lnq {entropart} R Documentation

## Logarithm of order q

### Description

Calculates the deformed logarithm of order q.

### Usage

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


### Arguments

 x A numeric vector. Profile A CommunityProfile. q A number.

### 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)}.

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

### Value

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

### References

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

expq
curve(log(x), 0, 1, lty=1)