# [R] How to find local minimum between distributions using mixtools?

Luigi Marongiu m@rong|u@|u|g| @end|ng |rom gm@||@com
Wed Oct 13 11:11:13 CEST 2021

```Hello,
I have two peaks distributions (and some noise values in between), and
I used mixtools to characterize the two overlapping data. How can I
find the minimum between the peak distributions?
The sigma value of the second population is close to that value, but I
am not sure if this is really the cut-off point between the two
distributions (by eye, I would say the value is 0.125 against 0.1 of
the sigma value). Is there a better approach?
Thanks

```
set.seed(10)
negative_mr <- runif(50, 0, 0.099)
negative_fcn <- runif(50, 1, 40)
positive_mr <- c(runif(30, 0.2, 0.5), runif(20, 0.4, 0.5))
positive_fcn <- c(runif(30, 25, 40), runif(20, 10, 25))
uncertain_mr <- runif(10, 0.099, 0.2)
uncertain_fcn <- runif(10, 2, 40)
df <- data.frame(Y=c(negative_mr, uncertain_mr, positive_mr),
X=c(negative_fcn, uncertain_fcn, positive_fcn),
GROUP=c(rep("negative", length(negative_mr)),
rep("uncertain", length(uncertain_mr)),
rep("positive", length(positive_mr))))
library(mixtools)
model = normalmixEM((x = df\$Y))
summary(model)
# plot
plot(model, which=2)
Cut_off <- model\$sigma[2]
Cut_offE <- 0.125
abline(v=Cut_off, col="blue", lwd=2)
abline(v=Cut_offE, col="blue", lwd=2, lty=2)
plot(df\$Y[df\$GROUP=="negative"]~df\$X[df\$GROUP=="negative"],
pch=1, ylim=c(0,0.5), xlim=c(0,41), cex=1.5,
xlab=expression(bold("X")),
ylab=expression(bold("Y")))
points(df\$Y[df\$GROUP=="positive"]~df\$X[df\$GROUP=="positive"],
pch=16, cex=1.5)
points(df\$Y[df\$GROUP=="uncertain"]~df\$X[df\$GROUP=="uncertain"],
pch=16, cex=1.5, col="grey")
abline(h=Cut_off, col="blue", lwd=2)
abline(h=Cut_offE, col="blue", lwd=2, lty=2)
```

--
Best regards,
Luigi

```