The goal of admix is to provide code for estimation, hypothesis testing and clustering methods in admixture models.

We remind that an admixture model has the following cumulative distribution function (cdf) *L*(*x*) = *p**F*(*x*) + (1−*p*)*G*(*x*), *x* ∈ ℝ,

where *G* is a perfectly known cdf, and *p* and *F* are unknown.

The cdf *F* relates to the contamination phenomenon that is added to the well-known signal *G*, with proportion *p*.

The proportion of the unknown component in the two-component mixture model can be easily estimated under weak nonparametric assumptions on the related distribution. The decontaminated version of this unknown component distribution can then be tested against some other specified distribution (included another decontaminated unknown component). Finally, clustering of *K* populations is made possible, based on hypothesis tests that compare unknown component distributions. The package is suited to one-sample as well as multi-samples analysis.

# Installation

You can install the released version of admix from Github with:

```
#once on CRAN with : install.package("admix")
# from now on:
remotes::install_github(repo = "XavierMilhaud/admix@main", build_manual = TRUE, build_vignettes = FALSE)
```

The optional argument build_vignettes can be set to TRUE to get vignettes that help to understand the functionnalities of the package.

To get some help about the functionalities of the package, do once installed:

`help(package = 'admix')`

More details can also be found through the vignettes, available in admix github-pages (see https://xaviermilhaud.github.io/admix/, in Menu Articles).

## Example

This is a basic example which shows you how to estimate the unknown component proportion and the localization shift parameters in an admixture model where the unknown component density is assumed to be symmetric. In practice, the cdf *L* is given by *L*(*x*) = *p**F*(*x*−*μ*) + (1−*p*)*G*(*x*), *x* ∈ ℝ, where *p* is the unknown component weight, and *μ* is the localization shift parameter of the unknown cdf *F* with symmetric density.

The estimation would be made through the following commands:

```
library(admix)
## Simulate data:
list.comp <- list(f = 'norm', g = 'norm')
list.param <- list(f = list(mean = 3, sd = 0.5),
g = list(mean = 0, sd = 1))
data1 <- rsimmix(n = 1000, unknownComp_weight = 0.8, list.comp, list.param)[['mixt.data']]
## Perform the estimation of parameters in real-life:
list.comp <- list(f = NULL, g = 'norm')
list.param <- list(f = NULL, g = list(mean = 0, sd = 1))
BVdk_estimParam(data1, method = 'L-BFGS-B', list.comp, list.param)
#> [1] 0.7977239 3.0114174
```