Fisher scoring algorithm

• To: mathgroup at smc.vnet.net
• Subject: [mg90962] Fisher scoring algorithm
• From: Francogrex <franco at grex.org>
• Date: Fri, 1 Aug 2008 02:58:26 -0400 (EDT)

```Hello, this is very probably a mathematical question not really
technical but a technical advice might help. I am trying to find the
expectation by solving the following below:

FullSimplify[
Sum[(1/(n! Gamma[\[Alpha]]) z^
n \[Beta]^\[Alpha] (z + \[Beta])^(-n - \[Alpha])
Gamma[n + \[Alpha]])*(PolyGamma[1, a] -
PolyGamma[1, a + n]), {n, 0, Infinity}]]

It's the product of the log of the 2nd derivative of alpha (from the
likelihood) by the likelihood: negative binomial distribution (n is
integer z is real, and likelihood and 2nd deriv should be products and
sums respectively of many n(s) and z(s) but taken here as only one
point for simplicity). This has come from a poisson-gamma marginal
distribution, for which I am trying to find the (parameters) alpha and
the beta by using the fisher scoring algorithm. But mathematica does
not find a solution to the above. Any hints or help appreciated.
thanks.

```

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