Difference between power law distribution and exponential decay This is probably a silly one, I've read in Wikipedia about power law and exponential decay. I really don't see any difference between them. For example, if I have a histogram or a plot that looks like the one in the Power law article, which is the same as the one for $e^{-x}$, how should I refer to it?

$$
\begin{array}{rl}
\text{power law:} & y = x^{(\text{constant})}\\
\text{exponential:} & y = (\text{constant})^x
\end{array}
$$
That's the difference.
As for "looking the same", they're pretty different: Both are positive and go asymptotically to $0$, but with, for example $y=(1/2)^x$, the value of $y$ actually cuts in half every time $x$ increases by $1$, whereas, with $y = x^{-2}$, notice what happens as $x$ increases from $1\text{ million}$ to $1\text{ million}+1$.  The amount by which $y$ gets multiplied is barely less than $1$, and if you put "billion" in place of "million", then it's even closer to $1$.  With the exponential function, it always gets multiplied by $1/2$ no matter how big $x$ gets.
Also, notice that with the exponential probability distribution, you have the property of memorylessness.
