divent (version 0.5-3)

ln_q: Deformed logarithm

Description

Calculate the deformed logarithm of order q.

Usage

ln_q(x, q)

Value

A vector of the same length as x containing the transformed values.

Arguments

x

A numeric vector or array.

q

A number.

Details

The deformed logarithm Tsallis1994divent is defined as \(\ln_q{x}=\frac{(x^{(1-q)}-1)}{(1-q)}\).

The shape of the deformed logarithm is similar to that of the regular one. \(\ln_1{x}=\log{x}\).

For \(q>1\), \(\ln_q{(+\infty)}=\frac{1}{(q-1)}\).

References

Examples

curve(ln_q(1/ x, q = 0), 0, 1, lty = 2, ylab = "Logarithm", ylim = c(0, 10))
curve(log(1 / x), 0, 1, lty = 1, n =1E4, add = TRUE)
curve(ln_q(1 / x, q = 2), 0, 1, lty = 3, add = TRUE)
legend("topright",
  legend = c(
    expression(ln[0](1/x)),
    expression(log(1/x)),
    expression(ln[2](1/x))
  ),
  lty = c(2, 1, 3),
  inset = 0.02
 )