Predicting infectious disease outbreak risk via migratory waterfowl vectors

The spread of an emerging infectious disease is a major public health threat. Given the uncertainties associated with vector-borne diseases, in terms of vector dynamics and disease transmission, it is critical to develop statistical models that address how and when such an infectious disease could spread throughout a region such as the USA. This paper considers a spatio-temporal statistical model for how an infectious disease could be carried into the USA by migratory waterfowl vectors during their seasonal migration and, ultimately, the risk of transmission of such a disease to domestic fowl. Modeling spatio-temporal data of this type is inherently difficult given the uncertainty associated with observations, complexity of the dynamics, high dimensionality of the underlying process, and the presence of excessive zeros. In particular, the spatio-temporal dynamics of the waterfowl migration are developed by way of a two-tiered functional temporal and spatial dimension reduction procedure that captures spatial and seasonal trends, as well as regional dynamics. Furthermore, the model relates the migration to a population of poultry farms that are known to be susceptible to such diseases, and is one of the possible avenues toward transmission to domestic poultry and humans. The result is a predictive distribution of those counties containing poultry farms that are at the greatest risk of having the infectious disease infiltrate their flocks assuming that the migratory population was infected. The model naturally fits into the hierarchical Bayesian framework.     

Statistical analysis for Kumaraswamy’s distribution based on record data

In this paper we review some results that have been derived on record values for some well known probability density functions and based on m records from Kumaraswamy’s distribution we obtain estimators for the two parameters and the future sth record value. These estimates are derived using the maximum likelihood and Bayesian approaches. In the Bayesian approach, the two parameters are assumed to be random variables and estimators for the parameters and for the future sth record value are obtained, when we have observed m past record values, using the well known squared error loss (SEL) function and a linear exponential (LINEX) loss function. The findings are illustrated with actual and computer generated data.     

Parameter estimation in nonlinear regression models 1

Fisher information contained in record values, inter-record times and their concomitants from a sample of fixed size is derived in general and explicit expressions are deduced for some specific known bivariate classes of distributions. A comparison between fixed sampling and inverse sampling schemes with equal number of records and concomitants is also carried out. We also consider parameter estimation based on bivariate records and a small simulation study is done.     

Der Sequentieile Quotiententest bei irreduziblen homogenen Markovschen Ketten mit endlichem Zustandsraum

The Sequential Probaility Ratio Test is applied to test two simple hypotheses about the transition probability matrix of an irreducible homogeneous MARKOV chain with finite state space. An analogue (14) of Wald's Fundamental Identity, the Operating Characteristic Function (20-21) and the Average Sample Number (22-23) are given. These statements are generalizations of the MARKOV chain as well as some more conditions about the eigenvalues of the transition probability matrix.     

Book review

W.G.Cochran: Sampling Techniques, 3rd. Ed. John Wiley & Sons, New York-Santa Barbara-London-Sydney-Toronto 1977. 428 S., £ 12.50; $21.50.

H.Toutenburg: Vorhersage in linearen Modellen. Akademie-Verlag, Berlin 1975, VIII, 176b S., 3 Tab., 28,– M.

O.Kallenberg: Random Measure. Akademie-Verlag, Berlin 1975; Academic Press, London 1976. 104 pp., 28,– M.     

Book reviews

E. Kofler, G. Menges: Entscheidungen bei unvollständiger Information. Lecture Notes in Economics and Mathematical Systems 136. Springer-Verlag, Berlin-Heidelberg-NewYork 1976, 357 S., DM 31.

B. S. Everitt: The Analysis ot Contingency Tables. Chapman and Han, London 1977, 128 S., £ 3.75.

O. Barndorff-Nielsen: Information and Exponential Families in Statistical Theory. J. Wiley & Sons, Chichester-New York-Brisbane-Toronto 1978, 247 S., £ 13.50; $ 28.50.

W. Gilchrist: Statisticai Forecasting. J. Wiley & Sons, London-New York-Sydney-Toronto 1976, 321 S., £ 9.50; $ 19.00.

J. M. Chambers: Computational Methods for Data Analysis. J. Wiley & Sons, New York Chichester-Brisbane-Toronto 1977, 279 pp., £ 11.30.

A. Hughes, D. Grawoig: Statistics: A Foundation for Analysis. Addison-Wesley Publishing Company, Reading-Menlo-Park London-Don Mills 1971, 525 S., $ 11.50.

K.Krickeberg, H.Ziezold: Stochastiche Methoden. Springer Verlag, Berlin-Heidelberg-New York 1977, 201 S., 13 Abb., DM 28.

Ch. Schneeweiss: Inventory-Production Theory. A Linear Policy Approach. Lecture Notes in Economics and Mathematical Systems 151. Springer Verlag, Berlin-Heidelberg-NewYork 1977, 122 S., 13 Abb., 9 Tab., DM 18.

S. Dworatschek: Grundlagen der Datenverarbeltung, 6., völlig neu bearb. u. erw. Aufl., Walter de Gruyter, Berlin-New York 1977, 538 S., 200 Abb., 212 Üb.Aufg., 59 Fotos, DM 38.

H. E. Steinhagen, S. Fuchs:Objekterkennung. Einführung in die mathematischen Methoden der Zeichenerkennung. VEB Verlag Technik, Berlin 1976, 436 S., 165 Abb., 32 Tab., 49,–.M.

G. Tinhofer: Mathematik für Studlenanfänger, Carl Hanser Verlag, München 1977, 464 S., 191 Abb., DM 38.     

On second-order improved estimation of a gamma scale parameter

This paper concludes our comprehensive study on point estimation of model parameters of a gamma distribution from a second-order decision theoretic point of view. It should be noted that efficient estimation of gamma model parameters for samples ‘not large’ is a challenging task since the exact sampling distributions of the maximum likelihood estimators and its variants are not known. Estimation of a gamma scale parameter has received less attention from the earlier researchers compared to shape parameter estimation. What we have observed here is that improved estimation of the shape parameter does not necessarily lead to improved scale estimation if a natural moment condition (which is also the maximum likelihood restriction) is satisfied. Therefore, this work deals with the gamma scale parameter estimation as a separate new problem, not as a by-product of the shape parameter estimation, and studies several estimators in terms of second-order risk.     

On the type-B integral equation and the distribution of wilks statist for testing independence of several groups of variables

In this paper, WILKS'type-B integral equation is solved in the general form of a series of beta functions and a series of weighted gamma functions as proposed by WALD and BROOKNER 1941. The coefficients in both representations can be obtained by explicit recurrence relartions, therefore the results solve many distributional problems and have the fewest computational difficulties of any representation that has surfaced to date. The radius of convergence of the second series representation is given, whereas the convergence property of the first series representation is given, whereas the convergence property of the first series representation was studied by WALD and Brookner. The exact null distributions of WILKS' statistic A for testing the independence of several groups of variables and of V = -log A are given. The coefficients in all the series representration can be computed recursilvely and hence can be obtained easily with the help of modern computatinal facilities