Exponential of order q

Calculates the deformed exponential of order \(q\).

Usage

expq(x, q)
expq.CommunityProfile(Profile)

Arguments

x

A numeric vector.

Profile

A CommunityProfile.

q

A number.

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 \(x>\frac{1}{(q-1)}\).

expq.CommunityProfile calculates the deformed exponential of a CommunityProfile. Its $x item (the order of diversity) is kept unchanged whilst other items are set to their exponential of order $x. Thus, an entropy profile is transformed into a diversity profile.

Value

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

References

Marcon, E., Scotti, I., Herault, B., Rossi, V. and Lang, G. (2014). Generalization of the partitioning of Shannon diversity. PLOS One 9(3): e90289.

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)