entropart (version 1.1.3)

lnq: Logarithm of order q

Description

Calculates the deformed logarithm of order $q$.

Usage

lnq(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 logarithm 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

Tsallis, C. (1994). What are the numbers that experiments provide? Quimica Nova 17(6): 468-471.

See Also

expq

Examples

curve(log(x), 0, 1, lty=1)
  curve(lnq(x, 2), 0, 1, lty=2, add=TRUE)
  curve(lnq(x, 3), 0, 1, lty=3, add=TRUE)  
  legend("topleft", legend = c("log(x)", "ln2(x)", "ln3(x)"), lty = c(1, 2, 3), inset=0.02)