Estimation for the hermite distribution with special reference to time series
R Sym · Spiral (Imperial College London) · 1971
There of distributions of discrete valued °fuller r dox cables having probability generating functions of the form (0.040) and sno, a as generalised Poisson distributions; see Kemp and Kemp (1965).This class has a natural extension to multivariate distributions having p.g.f.'s of the form A meMber of this class he multivariate Berate distribution, the definition some properties of which are given in Chapter 1 The problems of parametric estimation for this distribution in multivariate and time series situations are investigated in Chapters 2 and 3 respe vely with speeial reference to comparing methods based on maximum likelihood with, methods using sample moments.* the oo fio eat of .40st 44A illpirom, then expressions or thederivatives of the `likelihood may be obtained formally by .(.1.6.1)-where is one of the parameters in it or 27 .can be established by an inductive argument using the ordering of the vectors r given in section 2.1, it is unlikely that a general theorem may be applied here as it not Possible to show that 8110 is stablished.Now n acid 'Il.(1 14°1 in which the coefficient of z I rn .s Properties of the method of maximum likelihood are given in section 2.3 and in section 2.4 the efficiency of the method of moments is investigated with the univariate and bivariate cases as examples.-27-13*(1,141m) So o obtain a bound or the errors, it will be assumed, that t(s) P PUT may be 'taken as a sequenoe of dependent random variables, with, expected value zero.These assumptions can be instified for the.41)145 as some random number genera.tors are similar to (2.2.1), and in a single operation the rounding error will have expected value zero.To justify them for the t(2)10 it is noted that for a given , e(1) and c(& will be independent,' as e(g) is the iinsignificanti, unrecorded part of P I( ), If it is further assumed that the IWts 'are uniformly► distributed between 17 10_I t( )2 i0.41 however this need be used only to get some idea of the magnitude of the final bound.' I.