Cumulative Distribution and Quantiles for a univariate Gaussian mixture distribution

Compute the cumulative density function (cdf) or quantiles from an estimated one-dimensional Gaussian mixture fitted using densityMclust.

Usage

cdfMclust(object, data, ngrid = 100, ...)
quantileMclust(object, p, ...)

Arguments

object: a densityMclust model object.
data: a numeric vector of evaluation points.
ngrid: the number of points in a regular grid to be used as evaluation points if no data are provided.
p: a numeric vector of probabilities.
...: further arguments passed to or from other methods.

Details

The cdf is evaluated at points given by the optional argument data. If not provided, a regular grid of length ngrid for the evaluation points is used.

The quantiles are computed using bisection linear search algorithm.

Value

cdfMclust returns a list of x and y values providing, respectively, the evaluation points and the estimated cdf.

quantileMclust returns a vector of quantiles.

Author

Luca Scrucca

Examples

# \donttest{
x <- c(rnorm(100), rnorm(100, 3, 2))
dens <- densityMclust(x, plot = FALSE)
summary(dens, parameters = TRUE)
#> ------------------------------------------------------- 
#> Density estimation via Gaussian finite mixture modeling 
#> ------------------------------------------------------- 
#> 
#> Mclust V (univariate, unequal variance) model with 2 components: 
#> 
#>  log-likelihood   n df       BIC      ICL
#>       -424.0276 200  5 -874.5469 -942.139
#> 
#> Mixing probabilities:
#>         1         2 
#> 0.4813092 0.5186908 
#> 
#> Means:
#>          1          2 
#> -0.0617169  2.8923878 
#> 
#> Variances:
#>         1         2 
#> 0.8938594 4.3252118 
cdf <- cdfMclust(dens)
str(cdf)
#> List of 2
#>  $ x: num [1:100] -3.8 -3.66 -3.52 -3.38 -3.25 ...
#>  $ y: num [1:100] 0.000357 0.000458 0.000591 0.000766 0.001 ...
q <- quantileMclust(dens, p = c(0.01, 0.1, 0.5, 0.9, 0.99))
cbind(quantile = q, cdf = cdfMclust(dens, q)$y)
#>        quantile  cdf
#> [1,] -2.1730968 0.01
#> [2,] -0.9526056 0.10
#> [3,]  0.9295521 0.50
#> [4,]  4.6968529 0.90
#> [5,]  7.1950392 0.99
plot(cdf, type = "l", xlab = "x", ylab = "CDF")
points(q, cdfMclust(dens, q)$y, pch = 20, col = "red3")


par(mfrow = c(2,2))
dens.waiting <- densityMclust(faithful$waiting)
plot(cdfMclust(dens.waiting), type = "l", 
     xlab = dens.waiting$varname, ylab = "CDF")
dens.eruptions <- densityMclust(faithful$eruptions)
plot(cdfMclust(dens.eruptions), type = "l", 
     xlab = dens.eruptions$varname, ylab = "CDF")

par(mfrow = c(1,1))
# }