I am very new to Maple but it looks like a wonderful symbolic computing tool. I am hoping to gain some familiarity with it and one of my first questions is this: I have identified a nice formula refered to as a modified inverse gamma function. This is a "peak function" with a couple nice features. Firstly, it can describe both positively and negatively skewed distributions, and secondly its mode and amplitude are easily recognized as (X0,Ym). I have entered it into a Maple 2019 notebook as so:
Y = Ym*(c/((d + 1)*(X - X__0) + c))^(d + 1)*exp((X - X__0)*(d + 1)^2/((d + 1)*(X - X__0) + c))
What I would like to do is calculate the positions, X, of the two points where it is half-maximal. That is, where Y=1/2Ym. I would like to assume that all numbers are real, etc. I should point out that in the real world, I will have optimized the values of Ym, X0, c and d by first fitting to actual data, so this may helpfully constrain the problem.
Can someone explain how I might go about this? If you assume I know nothing, I will not be offended.