admix (version 2.3.4)

decontaminated_cdf: Estimates the decontaminated CDF of the unknown component in an admixture

Description

Estimates the decontaminated cumulative distribution function (CDF) of the unknown component in an admixture model, using inversion of the admixture CDF. 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

decontaminated_cdf(sample1, estim.p, admixMod)

Value

The decontaminated CDF F of the admixture model, of class 'stepfun' (step function).

Arguments

sample1

Observations of the sample under study.

estim.p

The estimated weight of the unknown component distribution, related to the proportion of the unknown component in the admixture model studied.

admixMod

An object of class 'admix_model', containing useful information about distributions and parameters.

Author

Xavier Milhaud

Details

The decontaminated CDF is obtained by inverting the admixture CDF, given by L = p*F + (1-p)*G, to isolate the unknown component F after having estimated p. This means that F = (1/hat(p)) * (hat(L)-(1-p)*G).

Examples

## Simulate mixture data:
mixt1 <- twoComp_mixt(n = 400, weight = 0.4,
                      comp.dist = list("norm", "norm"),
                      comp.param = list(list("mean" = 3, "sd" = 0.5),
                                        list("mean" = 0, "sd" = 1)))
mixt2 <- twoComp_mixt(n = 300, weight = 0.6,
                      comp.dist = list("norm", "norm"),
                      comp.param = list(list("mean" = 3, "sd" = 0.5),
                                        list("mean" = 5, "sd" = 2)))
data1 <- getmixtData(mixt1)
data2 <- getmixtData(mixt2)
## Define the admixture models:
admixMod1 <- admix_model(knownComp_dist = mixt1$comp.dist[[2]],
                         knownComp_param = mixt1$comp.param[[2]])
admixMod2 <- admix_model(knownComp_dist = mixt2$comp.dist[[2]],
                         knownComp_param = mixt2$comp.param[[2]])
## Estimation:
est <- admix_estim(samples = list(data1,data2),
                   admixMod = list(admixMod1,admixMod2), est_method = 'PS')
prop <- getmixingWeight(est)
## Determine the decontaminated version of the unknown CDF by inversion:
F1 <- decontaminated_cdf(sample1 = data1, estim.p = prop[1], admixMod = admixMod1)
F2 <- decontaminated_cdf(sample1 = data2, estim.p = prop[2], admixMod = admixMod2)
abs <- seq(from=-1, to=4, length.out=100)
plot(x=abs, y=F1(abs), xlim=c(-1,4), ylim=c(0,1), type="l")
par(new = TRUE)
plot(x=abs, y=F2(abs), xlim=c(-1,4), ylim=c(0,1), type="l", col="red")