expq {entropart}  R Documentation 
Exponential of order q
Description
Calculates the deformed exponential of order q
.
Usage
expq(x, q)
expq.CommunityProfile(Profile)
Arguments
x 
A numeric vector. 
Profile 

q 
A number. 
Details
The deformed exponential is defined as (x(1q)+1)^{\frac{1}{(1q)}}
.
For q>1
, \ln_q{(+\infty)}=\frac{1}{(q1)}
so \exp_q{(x)}
is not defined for x>\frac{1}{(q1)}
.
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): 468471.
See Also
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)