Calculates the deformed exponential of order $$q$$.

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 dversity) 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.

expq
curve(exp(x), -5, 0, lty=3)