The book "Manhunter" by Colin Wilson describes FBI effort to profile "serial" killers in the US. The concept of criminal profiling has been expressed in many movies and TV shows. The more I think about it the less I believe there is any substance to the effort.
According to Wikipedia there have been 243 serial killers caught and convicted in the US. There are, perhaps, another 50 or so who have been named (e.g. Zodiac) but not caught. Say something like 300 total. This amounts to 1 in a million in the US.
At the present time, about 1 person in 6,000 lives to be 100 years, and one in about 15 million lives to be 110. Whenever I have heard one of the the super-centenarians offer his/her reason for longevity it has never been anything we could live by.
Simply based upon numbers, it seems to me that trying to profile a serial killer would be like profiling someone who has lived to be 105 years old. Then, if you started to narrow the field down, say on the basis of victim's age or sex, the sample size would be correspondingly diminished.
I would appreciate any comments you might have about the how productive this profiling effort could be.