Please excuse me if I am making any logical error in posting this question since I am not a math major. However, let me post my question.
I am trying to fit multivariate parametric distribution to data. Mathematica has nice built in function such as FindDistributionParameters for that purpose. Mathematica also has function DistributionFitTest that helps us to test the goodness of the fit. But I want to test whether the fitted parameters are different form another vector (or a number in case of univariate distribution). Does Mathematica have any functions that help me to achieve this objective?
To be more precise, let me start with an example form Mathematica Documentation:
data = RandomVariate[BinormalDistribution[{1, 2}, {1/3, 4}, 3/4], 1000];
params = FindDistributionParameters[data,
BinormalDistribution[{Subscript[μ, 1], Subscript[μ,
2]}, {Subscript[σ, 1], Subscript[σ, 2]}, ρ]]
We get the following answer:
{Subscript[μ, 1] -> 1.02289, Subscript[μ, 2] -> 2.11384,
Subscript[σ, 1] -> 0.328791,
Subscript[σ, 2] -> 4.09696, ρ -> 0.75787}
Now I would like to test a null hypothesis as one of the expressions below. Or, may we try to test the joint hypothesis?
{Subscript[μ, 1] = 1, Subscript[μ, 2] = 2,
Subscript[σ, 1] = .4,
Subscript[σ, 2] = 4.5, ρ = 0.85}
In that case, does Mathematica has any helpful function to perform this kind of hypothesis?
Please guide me without much programming. Thank you in advance.
KolmogorovSmirnovTest
but better statisticians than me might have other suggestions. Also, I would strongly recommend against usingSubscript
for variable names. Try simple indices like\[Mu][1]
instead. $\endgroup$