entropart (version 1.1.1)

expq: Exponential of order q

Description

Calculates the deformed exponential of order $q$.

Usage

expq(x, q)

Arguments

x

A numeric vector.

q

A number.

Value

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

Details

The deformed exponential 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 $x>\frac{1}{(q-1)}$.

References

Marcon, E., Scotti, I., Herault, B., Rossi, V. and Lang, G. (in revision). Generalization of the partitioning of Shannon diversity. PLOS One. Tsallis, C. (1994). What are the numbers that experiments provide? Quimica Nova 17(6): 468-471.

See Also

expq

Examples

curve(exp(x), -5, 0, lty=3)  
  curve(expq(x, 2), -5, 0, lty=2, add=TRUE)
  curve(expq(x, 3), -5, 0, lty=1, add=TRUE)
  legend("topleft", legend = c("exp(x)", "exp2(x)", "exp3(x)"), lty = c(1, 2, 3), inset=0.02)