R: Expectiles of the Exponential Distribution

Expectiles-Exponential {VGAM} | R Documentation

## Expectiles of the Exponential Distribution

### Description

Density function, distribution function, and expectile function and random generation for the distribution associated with the expectiles of an exponential distribution.

### Usage

    deexp(x, rate = 1, log = FALSE)
    peexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE)
    qeexp(p, rate = 1, Maxit.nr = 10, Tol.nr = 1.0e-6,
          lower.tail = TRUE, log.p = FALSE)
    reexp(n, rate = 1)

### Arguments

`x, p, q` | See `deunif`.
`n, rate, log` | See `rexp`.
`lower.tail, log.p` | Same meaning as in `pexp` or `qexp`.
`Maxit.nr, Tol.nr` | See `deunif`.

### Details

General details are given in `deunif` including a note regarding the terminology used. Here, `exp` corresponds to the distribution of interest, F, and `eexp` corresponds to G. The addition of “`e`” is for the ‘other’ distribution associated with the parent distribution. Thus `deexp` is for g, `peexp` is for G, `qeexp` is for the inverse of G, `reexp` generates random variates from g.

For `qeexp` the Newton-Raphson algorithm is used to solve for y satisfying p = G(y). Numerical problems may occur when values of `p` are very close to 0 or 1.

### Value

`deexp(x)` gives the density function g(x). `peexp(q)` gives the distribution function G(q). `qeexp(p)` gives the expectile function: the value y such that G(y)=p. `reexp(n)` gives n random variates from G.

### Author(s)

T. W. Yee and Kai Huang

### See Also

`deunif`, `denorm`, `dexp`.

### Examples

    my.p <- 0.25; y <- rexp(nn <- 1000)
    (myexp <- qeexp(my.p))
    sum(myexp - y[y <= myexp]) / sum(abs(myexp - y))  # Should be my.p

    ## Not run:  par(mfrow = c(2,1))
    yy <- seq(-0, 4, len = nn)
    plot(yy, deexp(yy),  col = "blue", ylim = 0:1, xlab = "y", ylab = "g(y)",
         type = "l", main = "g(y) for Exp(1); dotted green is f(y) = dexp(y)")
    lines(yy, dexp(yy), col = "darkgreen", lty = "dotted", lwd = 2)  # 'original'

    plot(yy, peexp(yy), type = "l", col = "blue", ylim = 0:1,
         xlab = "y", ylab = "G(y)", main = "G(y) for Exp(1)")
    abline(v = 1, h = 0.5, col = "red", lty = "dashed")
    lines(yy, pexp(yy), col = "darkgreen", lty = "dotted", lwd = 2)
    ## End(Not run)

[Package VGAM version 1.1-3 Index]