loghp {FatTailsR} | R Documentation |
Inverse Power Hyperbolas and Inverse Power Hyperbolic Functions
Description
The inverse power hyperbolas and the inverse power hyperbolic functions: arc-cosine-hp, arc-sine-hp, arc-tangent-hp, arc-secant-hp, arc-cosecant-hp and arc-cotangent-hp.
Usage
loghp(x, k = 1)
acoshp(x, k = 1)
asinhp(x, k = 1)
atanhp(x, k = 1)
asechp(x, k = 1)
acosechp(x, k = 1)
acotanhp(x, k = 1)
Arguments
x |
a numeric value, vector or matrix. |
k |
a numeric value, preferably strictly positive. |
Details
loghp
function is defined on (0, +Inf) by:
acoshp
function is defined on [1, +Inf) by:
asinhp
function is defined on (-Inf, +Inf) by:
atanhp
function is defined on (-1, +1) by:
asechp
function is defined on (0, +1] by:
acosechp
function is defined on (-Inf, 0) U (0, +Inf) by:
acotanhp
function is defined on (-Inf, -1) U (1, +Inf) by:
If k is a vector of length > 1, then the use of the function
outer
is recommanded.
See Also
The power hyperbolic functions exphp
.
Examples
### Example 1 (acoshp, asinhp, atanhp)
loghp( c(ppoints(10), 1, 1/rev(ppoints(10))), k = 2)
acoshp( 1:10, k = 2)
asinhp( -5:5, k = 2)
atanhp( seq(-1, 1, by = 0.1), k = 2)
asechp( ppoints(20), k = 2)
acosechp( -5:5, k = 2)
acotanhp( c( -1/ppoints(10), 1/rev(ppoints(10))), k = 2)
x <- (-3:3)*3
loghp(exphp(x, k = 4), k = 4)
acoshp(coshp(x, k = 4), k = 4)
asinhp(sinhp(x, k = 4), k = 4)
atanhp(tanhp(x, k = 4), k = 4)
### Example 2 (loghp, acoshp, asinhp, atanhp)
k <- c(0.6, 1, 1.5, 2, 3.2, 10) ; names(k) <- k
olty <- c(2, 1, 2, 1, 2, 1, 1)
olwd <- c(1, 1, 2, 2, 3, 4, 2)
ocol <- c(2, 2, 4, 4, 3, 3, 1)
op <- par(mfrow = c(2, 2), mgp = c(1.5, 0.8, 0), mar = c(3, 3, 2, 1))
xld <- 0.05
xl <- seq(0.05, 20, xld) ; names(xl) <- xl
Tlcoshp <- ts(cbind(outer(xl, k, loghp), "2*log(x)" = 2*log(xl)),
start = xl[1], deltat = xld)
plot(Tlcoshp, plot.type = "single", xlim = c(0,20), ylim = c(-5,15),
lty = olty, lwd = olwd, col = ocol, xaxs = "i", yaxs = "i",
xlab="", ylab = "", main = "loghp(x, k)" )
legend("bottomright", title = expression(kappa), legend = colnames(Tlcoshp),
inset = 0.02, lty = olty, lwd = olwd, col = ocol, cex = 0.7 )
## acoshp(x, k)
xcd <- 0.5
xc <- seq(1, 20, xcd) ; names(xc) <- xc
Tacoshp <- ts(cbind(outer(xc, k, acoshp), "2*acosh(x)" = 2*acosh(xc)),
start = xc[1], deltat = xcd)
plot(Tacoshp, plot.type = "single", ylim = c(0,15), lty = olty, lwd = olwd, col = ocol,
xaxs = "i", yaxs = "i", xlab = "", ylab = "", main = "acoshp(x, k)" )
legend("bottomright", title = expression(kappa), legend = colnames(Tacoshp),
inset = 0.02, lty = olty, lwd = olwd, col = ocol, cex = 0.7 )
## asinhp(x, k)
xsd <- 0.5
xs <- seq(-10, 10, xsd) ; names(xs) <- xs
Tasinhp <- ts(cbind(outer(xs, k, asinhp), "2*asinh(x)" = 2*asinh(xs)),
start = xs[1], deltat = xsd)
plot(Tasinhp, plot.type = "single", ylim = c(-10,10), lty = olty, lwd = olwd, col = ocol,
xaxs = "i", yaxs = "i", xlab = "", ylab = "", main = "asinhp(x, k)" )
legend("topleft", title = expression(kappa), legend = colnames(Tasinhp),
inset = 0.02, lty = olty, lwd = olwd, col = ocol, cex = 0.7 )
## atanhp(x, k)
xtd <- 0.01
xt <- seq(-1, 1, xtd) ; names(xt) <- xt
Tatanhp <- ts(cbind(outer(xt, k, atanhp), "2*atanh(x)" = 2*atanh(xt)),
start = xt[1], deltat = xtd)
plot(Tatanhp, plot.type = "single", ylim = c(-10,10), lty = olty, lwd = olwd, col = ocol,
xaxs = "i", yaxs = "i", xlab = "", ylab = "", main = "atanhp(x, k)" )
legend("topleft", title = expression(kappa), legend = colnames(Tatanhp),
inset = 0.02, lty = olty, lwd = olwd, col = ocol, cex = 0.7 )
### End Example 2
[Package FatTailsR version 1.8-5 Index]