This is more of a comment in some ways, but it won't fit that easily into the space. Presumably your previous question Pearson 5/Inverse Gamma/ Double Pareto provides a context.
My first guess is that
event here means subset of your overall dataset
and
variables $a, b, y$ mean parameters you have fitted ($y$ is a non-conventional choice to denote a parameter, as it so often denotes a response variable). Some notation such as $\alpha, \beta, \gamma$ would be more conventional.
My second guess is thus that you have a three-parameter version of the inverse gamma, the third parameter being a location parameter that gives a minimum value.
My third guess is that you want to combine your data into some kind of combined distribution. It is not clear how much sense that makes, and averaging across your different fits would usually be a bad idea, but the usual way forward is to explore various models such as varying $\alpha, \beta, \gamma$; common $\gamma$, varying $\alpha, \beta$ etc. Usually I'd suggest a maximum likelihood formulation. It's hard to provide a concise summary of how to do that and journals in your field don't seem positive about providing the details. Otherwise no-one can comment precisely on a reference you don't give.
Using standard terminology and showing equations would help make your question clearer.
