There is as you might imagine a lot of research on window sizes in general, and you will see there's a lot of research in specifically what are the recommendations for initial window size in TCP.
The settings are more to do with IETF's recommendations, which have increased over time, than a given operating system.
IETF recommended MSSx10 in 2013's RFC 6928.
The APNIC survey (see below) shows peaks at 1, 2, 4, 10 xMSS, interpreted to indicate the age of the operating system. As initial window size is also customisable in many OS, high-traffic websites tend to have customised values tuned to their situation.
You might be interested in these papers and articles.
- APNIC's initial window size survey (link)
- RFC 6928 "Increasing TCP's Initial Window" (link)
- IETF 2010 "Increasing TCP's Initial Window" Dukkipati et al Paper (link)
- Internet draft "Automating the Initial Window in TCP" (link)
- Network Computing's article on window sizes (link)
- Search for works by Van Jacobson and Mark Allman, a couple of the leading researchers in this field.
From these you should be able to find what you're looking for.
[EDIT] Additionally, for actual concrete values, you might find NMAP helpful, as it has a network fingerprint database for recognising operating systems which includes, amongst many other things, the expected initial window size. NMAP's OS-detection explanation is here, the database source is here, and the description of the format is here.