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

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Angelavtc
Angelavtc 2021-10-11
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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Cris LaPierre
Cris LaPierre 2021-10-11
Ran in:
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
Angelavtc 2021-10-11
Ran in:
@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
Skew1 and Skew2 are completely different, being Skew1 the one close to 0 (my correct answer). How can I correct this?
Thank you!

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