# Is it possible to build a curve with a given skewness and kurtosis?

I have data in the following form:

Day  Kurtosis    Skewness   Total Inflows
163     .3          .5        435670


I'm attempting to do some modeling of an inflow regime between a river and a reservoir. To do this, I need a simulated inflow regime based on observed data.

My original plan was to build a distribution based on a given kurtosis and skewness since I'm able to randomize those easily. The idea was that I could generate a curve from those two data points and the area under the curve to give me valid curves similar to the observed data. The resultant curve should look something like this (although there is significant variation year to year):

I can add the daily variation after the curve is created without issue (I think).

Unfortunately, I'm very new to the math and stats that are in play here, and I'm now unsure if it is possible to do anything with this data to give me fabricated curves. Does anyone know of a method for creating curves in this way? Alternatively, are there other methods that I might be able to employ to the same effect given different data?

I also have data for each (observed) year in the following form:

Date             Inflows
12-Oct- 2002     23000


with a similar entry for each day.

• It is - as discussed for example here, here, here, and here ... but I don't think that's a suitable way to approach modelling the shape of what's clearly a time-series. For starters, you have dependence over time that isn't accounted for by the approach you're taking here. Jul 9, 2014 at 0:22
• @Glen_b Thanks for the links! I've seen some of them before but I'm new enough to this that I was having a hard time discerning if they solved my problem or not. Guess I'll need to spend more time with them... With regards to the rest of your comment, do you have any suggestions for better methods that I might be able to pursue? Note: The only area of the graph I'm attempting to replace is the green portion, as the other portion of the year is insignificant to the problem I'm looking to solve. Jul 9, 2014 at 0:29
• Are you sure you want to ask a question about curves? The graph you posted is a time series, not a density plot. Jul 9, 2014 at 8:13
• @StasK Frankly, I'm not sure. Is there a better method for generating a randomized time series based on the data I have? I was approaching it this way because it seemed like I could generate a curve and then pull points from it to give myself a time series, then add scatter to those points to account for the daily variation. Unfortunately, I'm pretty out of my depth with this stuff. Any insights or resources you can recommend would be greatly appreciated. Jul 9, 2014 at 18:01
• I don't really, other than to find an environmental statistician near you (community.amstat.org/ENVR/home). This is a pretty specialized task, and I am still not sure I understand what you are asking. Jul 10, 2014 at 12:00