Piecewise and ProbabilityDistribution malfunction when used together

Yesterday I opened this question, what had a happy end after all.

But when I tried to model more complex discrete random variables using Piecewise instead of If I discovered that it doesnt work at all!! Example:

1.This code works perfectly:

(*Our pseudo-generating function*) g[x_, m_, c_, bigD_, t_, d_] := ((c/bigD)/x + (bigD - t - c)/bigD + (t - d) x/bigD + (d/bigD) x^2)^m (*Probability mass function of k*) f[k_, m_, c_, bigD_, t_, d_] := If[k == 0, Sum[Coefficient[g[x, m, c, bigD, t, d], x, i], {i, -m, 0}], Coefficient[g[x, m, c, bigD, t, d], x, k]] (*We make a probability distribution*) dist[m_, bigD_: 6, t_: 2, d_: 0, c_: 0] := ProbabilityDistribution[f[k, m, c, bigD, t, d], {k, 0, 2 m, 1}, Assumptions -> {bigD \[Element] Integers, 0 <= d < bigD, 0 <= c < bigD, 1 <= t < bigD, m \[Element] Integers && m > 0}]; (* Testing some statistics*) {Mean[#], StandardDeviation[#], Table[Evaluate@CDF[#, k], {k, 0, 5}]} &@dist[5] 

2.But this alternative code (based in the function g above described) doesnt work from dist2:

(*Alternative probability mass function of k*) h[k_, m_, c_, bigD_, t_, d_] := Piecewise[ { {Sum[Coefficient[g[x, m, c, bigD, t, d], x, i], {i, -m, 0}], k == 0}, {Coefficient[g[x, m, c, bigD, t, d], x, k], k != 0} }] (*Probability distribution based on h (this is where the code seems fail)*) dist2[m_, bigD_: 6, t_: 2, d_: 0, c_: 0] := ProbabilityDistribution[h[k, m, c, bigD, t, d], {k, 0, 2 m, 1}, Assumptions -> {bigD \[Element] Integers, 0 <= d < bigD, 0 <= c < bigD, 1 <= t < bigD, m \[Element] Integers && m > 0}]; (* The test reveal that dist2 is not working as expected *) Table[Evaluate@PDF[dist2[5], k], {k, 0, 5}] 

I discovered that the function h evaluates correctly, and give the same results than f, but when I used together with ProbabilityDistribution to define dist2 it seems that the code dont work correctly.

There is a way to fix this? And in general, there is a way to use piecewise functions (with more than two pieces) together with ProbabilityDistribution? Thank you in advance.

UPDATE: the Boole function, as someone commented, is not working either but I found an (ugly) solution by the moment that is based in nesting If statements to define a piecewise function of more than two pieces inside of ProbabilityDistribution.