## Description

Coefficient q_c(u) of eq. (15.15) in Eichner (2017).

## Usage

 `1` ```qc(u, cc = sqrt(5/3)) ```

## Arguments

 `u` Numeric vector. `cc` Numeric constant, defaults to √(5/3).

## Details

q_c(u) = 2/5 * c^5 / (3 - c^2) * (1 - 2 * u)

For further details see p. 297 f. in Eichner (2017) and/or Eichner & Stute (2013).

## Value

Vector of same length and mode as `u`.

## Note

q_c(u) should be undefined for c = √ 3, but `qc` is here implemented to return `Inf * (1 - 2*u)` if `cc` contains R's value of `sqrt(3)`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```u <- c(0, 1) # seq(0, 1, by = 0.1) c0 <- expression(sqrt(5/3)) c1 <- expression(sqrt(3) - 0.05) cgrid <- seq(1.4, 1.6, by = 0.1) cvals <- c(eval(c0), cgrid, eval(c1)) Y <- sapply(cvals, function(cc, u) qc(u, cc = cc), u = u) cols <- rainbow(ncol(Y), end = 9/12) matplot(u, Y, type = "l", lty = "solid", col = cols, ylab = expression(q[c](u))) abline(h = 0, lty = "dashed") legend("topright", title = "c", legend = c(c0, cgrid, c1), lty = 1, col = cols, cex = 0.8) ```

kader documentation built on May 1, 2019, 10:13 p.m.