## Plot the decontaminated density of the unknown component for an estimated admixture model

### Description

Plot the decontaminated density of the unknown component in the admixture model under study, after inversion of the admixture cumulative distribution function. Recall that an admixture model follows the cumulative distribution function (CDF) L, where L = p*F + (1-p)*G, with g a known CDF and p and f unknown quantities.

### Usage

```plot_decontamin_density(x_val, decontamin_obj, add_plot = FALSE)
```

### Arguments

 `x_val` A vector of X-axis values at which to plot the decontaminated density f. `decontamin_obj` An object from function 'decontamin_density_unknownComp', containing the X-axis values and range for plotting, the corresponding Y-axis values, and the support over which to plot the results. `add_plot` (default to FALSE) A boolean specifying if one plots the decontaminated density over an existing plot. Used for visual comparison purpose.

### Details

The decontaminated density is obtained by inverting the admixture density, given by l = p*f + (1-p)*g, to isolate the unknown component f after having estimated p.

### Value

The plot of the decontaminated density.

### Author(s)

Xavier Milhaud xavier.milhaud.research@gmail.com

### Examples

```####### Continuous support:
## Simulate data:
list.comp <- list(f1 = 'norm', g1 = 'norm',
f2 = 'norm', g2 = 'norm')
list.param <- list(f1 = list(mean = 3, sd = 0.5), g1 = list(mean = 0, sd = 1),
f2 = list(mean = 3, sd = 0.5), g2 = list(mean = 5, sd = 2))
sample1 <- rsimmix(n=3000, unknownComp_weight=0.7, comp.dist = list(list.comp\$f1,list.comp\$g1),
comp.param=list(list.param\$f1,list.param\$g1))
sample2 <- rsimmix(n=2500, unknownComp_weight=0.8, comp.dist = list(list.comp\$f2,list.comp\$g2),
comp.param=list(list.param\$f2,list.param\$g2))
## Estimate the mixture weight in each of the sample in real-life setting:
list.comp <- list(f1 = NULL, g1 = 'norm',
f2 = NULL, g2 = 'norm')
list.param <- list(f1 = NULL, g1 = list(mean = 0, sd = 1),
f2 = NULL, g2 = list(mean = 5, sd = 2))
estimate <- IBM_estimProp(sample1[['mixt.data']], sample2[['mixt.data']], comp.dist = list.comp,
comp.param = list.param, with.correction = FALSE, n.integ = 1000)
## Determine the decontaminated version of the unknown density by inversion:
res1 <- decontamin_density_unknownComp(sample1 = sample1[['mixt.data']],
comp.dist = list.comp[1:2], comp.param = list.param[1:2],
estim.p = estimate\$prop.estim[1])
res2 <- decontamin_density_unknownComp(sample1 = sample2[['mixt.data']],
comp.dist = list.comp[3:4], comp.param = list.param[3:4],
estim.p = estimate\$prop.estim[2])
## Use appropriate sequence of x values:
plot_decontamin_density(x_val = seq(from=0, to=6, length.out=100), decontamin_obj = res1,
plot_decontamin_density(x_val = seq(from=0, to=6, length.out=100), decontamin_obj = res2,
####### Countable discrete support:
list.comp <- list(f1 = 'pois', g1 = 'pois',
f2 = 'pois', g2 = 'pois')
list.param <- list(f1 = list(lambda = 3), g1 = list(lambda = 2),
f2 = list(lambda = 3), g2 = list(lambda = 4))
sample1 <- rsimmix(n=4000, unknownComp_weight=0.7, comp.dist = list(list.comp\$f1,list.comp\$g1),
comp.param=list(list.param\$f1,list.param\$g1))
sample2 <- rsimmix(n=3500, unknownComp_weight=0.85, comp.dist = list(list.comp\$f2,list.comp\$g2),
comp.param=list(list.param\$f2,list.param\$g2))
## Estimate the mixture weight in each of the sample in real-life setting:
list.comp <- list(f1 = NULL, g1 = 'pois',
f2 = NULL, g2 = 'pois')
list.param <- list(f1 = NULL, g1 = list(lambda = 2),
f2 = NULL, g2 = list(lambda = 4))
estimate <- IBM_estimProp(sample1[['mixt.data']], sample2[['mixt.data']], comp.dist = list.comp,
comp.param = list.param, with.correction = FALSE, n.integ = 1000)
## Determine the decontaminated version of the unknown density by inversion:
res1 <- decontamin_density_unknownComp(sample1 = sample1[['mixt.data']],
comp.dist = list.comp[1:2], comp.param = list.param[1:2],
estim.p = estimate\$prop.estim[1])
res2 <- decontamin_density_unknownComp(sample1 = sample2[['mixt.data']],
comp.dist = list.comp[3:4], comp.param = list.param[3:4],
estim.p = estimate\$prop.estim[2])
## Use appropriate sequence of x values:
plot_decontamin_density(x_val = seq(from=0, to=15, by=1), decontamin_obj = res1,
plot_decontamin_density(x_val = seq(from=0, to=15, by=1), decontamin_obj = res2,
####### Finite discrete support:
list.comp <- list(f1 = 'multinom', g1 = 'multinom',
f2 = 'multinom', g2 = 'multinom')
list.param <- list(f1 = list(size=1, prob=c(0.3,0.4,0.3)), g1 = list(size=1, prob=c(0.6,0.3,0.1)),
f2 = list(size=1, prob=c(0.3,0.4,0.3)), g2 = list(size=1, prob=c(0.2,0.6,0.2)))
sample1 <- rsimmix(n=4000, unknownComp_weight=0.8, comp.dist = list(list.comp\$f1,list.comp\$g1),
comp.param=list(list.param\$f1,list.param\$g1))
sample2 <- rsimmix(n=3500, unknownComp_weight=0.9, comp.dist = list(list.comp\$f2,list.comp\$g2),
comp.param=list(list.param\$f2,list.param\$g2))
## Estimate the mixture weight in each of the sample in real-life setting:
list.comp <- list(f1 = NULL, g1 = 'multinom',
f2 = NULL, g2 = 'multinom')
list.param <- list(f1 = NULL, g1 = list(size=1, prob=c(0.6,0.3,0.1)),
f2 = NULL, g2 = list(size=1, prob=c(0.2,0.6,0.2)))
estimate <- IBM_estimProp(sample1[['mixt.data']], sample2[['mixt.data']], comp.dist = list.comp,
comp.param = list.param, with.correction = FALSE, n.integ = 1000)
## Determine the decontaminated version of the unknown density by inversion:
res1 <- decontamin_density_unknownComp(sample1 = sample1[['mixt.data']],
comp.dist = list.comp[1:2], comp.param = list.param[1:2],
estim.p = estimate\$prop.estim[1])
res2 <- decontamin_density_unknownComp(sample1 = sample2[['mixt.data']],
comp.dist = list.comp[3:4], comp.param = list.param[3:4],
estim.p = estimate\$prop.estim[2])
## Use appropriate sequence of x values:
plot_decontamin_density(x_val = seq(from=0, to=6, by=1), decontamin_obj = res1,