According to edgeR package, I can estimate the dispersion of my dataset using:

y <- estimateDisp(y, design, robust=TRUE)

y$common.dispersion

The square root of the common dispersion gives the coefficient of biological variation. And, the dispersion estimates can be viewed in a BCV plot:

plotBCV(y)

How do I know the function that generate this graph?

I need to know the coordinates (x,y) of the vertex (max and min value of "trend" in the Y-axis to each vertex) of the "trend dispersion" and the values of X where the "trend" (blue) intercepts the commun dispersion line (red)

Don´t worry about the spread of the data, the high variability is expected in my case.

**Moderator edit:** Here's a link to the BCV plot:

https://www.dropbox.com/s/h9p7356rpwkwwh1/GraphDispersion.png?dl=0

I'm not sure what you mean - are you referring to a bimodal distribution for the dispersions? The concept of a "binomial dispersion" doesn't make any sense, as the binomial distribution is underdispersed relative to the Poisson. Your question would be a lot clearer if you posted an image of the actual BCV plot.

Yes, bimodal, sorry. But my question is simple. I just need to know the "X1,x2,x3,x4,x5" (where the "trend" crosses the "common dispersion average line") and the "Yv" that is the maximum and minimum value to the Y(trend's valley)

The trend curve is not a parabola, and it never crosses the x-axis, so again, we're not really sure what you're asking for. Are you looking for where the trend intersects the red line representing the common dispersion estimate across all genes? If so, I'm not aware of any interesting or useful information that can be gleaned from determining these points. Any continuous curve is going to equal its average at some point. You should take Gordon's advice and figure out why your dispersions are so high. Chances are that if you can solve that problem, the funny-looking trend will go away too.

Yes, I just need to know the function (x) that generate this dispersion plot to be able to determine the maximum and minimum values for the Y axis "trend" (valleys).

My data is not RNA seq, this is kind of expected dispersion for my data.

Thank you so much

The name of your image suggests that it's MeDIP data. I don't work with MeDIP, but I have done a lot of ChIP-seq stuff which (obviously) also has an IP step. In ChIP-seq, the signal is moderately variable due to differences in IP efficiency across samples, and this can result in some larger BCVs. Even so, the common/trended values that I see are rarely above 0.5, and never above 1. Your values indicate that there is a strong batch effect between your replicates, which is not unsurprising due to the nature of the IP step. You may need to consider blocking on the batch effect, if you can; or doing some appropriate normalization to get rid of the differences between samples.

only an additional information (according to the manual):

"The BCV is the square root of the "negative binomial dispersion". This function displays the common, trended and tagwise BCV estimates".