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Question: Statistics fails to reject invalid parameter values

Question:Statistics fails to reject invalid parameter values

mmcdara 6635 Maple 2015
statistics
August 27 2019
2

Maple doesn't completely check the condition on the number of trials "n" for Binomial and NegativeBinomial distributions (package Statistics).
The attribute "Conditions" explicitely says that n must be a strictly positive integer but no strictly positive real valuereturna an error (ok, it would be stupid to set n to a non integer value !!!).

I think it is a default that ought to be corrected in future releases (this default still exists in Maple 2018)

 

> 

restart
> 

kernelopts(version)

`Maple 2015.2, APPLE UNIVERSAL OSX, Dec 20 2015, Build ID 1097895`

 (1)
> 

with(Statistics):


BINOMIAL DISTRIBUTION

> 

X := RandomVariable(Binomial(n, p)):
L := [attributes(X)][3]:
A := exports(L)

Conditions, ParentName, Parameters, CDF, CharacteristicFunction, Kurtosis, Mean, Median, Mode, MGF, ProbabilityFunction, Skewness, Support, Variance, VariationCoefficient, CDFNumeric, QuantileNumeric, RandomSample, RandomSampleSetup, RandomVariate

 (2)
> 

L:-Conditions

[0 <= p, p <= 1, n::posint]

 (3)
> 

# Maple should return an error for N is not of type posint
#
# It seems that Sample uses floor(N)

N := 10.49; type(N::posint);
P := 1/2:
X := RandomVariable(Binomial(N, P)):
Mean(X), N*P;
ProbabilityFunction(X, k);
S := Sample(X, 10^6):
Mean(S);


# A non consistent result (only non negative values of k should be accepted)

eval(ProbabilityFunction(X, k), k=evalf(Pi));

N := 10.49

  

false

  

5.245000000, 5.245000000

  

piecewise(k < 0, 0, binomial(10.49, k)*(1/2)^k*(1/2)^(10.49-k))

  

HFloat(4.998903)

  

.1096019539

 (4)


NEGATIVE BINOMIAL DISTRIBUTION

> 

X := RandomVariable(NegativeBinomial(n, p)):
L := [attributes(X)][3]:
A := exports(L):
L:-Conditions

[0 < n, 0 < p, p <= 1]

 (5)
> 

N := 10.49:
P := 1/2:
X := RandomVariable(NegativeBinomial(N, P)):

Mean(X)


 

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