The Maths of Mahjong

Have there been any reputable studies on the probabilities of various hands in standard Chinese Mahjong (Mah-Jongg), from the lowly, bog-common "Chicken Hand" all the way up to the (allegedly) ultra-rare Special Limit Hands (e.g. "13 Orphans" or "Nine Gates")? Unfortunately I do not have a professional background in Mathematics to probe into this matter on my own, and require the input of those who have such qualifications. By what means can a person establish the probabilities of the commonly-known hands of Mahjong, to determine if their traditional ranking is mathematically justified?

The upper limit of combinations should be (144 choose 14), or a staggering 9,844,971,586,905,715,128, (9.84 quintillion), but the number of winning hands would obviously be a tiny subset of that figure.

Any help or suggestions will be most appreciated!

Somebody published a math paper on this.
Mathematical aspects of the combinatorial game “Mahjong”