The exponential family is characterized by the structure of different generating functions and by recursion relations for moments and cumulants. the derived characteriza-tion theorems generalize all previous results on this subject. especially, the assumption of linearity of the exponential family is dropped. Furthermore, the distribution of a sum of independent exponential family distributed random variables is considered and an equivalent condition is derived for the sum being exponential family distributed.

János Galambos: The Asymptotic Theory of Extreme Order Statistics. John Wiley & Sons. New York 1978, 352 pp., £ 17,75; $34.15. K.S.Miller: Hypothesis Testing with Complex Distributions. Robert E. Krieger Publishing Company, Huntington, New York 1980, 184 S., $ 14.50. H.Büning, G. Trenkler: Nichtparametrische statistische Methoden. W. de Gruyter, Berlin-New York 1978, 435 S., DM 48, –. J.G. Kalbfleisch: Probability and Statistical Inference I, II. Springer-Verlag, Berlin-Heidelberg-New York 1979. I: x, 342 pp., 35 figs., 25 tab., DM 28, –. P.J.M. Kallenbero: Branching Processes with Continuous State Space. Mathematical Centre Tracts 117. Mathematisch Centrum, Amsterdam 1979, 122 S., Dfl. 15,–. P.J. Weeda: Finite Generalized Markov Programming. Mathematical Centre Tracts 92. Mathematisch Centrum, Amsterdam 1979, VII, 127 pp. T.M.ODonovan:Gpss Simulation Made Simple. J. Wiley & Sons, Chichester-New York. Brisbane-Toronto 1979, XII, 127 S., £ 7.75. G. Sahner: Digitale Meßverfabren. VER Verlag Technik, Berli 1979, 172 S., 112 Abb., 12 Tab., 24, –M. U. Feldmann: Wachstumskinetik. Mathematische. Modelle und Methoden zur Analyse altersabhängiger populationskinetischer Prozesse (medizinische Informatik und Statistik, Bd. 11). Springer-Verlag, Berling-Heidelberg-New York 1979 viii, 137 S., 58 Abb., 1 Tab., DM 24, –. H. Riedwyl: angewandre mathematische Statistik in wissenschaft, Administration und Technik. Eine Einführung. Verlag paul Haupt, Bern und Stuttgart 1978, 272 S., Fr. J. Keilson: Markov Chain Models – Rarity and Exponentiality- Springer-Verlag, Berlin-Heidelberg-New York 1979, XIII, 184 pp, DM 24, –.

Geometric aspects of linear model theory are surveyed as they bear on mean estimation, or variance covariance component estimation. It is outlined that notions associated with linear subspaces suffice for those of the customary procedures which are solely based on linear, or multilinear algebra. While conceptually simple, these methods do not always respect convexity constraints which naturally arise in variance component estimation. Previous work on negative estimates of variance is reviewed, followed by a more detailed study of the non-negative definite analogue of the MINQUE procedure. Some characterizations are proposed which are based on convex duality theory. Optimal estimators now correspond to (non-linear) projections onto closed convex cones, they are easy to visualise, but hard to compute. No ultimate solution can be recommended, instead the paper concludes with a list of open problems.

We consider the covariance estimate of a stationary random sequence {X t} with zer mean. It is proved, that the distribution function of to the normal distribution with the order in the case of linear processes with finite 6th moments.

Asymptotic distributions for parameter estimates in inadequate nonlinear regression models are considered. In comparison with earlier results no fictive limit design appears in the formulation. In this form the results can be applied for approximation using only finite sample size data.

Let {X t} be a p-dimensional ARMA (m n) process. Write where have q and r components, respecctivelyq+r=p). Put . It is proved that {Y t} is an ARMA (m -1. n + 1) process and a procedure for evaluation of its matrices of coefficients is given. If {X t} is an AR (m) process, then {Y t is an AR (m -f1) process; if {X,tis an MA(n-) process, then {Y t} is an MA (n +1) process. Explicit formulas are derived for p = 2m = 1n = 0. The repeated use of the described procedure leads to a model for , The results can be applied in theorv of extrapolation in multiple ARMA processes when the different components of a process are known to different points of time.

In the paper surface processes are considered, i.e. sets of surfaces distributed at random in the space. For translation invariant surface processes the PALM distribution of the direction of the normal in a typical surface point is defined and related to two roses of intersection. Fibre and point processes are studied which result by intersections with planes and lines respectively. For these processes stereological formulas are proved which connect some quantities with such of the surface process. As a special ease motion invariant, i.e. translation invariant and isotropic, surface processes are treated, Furthermore, weighted surface processes are considered.

A method of estimation of the rose of directions of fibre processes is suggested which bases on the measurement of intersection angles with suitable test curves.

Some series of m-associate triangular PBIB designs have been constructed. A table of now three associate designs in the range b, v ≦ 100; r, k ≦ 10 with their average efficiencies has been given. These designs with (v, b, r, k) are new in the sense that the existence of two associate PBIB designs (e.f. Clatworthy (1973), John & Turner (1977), Dey (1978)) with these parameters are not known. The constructions presented herein also yield partially balanced weighing designs, nested PBIB designs and PBIB designs for m11111 response exoeriments.