Generation of large data sets (10^4) for log Pearson type III distribution and finding its parameters

Dear All, I have a data set which is log pearson type III distributed fitted. Using that data how can I find the parameters associated with that distribution. further using that paramters I have to generate more number of samples. That samples which I have generated should overlap twith the data given below. Can anyone please help me with this I am working on this from a long time.

Q PDF(LP3)

14.162562 0.000011

28.325123 0.000723

31.403941 0.001391

33.866995 0.002169

36.945813 0.002904

39.408867 0.003638

41.871921 0.004439

45.566502 0.005262

49.261084 0.006063

53.571429 0.006875

59.729064 0.007632

70.197044 0.008288

89.901478 0.007654

100.369458 0.006875

113.300493 0.005996

125.000000 0.005173

137.315271 0.004350

150.862069 0.003571

167.487685 0.002815

192.118227 0.002025

225.985222 0.001246

275.246305 0.000679

326.970443 0.000345

370.073892 0.000211

418.103448 0.000133

459.359606 0.000089

500 5.56242E-05

[John D'Errico]

That is NOT a data set of samples from a pearson distributon, but apparently a set of points generated from the PDF. There is a SIGNIFICANT difference. It is a common mistake.