Several common flexible functional forms are evaluated for Texas agricultural production utilizing three procedures. Nested hypothesis tests indicate that the normalized quadratic is the marginally-preferred functional form followed by the generalized Leontief. Predictive accuracy results are ambiguous between the generalized Leontief and the normalized quadratic. Statistical performance favors the normalized quadratic. These two functional forms consistently dominate the translog.

Farmland offered for its productive or consumptive value may be viewed as a class of goods characteristic of product differentiation. Using the generalized Box-Cox transformation, an unrestricted hedonic model was employed to derive implicit valuations of parcel attributes. Results suggest that the significance and level of importance of attributes on land pricing depends on the spatial extent of markets in Georgia. Differences in the productive or consumptive use of farmland may imply that different factors and functional forms are appropriate to different farmland markets.

Estimation of pure premiums for alternative rate classes using regression methods requires the choice of a functional form for the statistical model. Common choices include linear and log-linear models. This paper considers maximum likelihood estimation and testing for functional form using the power transformation suggested by Box and Cox. The linear and log-linear models are special cases of this transformation. Application of the procedure is illustrated using auto insurance claims data from the state of Massachusetts and from the United Kingdom. The predictive accuracy of the method compares favorably to that for the linear and log-linear models for both data sets.

Seneta, in a recent paper, presented a general treatment of the concept of ‘coefficient of ergodicity', τ (P), for a finite stochastic matrix P. In this paper, a functional form for τ∞(P) in terms of the attributes of P is determined. It is shown that, by increasing the dimension of P, τ∞(Ρ) can assume any large value. In view of this, τ∞ will be practically useful only in the case τ∞(P) ≦ τ1(P), where τ1(P) is the well-known Dobrushin or delta coefficient.

The purpose of this note is to extend results on critical Galton-Watson branching processes, due to Feller and Lamperti: if the number of individuals at time zero tends to infinity, the process converges, with two different normalizations, to certain diffusion processes in the functional form, discussed in, e.g., Billingsley.