Question: How to properly invert and add scale and location parameters to a probability distribution from a built-in distribution?

restart;
st:=time():

with(Statistics):

InvChi2:=proc(a,b,n)
        description "inverse chisquare distribution with a=location, b=scale, n=degrees of freedom";


        local CHI := RandomVariable(ChiSquare(n)):
        
        Distribution(
                CDF = unapply(CDF(b*n/CHI+a,t),t),
                PDF = unapply(PDF(b*n/CHI+a,t),t),
                Mean = a+~Mean(b*n/CHI),
                Median = a+~Median(b*n/CHI),
                Variance = simplify(CentralMoment(a+b*n/CHI,2)),
                Skewness = simplify(CentralMoment(b*n/CHI, 3) / CentralMoment(b*n/CHI,2)^(3/2)),
                Kurtosis = simplify(CentralMoment(b*n/CHI, 4) / CentralMoment(b*n/CHI,2)^2),
                Conditions = [b > 0],
                RandomSample = proc(N::nonnegint)
                                a+~Sample(b*n/CHI,N)
                        end proc
                );
        end proc:

T:= RandomVariable(InvChi2(2,4.32,3))

evalf(Median(T))

evalf(Mean(T))

Variance(T)

Skewness(T)

Kurtosis(T)

Quantile(T,.25)

A:=Sample(T,10^5):

Median(A)

Mean(A)

Variance(A)

Skewness(A)

Quantile(A,.25)

Quantile(A,.75)

printf("Time to execute worksheet = %a seconds", time() - st)

Time to execute worksheet = 2.813 seconds