# cdfMclust: Cumulative Distribution and Quantiles for a univariate... In mclust: Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation

## Description

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

## Usage

 1 2 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.

Luca Scrucca

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x <- c(rnorm(100), rnorm(100, 3, 2)) dens <- densityMclust(x) summary(dens, parameters = TRUE) cdf <- cdfMclust(dens) str(cdf) q <- quantileMclust(dens, p = c(0.01, 0.1, 0.5, 0.9, 0.99)) cbind(quantile = q, cdf = cdfMclust(dens, q)\$y) 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))

### Example output

Package 'mclust' version 5.3
Type 'citation("mclust")' for citing this R package in publications.
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Density estimation via Gaussian finite mixture modeling
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Mclust E (univariate, equal variance) model with 2 components:

log.likelihood   n df       BIC       ICL
-423.2397 200  4 -867.6726 -895.7996

Clustering table:
1   2
140  60

Mixing probabilities:
1        2
0.685091 0.314909

Means:
1         2
0.4079899 4.2651792

Variances:
1       2
1.52995 1.52995
List of 2
\$ x: num [1:100] -3.6 -3.48 -3.35 -3.22 -3.1 ...
\$ y: num [1:100] 0.000407 0.000579 0.000815 0.001137 0.001571 ...
quantile  cdf
[1,] -2.2895514 0.01
[2,] -0.8956196 0.10
[3,]  1.1551263 0.50
[4,]  4.8533915 0.90
[5,]  6.5604061 0.99

mclust documentation built on Nov. 5, 2021, 5:07 p.m.