans = 
   NaN
skewness(Qd)
ans = 
   NaN
var(Qd)
ans = 
     0

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Angelavtc 2021-10-11

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@Cris LaPierre However, this is creating another kind of problem for simulations with variance different than 0. For example when:

clear, clc;
Np=20; 
cb=1.1; 
ab = 30*(Np/100)^(cb-1); 
n=10000;
Qd = normrnd(108,3,n,1);
Pw=ab*((Qd/Np).^(cb-1)); 
Skew1=skewness(Pw)
Skew1 = -0.0787
Skew2=skewness(round(Pw))
Skew2 = 33.2883