DstarM (version 0.4.0)

estQdf: Estimate quantiles of distribution

Description

Estimate quantiles of distribution

Usage

estQdf(p, x, cdf)

Value

Quantiles of cumulative distribution function(s). If the input was a matrix of cumulative distributions functions, a matrix of quantiles is returned.

Arguments

p

A vector of probabilities.

x

The x-axis values corresponding to the cumulative distribution function.

cdf

A cumulative distributions function, i.e. output of estCdf.

Details

Quantiles are obtained in the following manner. For p = 0 and p = 1, the minimum and maximum of x is used. For other probabilities the quantiles are obtained via q[i] = uniroot(x, cdf - p[i])$root. Y values are interpolated via approxfun.

Examples

x = seq(-9, 9, .1) # x-grid
d = dnorm(x) # density functions
p = seq(0, 1, .2) # probabilities of interest
cEst = estCdf(d) # estimate cumulative distribution functions
qEst = estQdf(p = p, x = x, cdf = cEst) # estimate quantiles
plot(x, cEst, bty = 'n', las = 1, type = 'l', ylab = 'Probability') # plot cdf
abline(h = p, v = qEst, col = 1:6, lty = 2) # add lines for p and for obtained quantiles
points(x = qEst, y = p, pch = 18, col = 1:6, cex = 1.75) # add points for intersections