variability among signals
As an example of what I mean, let's have a look at a simple sinusoid (though I see you're actually assuming double gamma functions; I may rework this later to use those).

This models the signals as:
$$
y_p(t) = \sin(\omega t + \phi_p)
$$
so the only difference between them is the phase $\phi_p = (p-1)\pi/6$.

The top plot is the mean signal $\bar{y}(t)$ and the bottom plot shows the Pearson coefficient between $\bar{y}$ and $y_p$ for $p=1\ldots 6$ (so $n=6$).



As you can see, the Pearson coefficient varies quite widely even in this simple example.



R Code Below

# 26438

Nsigs &lt;- 6
T&lt;- 1024
omega &lt;- 2*pi*0.00982734982
t &lt;- 0:(T-1)

y &lt;- matrix(,nrow = T, ncol = Nsigs)
phi &lt;- c(0, 1*pi/6, 2*pi/6, 3*pi/6, 4*pi/6, 5*pi/6 )

for (idx in 1:Nsigs)
{
  #phi[idx] &lt;- runif(1)*2*pi
  y[,idx] &lt;- sin(omega*t + phi[idx])  
}

mean &lt;- rowSums(y) / Nsigs

total &lt;- matrix(,nrow = T, ncol = Nsigs+1)
total[,1] &lt;- mean
total[,2:(Nsigs+1)] = y

pearson &lt;- cor(total,use="complete.obs", method="pearson")

par(mfrow=c(2,1),pty="m")
plot(t,mean, type="l")
title("Mean value")

plot(1:6, pearson[1,2:7], pch=19, col="blue")
title("Pearson coefficient")