I asked myself, what on earth is a Pearson type IV distribution?

(I had a rough memory that Student (1908) mentioned a Pearson type III distribution and used that to develop what later became known as the t-test.)

I found this

link about the Pearson type IV distribution. I hope it helps.

Also, if it is any good you can expect to find it in R, don't you agree?

I found this package (

Package ‘PearsonDS’) about these distributions. Type IV on page 15.

It also says:

"The Pearson Type 0 (aka Normal) Distribution"

"The Pearson Type I (aka Beta) Distribution"

"The Pearson Type II (aka Symmetric Beta) Distribution"

"The Pearson Type III (aka Gamma) Distribution"

"The Pearson Type IV Distribution"

"The Pearson Type V (aka Inverse Gamma) Distribution"

"The Pearson Type VI (aka Beta Prime) Distribution"

"The Pearson Type VII (aka Student’s t) Distribution"

So now maybe these distributions (with nomenclature from 1900) are a little bit less mysterious to us.

The inverse, the quantile values, can be found with the qpearsonIV() function (page 15).

Maybe the OP must do the computations in excel. But it could be good to check that the results corresponds to what you can get from the R-package. (Also, many of us would trust the results much more from an R package.)