NanaP

Ask a Question

Create a Post

3 Badges

Member for: 1 years, 289 days

Contact NanaP

MaplePrimes Activity

These are questions asked by NanaP

How to properly invert and add scale and...

Asked: NanaP 40 Product: Maple 2023

June 23 2023

1 4

Hello community,

Could I please get help on how to invert a probability distribution (reciprocal of) and add the location and scale parameters? The distribution in question is from the built-in (Statistics package) of ChiSquare(n) transformed into a scaled inverse Chi Square with location (shift) parameters.

I have tried the following which results in verified (correct) empirical (sampled) data, but have not been equally successful in the theoretical moments and its quantiles.

>	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))

(1)

>	evalf(Median(T))

(2)

>	evalf(Mean(T))

(3)

>	Variance(T)

(4)

>	Skewness(T)

(5)

>	Kurtosis(T)

(6)

>	Quantile(T,.25)

(7)

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

Median(A)

(8)

Mean(A)

(9)

>	Variance(A)

(10)

>	Skewness(A)

(11)

>	Quantile(A,.25)

(12)

>	Quantile(A,.75)

(13)

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

Time to execute worksheet = 2.813 seconds

Download invChi2.mw

Thank you

How do I re-parameterize a triangular di...

Asked: NanaP 40 Product: Maple 2023

June 13 2023

1 11

Hi community!

In the mw file attached, I have worked a numerical solution to get the standard parameters of minimum and maximum of the distribution Triangular(a,b,c) given 2 quantiles (and its values) and c. The code works and was simple. Now, how do I solve this more elegantly to have the reparameterization directly inputed instead of indirectly by solving a & b first (like the attached file does)? Thanks people,altTriangular2.mw

How do I make the Beta "Subjective" Dist...

Asked: NanaP 40 Product: Maple 2023

June 07 2023

1 14

Hello community, I am new in this forum and sorry if the following seems rudimentary:

I am replicating a distribution function using Statistics[Distribution] as defined here:

Vose Software's Beta Subjective

I have tested numerically and the function works for this initial values: Min := 3; Mlikely := 8; Avg := 9; Max := 18;

But failed to complete with these values (which I tested works in another software) Min := 1000; Mlikely := 1400; Avg := 1500; Max := 2100;

What puzzles me is the inconsistency of handling the functions (be aware that the server kernel could be slow at times). I hope I don't have to give up and continue my custom distribution project in another software.

Here is the document:

The Beta Subjective Distribution

(1)

(2)

(3)

(4)

f := simplify(piecewise(Min <= x and x <= Max, (x-Min)^(alpha-1)*(Max-x)^(beta-1)/(Beta(alpha, beta)*(Max-Min)^(alpha+beta-1)), 0))

piecewise(x < 3, 0, x <= 18, (4/16875)*(x-3)*(-18+x)^2, 18 < x, 0)

(5)

MD := Distribution(PDF = unapply(f, x), Conditions = [`and`(Min < Mlikely and Mlikely < Max and Min < Avg and Avg < Max and Mlikely <> Avg, piecewise(Avg < Mlikely, Mlikely > Mid, Mid > Mlikely))])