I am trying to find the local maxima for a probability density function (found using R’s

`density`

method). I cannot do a simple “look around neighbors” method (where one looks around a point to see if it’s a local maximum with respect to its neighbors) as there is a large volume of data. Furthermore, it seems more efficient and generic to use something like Spline interpolation and then find the roots of the 1st derivative, as opposed to building a “look around neighbors” with fault tolerance and other parameters.So, my questions:

- Given a function from
`splinefun`

, what methods will find the local maxima?- Is there an easy / standard way to find derivatives of a function returned using
`splinefun`

?- Is there a better/standard way to find the local maxima of a probability density function ?
For reference, below is a plot of my density function. Other density functions I’m working with are similar in form. I should say that I am new to R, but not new to programming, so there may be a standard library or package for achieving what I need.

Thanks for your help!!

**Answer**

What you want to do is called peak detection in chemometrics. There are various methods you can use for that. I demonstrate only a very simple approach here.

```
require(graphics)
#some data
d <- density(faithful$eruptions, bw = "sj")
#make it a time series
ts_y<-ts(d$y)
#calculate turning points (extrema)
require(pastecs)
tp<-turnpoints(ts_y)
#plot
plot(d)
points(d$x[tp$tppos],d$y[tp$tppos],col="red")
```

**Attribution***Source : Link , Question Author : aaronlevin , Answer Author : Roland*