A bug in pearsrnd?

With the following values for mean, std, skewness, and kurtosis, pearsrnd stalls without warning:

mean = -9.0000e-08 std = 0.6400 skewness = 2.2500e-19 kurtosis = 3.0000

Is it just my system, or do other people experience the same event?

[David Goodmanson]

Hi Ulrik,

Works for me in version 2017b. But it does have some interesting behavior. For your four parameter values with the minuscule but nonzero value of skewness,

[a b] = pearsrnd(mean,std,skewness,kurtosis,1,10)

gives 10 identical draws that all equal the mean, and pearson type 3. If you change the skewness to 0, the function gives sensible values for the draws and pearson type 0 (normal distribution) as it should.

[Ulrik William Nash]

Hi David, later today I did notice that MATLAB outputs something, but it strangely takes much longer than normal under the specified setting.

Answer 1

[John D'Errico]

I'm not amazed. These things can be tricky. Looks like pearsrnd is tripping over the very near zero skewness.

X = pearsrnd(-9.0000e-08,0.6400,0, 3.0000,1,10)
X =
  Columns 1 through 7
         -0.66873960681121         0.271599778145953         0.316496827107004        -0.557976990199874       -0.0679667761010375      -0.00640246071921475        -0.322436885401314
  Columns 8 through 10
         0.143696162106232        -0.024154191418116        -0.148957358392865

X = pearsrnd(-9.0000e-08,0.6400,2.25e-19, 3.0000,1,10)
X =
  Columns 1 through 7
                    -9e-08                    -9e-08                    -9e-08                    -9e-08                    -9e-08                    -9e-08                    -9e-08
  Columns 8 through 10
                    -9e-08                    -9e-08                    -9e-08

Yet, we see this, if we make the skewness a bit larger.

X = pearsrnd(-9.0000e-08,0.6400,2.25e-8, 3.0000,1,10)
X =
  Columns 1 through 7
         0.106139493587646        -0.217350258228149        -0.758287810680237         -1.06893690049347         0.127482009533081        -0.661103934642639         0.233781877163086
  Columns 8 through 10
         0.858859763744507         0.170714274051819         0.595377956035767

So it seems to be working properly here again. The way these things work is they test the parameters, depending on where they live, you get a different distribution. But some of those distributions can be rather nasty as I recall. So it looks like pearsrnd is getting stuck in a rabbit hole, depending on the value of skewness. Technically, a bug I guess, worth reporting as such.

The speed differential is not a bug though, just a feature. ;-)) Again, when you change parameters, the underlying distribution must some times change. And some distributions are MUCH, MUCH simpler to sample from. (One of the flaws with distribution systems like Pearson and Johnson families.)