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.)
