lnq {entropart}  R Documentation 
Calculates the deformed logarithm of order q
.
lnq(x, q)
lnq.CommunityProfile(Profile)
x 
A numeric vector. 
Profile 

q 
A number. 
The deformed logarithm is defined as \ln_q{x}=\frac{(x^{(1q)}1)}{(1q)}
.
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}{(q1)}
.
lnq.CommunityProfile
calculates the deformed logarithm of a CommunityProfile
. Its $x
item (the order of diversity) is kept unchanged whilst other items are set to their logarithm of order $x
. Thus, a diversity profile is transformed into an entropy profile.
A vector of the same length as x
containing the transformed values or a CommunityProfile
.
Tsallis, C. (1994). What are the numbers that experiments provide? Quimica Nova 17(6): 468471.
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)