Mutual information via the Gaussian copula

Empirical copula transform rank/(n+1) with average ranks on ties, normal scores z = qnorm(u), then the Gaussian-copula closed form I = -log(1 - rho^2)/2 at the normal-scores correlation. Being rank-based, the estimate is exactly invariant under strictly increasing marginal transformations. Also returns Linfoot's informational coefficient of correlation sqrt(1 - exp(-2 I)).

Usage

morie_cmuti(x, y)

Arguments

x, y

Paired numeric vectors (n >= 3).

Value

A list with elements estimate (MI in nats), rho, linfoot_r, n, method.

References

Calsaverini, R. S. and Vicente, R. (2009). An information-theoretic approach to statistical dependence: Copula information. EPL, 88, 68003. Linfoot, E. H. (1957). An informational measure of correlation. Information and Control, 1, 85-89.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_cmuti(V, V)
#> $estimate
#> [1] 13.46895
#> 
#> $rho
#> [1] 1
#> 
#> $linfoot_r
#> [1] 1
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Gaussian-copula MI, I = -log(1-rho^2)/2 (Calsaverini & Vicente 2009; Linfoot 1957)"
#>