Power laws are explained in wikipedia and elsewhere. As the links explain, a power law describes a distribution - it appears that the distribution is of something of which there is a shortage. Hence, power laws can be illustrated by the distribution of money among a population.
Imagine that Bill Gates is the richest man in the world, to illustrate a simple power law (with an exponent of 1/2), there will be two people in the world who have half as much money as him; four people who have a quarter as much; eight people who have an eighth, etc, etc. The exponent could be anything, it has to be determined empirically but it gives a simple illustration of a power law, which can also be plotted.
Do power laws exist with respect to murder within the medical profession?
Take Dr John Bodkin Adams, he's supposedly killed more than 160 people during the mid-forties and mid-fifties. If there's a power law that describes the number of murdering medics, then at the time, and assuming that the exponent of the power law was 1/2, there were two medics who had murdered 80 people, four medics who had killed 40 people, eight how had killed 20, and so on. It isn't clear whether or not there is a power law that describes this phenomenon; further, even if there is a power law, the value of the exponent that helps to describe it isn't known. Changing the exponent changes the shape of the curve.
It's disturbing and difficult to think about. It's disturbing for the obvious reason that someone who we would reflexively trust is not to be trusted. But it is difficult to consider because of the issue of euthanasia. What is the distinction between releasing someone from an agonising few months of suffering by giving them an overdose of diamorphine, and giving someone an overdose of diamorphine 'just because you can'?
Untangling the cases of negligence and euthanasia from those of murder leaves us with people such as Adams. But bringing in the idea of power laws suggests that there are others who have not been caught and are still murdering.
The last one to be caught was Dr Shipman: how many more are undetected?