So, I will save you from an explanation of what is XKCD, who is Randall and even what is the Beanish language, as you likely already know it if you are reading this. If you need help, google “xkcd time”, read the XKCD Time wikia and, of course, read the comic.
There are two possibilities concerning the Beanish language: it could be a “true” language, designed by Randall ex novo or by modifying some existing languages (as the comic is set in the future), or it could be just pure, random garbage.
As a regular reader of XKCD, and considering the care in the construction of the XKCD Time world (topographic research, the astronomical correctness, etc.), I find it unlikely that Randall just fired up a random generator, even though he is undoubtedly capable of creating a set of sequence that look like a true language but it is not (remember that he is familiar with the Voynich manuscript and, thus, with one of the main hypothesis that consider it just random garbage).
Before performing a statistical analysis of the language, we need to analyze it and make sure the effort is worth. As said in the previous paragraph, Randall could very well have generated a set of sequences with morphology, syntax and, in particular, information entropy similar to those of natural or, at least, constructed languages. However, even a simple entropy calculation is worthless when we cannot even identify what is a symbol; while the “letters” in the comics look very much like a normal alphabetic or syllabic script, with a certain Semitic and Brahmanic feeling given by diacritics that look like vowel marks, we are not sure of what constitutes a single symbol, if there equivalent or quasi-equivalent sumbols (vowels as diacritics, capital letters…), if some or all symbols are combinations and so on.
It is necessary to first collect the corpus we have and transcript it so it can be easily discussed and studied, while reading the theories and interpretations of other people on the internet (unfortunately, Beanish does not seem to have drawn much attention, even among XKCD enthusiasts).
I will use, adapting where needed, the transcriptions and trascription guide found on the XKCD Time wikia page (http://xkcd-time.wikia.com/wiki/Beanish):