exp_q: Deformed exponential

In divent: Entropy Partitioning to Measure Diversity

Deformed exponential

Description

Calculate the deformed exponential of order q.

Usage

exp_q(x, q)

Arguments

x	A numeric vector or array.
q	A number.

Details

The deformed exponential is the reciprocal of the deformed logarithm \insertCiteTsallis1994divent, see ln_q. It is defined as (x(1-q)+1)^{\frac{1}{(1-q)}}.

For q>1, \ln_q{(+\infty)}=\frac{1}{(q-1)} so \exp_q{(x)} is not defined for x>\frac{1}{(q-1)}. When x is very close to this value, the exponential is severely subject to rounding errors.

Value

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

References

\insertAllCited

Examples

curve(exp_q(x, q = 0), from = -5, to = 0, lty = 2)
curve(exp(x), from = -5, to = 0, lty= 1, add = TRUE)
curve(exp_q(x, q = 2), from = -5, to = 0, lty = 3, add = TRUE)
legend("bottomright",
  legend = c(
    expression(exp[0](x)),
    expression(exp(x)),
    expression(exp[2](x))
  ),
  lty = c(2, 1, 3),
  inset = 0.02
)

divent documentation built on April 3, 2025, 7:40 p.m.