Hi Rstudio community,

I am a student of the university of Leuven, and I’m new to this community and Rstudio in general. I am struggling to implement the function smsn.mix from the package mixsmsn, Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions. In my research I measure particles and the result is a long list (3059 observations) of diameters, data set is called Diameter1. I will give the code and the result in order to clarify my problem.

**Code:**

hist(Diameter1, breaks = 100, main = "Histogram of caps", xlab = "diameter")

**Result:**

See figure below, only the histogram, not the red curve. I obtain a distribution curve with two distinct modes (bimodal estimated means 1.5 and 17). The curves are not normal distribution, it shows large tailing. Now I would like to know the mean and the sigma value for each distribution around each mode.

**Code:**

Skew.map2 <- smsn.mix(Diameter1, nu =23, g =2, mu=c(1.5,17), sigma2=c(2,100), family = "Skew.t", calc.im = FALSE)

mix.hist(Diameter1, Skew.map2, breaks = 100)

Result:

Seemingly, only one mode was found (red curve). Details of the analysis by smsn.mix show indeed two modes, but they are unexpected.

Code:

mix.print(Skew.map2)

Result:

Number of observations: 3059

Hyperparameter(nu): 8.022694

```
group 1 group 2
```

mu 18.578 19.297

sigma2 241.148 62.370

shape 1.671 -1.135

AIC: 22361.43

BIC: 22403.61

EDC: 22424.86

ICL: 23013.31

EM iterations: 11

The first mode around 1.5, is not seen by the function. When I ask to look for 3 modes, g = 3 in the function I do get a nice fit (red curve) and the first mode is observed, however still two modes are seen in the second part of the curve which seems strange.

**Code:**

Skew.map2 <- smsn.mix(Diameter1, nu =23, g =3, mu=c(1.5,17), sigma2=c(2,100),family = "Skew.t", calc.im = FALSE)

mix.hist(Diameter1, Snorm.map2, breaks = 100)

**Result:**

mix.print(Snorm.map2)

Number of observations: 3059

Hyperparameter(nu): 3.30653

```
group 1 group 2 group 3
```

mu 21.634 1.539 12.499

sigma2 202.873 2.207 34.779

shape 3.454 24.159 2.480

AIC: 20687.02

BIC: 20753.3

EDC: 20786.7

ICL: 21232.43

EM iterations: 101

So my question is, how do I get a fit of the two peaks of my distribution, together with the info of means and sigma with this function smsn.mix. Why does it see 3 modes and I do not?

Thank you all in advance