# inverse integration of multimodal distribution

I have a probability distribution, with a number of modes with different peak values, and I have to capture the 90% most significant value ranges.

My idea is to apply a threshold starting from the maximum distribution kde or histogram value, and including all ranges surpassing the thresholds, decreasing the bar until 90% of the samples are covered.

My question is: is this a common analysis, and what is its name? Are there other significant ways of getting the most significant value ranges in a multimodal distribution?

• Very generally, it's called "root finding." That might seem like a trivial observation, but if you investigate the literature on numerical analysis--any intro textbook will cover this--knowing this name will help you find better algorithms to achieve the same result, ranging from bisection, the secant method, and on to derivative-based methods like Newton-Raphson if they are applicable to your model. – whuber Jan 12 '18 at 16:45
• Maybe I didn't explain myself well. My idea is to apply a threshold, and integrate all the histogram bars surpassing that threshold. Iteratively, I continue lowering the threshold until the integral of the covered segments is greater than 90%. In a multimodal distribution, the effect is that it starts integrating the modes by the peaks, thus I capture the most frequent values first. – Rodolfo Bonnin Jan 12 '18 at 21:43
• Yes, that's understood. You describe a function $f$ of the threshold $t$ and you seek a root of the function $f(t) - 0.90$. – whuber Jan 12 '18 at 22:16
• Thank you for the clarification regarding the calculation o the integral, its very useful advice. What I'm more interested in is in the detection and analytical analysis of the peaks, like baseline detection, peak integration like in chromatography, peaks over thresholds methods, in summary, getting the most useful distribution modes, and rejecting noise and outliers. The threshold technique was meant more like an example of the type of analysis I want to do. Thank you again. – Rodolfo Bonnin Jan 12 '18 at 22:53
• It's important to articulate the question you actually have rather than posting a question that--as in this case--turns out to have little or no bearing on what concerns you. Since nobody has yet ventured an answer to your post, feel free to edit it as much as you need. – whuber Jan 16 '18 at 16:04