# Cumulative distribution and quantiles of univariate model-based mixture density estimation for bounded data Compute the cumulative density function (cdf) or quantiles of a one-dimensional density for bounded data estimated via the transformation-based approach for Gaussian mixtures in `densityMclustBounded()`. Diagnostic plots for density estimation of bounded data via transformation-based approach of Gaussian mixtures. Only available for the one-dimensional case. The two diagnostic plots for density estimation in the one-dimensional case are discussed in Loader (1999, pp- 87-90). ```r cdfDensityBounded(object, data, ngrid = 100, ...) quantileDensityBounded(object, p, ...) densityMclustBounded.diagnostic( object, type = c("cdf", "qq"), col = c("black", "black"), lwd = c(2, 1), lty = c(1, 1), legend = TRUE, grid = TRUE, ... ) ``` ## Arguments - `object`: An object of class `'mclustDensityBounded'` obtained from a call to `densityMclustBounded()` function. - `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. - ``...``: Additional arguments. - `p`: A numeric vector of probabilities corresponding to quantiles. - `type`: The type of graph requested: * `"cdf"` A plot of the estimated CDF versus the empirical distribution function. * `"qq"` A Q-Q plot of sample quantiles versus the quantiles obtained from the inverse of the estimated cdf. - `col`: A pair of values for the color to be used for plotting, respectively, the estimated CDF and the empirical cdf. - `lwd`: A pair of values for the line width to be used for plotting, respectively, the estimated CDF and the empirical cdf. - `lty`: A pair of values for the line type to be used for plotting, respectively, the estimated CDF and the empirical cdf. - `legend`: A logical indicating if a legend must be added to the plot of fitted CDF vs the empirical CDF. - `grid`: A logical indicating if a `grid()` should be added to the plot. ## Returns `cdfDensityBounded()` returns a list of `x` and `y` values providing, respectively, the evaluation points and the estimated cdf. `quantileDensityBounded()` returns a vector of quantiles. No return value, called for side effects. ## 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. ## Examples ```r # univariate case with lower bound x <- rchisq(200, 3) dens <- densityMclustBounded(x, lbound = 0) xgrid <- seq(-2, max(x), length=1000) cdf <- cdfDensityBounded(dens, xgrid) str(cdf) plot(xgrid, pchisq(xgrid, df = 3), type = "l", xlab = "x", ylab = "CDF") lines(cdf, col = 4, lwd = 2) q <- quantileDensityBounded(dens, p = c(0.01, 0.1, 0.5, 0.9, 0.99)) cbind(quantile = q, cdf = cdfDensityBounded(dens, q)$y) plot(cdf, type = "l", col = 4, xlab = "x", ylab = "CDF") points(q, cdfDensityBounded(dens, q)$y, pch = 19, col = 4) # univariate case with lower & upper bounds x <- rbeta(200, 5, 1.5) dens <- densityMclustBounded(x, lbound = 0, ubound = 1) xgrid <- seq(-0.1, 1.1, length=1000) cdf <- cdfDensityBounded(dens, xgrid) str(cdf) plot(xgrid, pbeta(xgrid, 5, 1.5), type = "l", xlab = "x", ylab = "CDF") lines(cdf, col = 4, lwd = 2) q <- quantileDensityBounded(dens, p = c(0.01, 0.1, 0.5, 0.9, 0.99)) cbind(quantile = q, cdf = cdfDensityBounded(dens, q)$y) plot(cdf, type = "l", col = 4, xlab = "x", ylab = "CDF") points(q, cdfDensityBounded(dens, q)$y, pch = 19, col = 4) # univariate case with lower bound x <- rchisq(200, 3) dens <- densityMclustBounded(x, lbound = 0) plot(dens, x, what = "diagnostic") # or densityMclustBounded.diagnostic(dens, type = "cdf") densityMclustBounded.diagnostic(dens, type = "qq") # univariate case with lower & upper bounds x <- rbeta(200, 5, 1.5) dens <- densityMclustBounded(x, lbound = 0, ubound = 1) plot(dens, x, what = "diagnostic") # or densityMclustBounded.diagnostic(dens, type = "cdf") densityMclustBounded.diagnostic(dens, type = "qq") ``` ## References Loader C. (1999), Local Regression and Likelihood. New York, Springer. ## See Also `densityMclustBounded()`, `plot.densityMclustBounded()`. `densityMclustBounded()`, `plot.densityMclustBounded()`. ## Author(s) Luca Scrucca

densityMclustBounded.diagnostic function