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

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 interpolating splines on an adaptive finer grid.

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

See also

Examples

x <- c(rnorm(100), rnorm(100, 3, 2)) dens <- densityMclust(x) 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$waiting) plot(dens.waiting)
plot(cdfMclust(dens.waiting), type = "l", xlab = dens.waiting$varname, ylab = "CDF") dens.eruptions <- densityMclust(faithful$eruptions) plot(dens.eruptions)
plot(cdfMclust(dens.eruptions), type = "l", xlab = dens.eruptions$varname, ylab = "CDF") par(mfrow = c(1,1))