A multivariate gamma distribution arising from a Markov model |
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Authors: | D Warren |
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Institution: | (1) Mathematics Dept., Lancaster University, LA1 4YF Lancaster, United Kingdom |
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Abstract: | A Markov chain{X
t
}, which has been useful for modelling in hydrology, can be specified by the Laplace transform (LT) of the conditional p.d.f. ofX
t+1 givenX
t
=x
t
, which is assumed to be of the exponential formH( )exp{-G( )x
t
}. For appropriate choice ofH andG the marginal distribution ofX
t
is the (univariate) gamma distribution. In this case, the joint p.d.f. ofX
t
+1,...,X
t+n and its LT, are obtained, and this is extended to a seasonal version of the chain. A simple method of generating observations from these multivariate gamma distributions is noted, and the joint LT is applied to the problem of determining moments of weighted sums of such variables. |
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Keywords: | Markov chains seasonality multivariate gamma distributions weighted sums of gammas |
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