# [R] Bivariate normal equal-probability curve...

David B. Thompson, Ph.D., P.E. drdbthompson at gmail.com
Fri Jan 4 15:04:17 CET 2008

```Good morning and I appreciate the availability of a help-list. I am a
professional hydrologist, but not a professional statistician. Yet I
find myself using statistical tools at least part of the time. My
discovery of the R-project through a friend has been most helpful.

Here is my problem:

I'm tasked with fitting a dataset comprising correlated discharges
from adjacent watersheds to bivariate normal and bivariate Gumbel
distributions (data untransformed and then log-transformed to reduce
skew). (In addition, I'm tasked with exploring a couple of Archimedian
copulas to link univariate Pearson Type III distributions fit to log-
transformed discharges, but that's a topic for later after I educate
myself a bit more. ;)

In working with the bivariate normal, I can fit the marginal
distributions to the data and determine the correlation coefficient
relatively easily. I know how to do that. But, I'm struggling to find
a routine or routines that will define a curve of equal exceedence (or
non-exceedence) probability so I know the combination of discharges
from each watershed that produce the same risk of exceedence. Part of
my problem may result from the difference in my professional jargon
and statistical terminology.

I'm interested in solving the general problem so I can apply it to a
variety of sub-tasks associated with this work. I spent some time
(several hours) yesterday reviewing the available packages and am
impressed with what is available. However, I have not been able to
identify an appropriate package or routine to solve my problem.

To summarize, I'm trying to determine the line of equal cumulative
probability (what I learned to call exceedence or non-exceedence
probability) that defines combinations of discharges from adjacent
watersheds that have an equal exceedence (or non-exceedence)
probability of occurrence. A pointer to appropriate code would be most
appreciated.

Thanks...

-=d

Dr. David B. Thompson, Ph.D., P.E
Civil Engineering/Hydrologist

```