caa a22 4500 46904070X CHVBK 20180323132810.0 cr unu---uuuuu 170328e19920901xx s 000 0 eng 10.1007/BF01581449 doi (NATIONALLICENCE)springer-10.1007/BF01581449 Warren D. Mathematics Dept., Lancaster University, LA1 4YF, Lancaster, United Kingdom aut A multivariate gamma distribution arising from a Markov model [Elektronische Daten] [D. Warren] 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(θ)exp{-G(θ)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. Springer-Verlag, 1992 Markov chains nationallicence seasonality nationallicence multivariate gamma distributions nationallicence weighted sums of gammas nationallicence Stochastic Hydrology and Hydraulics Springer-Verlag 6/3(1992-09-01), 183-190 0931-1955 6:3<183 1992 6 477 https://doi.org/10.1007/BF01581449 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01581449 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Warren D. Mathematics Dept., Lancaster University, LA1 4YF, Lancaster, United Kingdom aut NATIONALLICENCE 773 0- Stochastic Hydrology and Hydraulics Springer-Verlag 6/3(1992-09-01), 183-190 0931-1955 6:3<183 1992 6 477 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer