Will Radford and Mathias Gallé have a new and interesting paper on this topic, here is one excerpt:
Law and corporate professions had around 15% of female representation…the medical domain (doctors) had a female probability of 0.23…Religion does not score at the bottom with regards to female presentation (although very low with 0.08). From the professions we selected, Engineering was the lowest (0.05). The highest scoring profession was IT (0.52), which is partly due to the fact that many computer voices were female (computer had 460 female occurrences, versus 247 male ones; and enterprise computer from “Star Trek” was almost exclusively female)
By the way, the number of female writers and directors (in their IMDB database) was at a six year low in 2014.
If you look at most frequent roles for gender, women are assigned hostess, girl, woman, waitress, and mother. For men, the list swings toward narrator, announcer, doctor, detective, bartender, soldier, and police officer.
In 1980-200, the top “newly popular” role (for both sexes) was “additional voices.” For the time period 2000-present it was “zombie,” next was “housemate.”
The paper is here (pdf), hat tip goes to Samir Varma.
Here is a new and interesting article on whether there is greater female influence over cinematic box office these days.