       Finding distribution parameters for a mixture of product distributions

• To: mathgroup at smc.vnet.net
• Subject: [mg122244] Finding distribution parameters for a mixture of product distributions
• From: Koslicki <koslicki at math.psu.edu>
• Date: Sat, 22 Oct 2011 06:06:42 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```I am trying to estimate parameters for a mixture of product
distributions, and Mathematica does not like my inclusion of product
distributions.

Ignoring the stupidity of the following choice of distributions,
consider the following:

In:= data=RandomVariate[MixtureDistribution[{.1,.9},
{BernoulliDistribution,BernoulliDistribution}],100];

In:= dist1=MixtureDistribution[{p,1-p},
{BernoulliDistribution[a1],BernoulliDistribution[a2]}];

In:= FindDistributionParameters[data,dist1]

Out= {p->0.261107,a1->0.919502,a2->0.960777}

So everything works just fine.

Yet if I want to look at a *product* of Bernoulli distribution

In:= data=RandomVariate[MixtureDistribution[{.1,.9},
{ProductDistribution[BernoulliDistribution,BernoulliDistribution],ProductDistribution[BernoulliDistribution,BernoulliDistribution]}],
100];

In:= dist1=MixtureDistribution[{p,1-p},
{ProductDistribution[BernoulliDistribution[a1],BernoulliDistribution[a2]],ProductDistribution[BernoulliDistribution[a3],BernoulliDistribution[a4]]}];

In:= FindDistributionParameters[data,dist1]

During evaluation of In:= FindDistributionParameters::ntsprt: One
or more data points are not in support of the distribution ...

How can it be that one of the data points is not in the support of the
distribution when I chose the data points from the distribution
itself?

This problem seems to arise whenever I am trying to find parameters
for a mixture of product distributions...

Any thoughts?

Thanks,

~David

```

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