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Is there a way to define a multivariate exponential distribution based on independent univariate exponential distributions (Akin to multinormal distribution):

MultivariateExponentialDistribution[lambda1, lambda2, lambda3] = {ExponentialDistribution[lambda1], ExponentialDistribution[lambda2], ExponentialDistribution[lambda3]}

I need this distribution to model a hidden Markov process where each state emits three values coming from different exponential distributions.

Right now I am solving this problem for each dimension independently (resulting in different transition matrices)

hmm1 = HiddenMarkovProcess[4, ExponentialDistribution[lambda1]]
hmm2 = HiddenMarkovProcess[4, ExponentialDistribution[lambda2]]
hmm3 = HiddenMarkovProcess[4, ExponentialDistribution[lambda3]]

My goal is:

hmm = HiddenMarkovProcess[4, MultivariateExponentialDistribution[lambda1, lambda2, lambda3]]

thanks

Hani

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dist = ProductDistribution[ExponentialDistribution[\[Lambda]1], ExponentialDistribution[\[Lambda]2], ExponentialDistribution[\[Lambda]3]];

data = TemporalData[RandomReal[{0, 1}, {10, 100, 3}], {Range[100]}];

hmm = EstimatedProcess[data, HiddenMarkovProcess[4, dist]]
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  • 1
    $\begingroup$ Thank you Alexey, that is right on the spot! $\endgroup$ – Hani Safadi Apr 1 '15 at 19:47

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