INTELLECTUAL PROPERTY RIGHTS POLICY,COMPETITION AND INNOVATION

To what extent and in what form should the intellectual property rights (IPR) of innovators be protected? Should a company with a large technology lead over its rivals receive the same IPR protection as a company with a more limited advantage? In this paper, we develop a dynamic framework for the study of the interactions between IPR and competition, in particular to understand the impact of such policies on future incentives. The economy consists of many industries and firms engaged in cumulative (step‐by‐step) innovation. IPR policy regulates whether followers in an industry can copy the technology of the leader. We prove the existence of a steady‐state equilibrium and characterize some of its properties. We then quantitatively investigate the implications of different types of IPR policy on the equilibrium growth rate and welfare. The most important result from this exercise is that full patent protection is not optimal; instead, optimal policy involves state‐dependent IPR protection, providing greater protection to technology leaders that are further ahead than those that are close to their followers. This is because of a trickle‐down effect: providing greater protection to firms that are further ahead of their followers than a certain threshold increases the R&D incentives also for all technology leaders that are less advanced than this threshold.     

Smoothing fertility trends in agricultural field experiments

Fertility trend within blocks and local variations are the major obstacles to estimate cultivar contrasts in agricultural field trials. This paper examines methods of smoothing fertility trends in field trials using the P-spline. We begin by smoothing trend within block and for each block, and proceeds to demonstrate how it can be extended to smooth trends in trials with two-dimensional setting. We propose simultaneous modelling of trends and local variation. We use Papadakis [J.S. Papadakis, Comparison de differentes methds d'expermentation phytotechnique, Rev. Argen. Agronom. 7 (1940), pp. 297–362.] and kriged covariate to model local variation. We emphasize on the benefit of using P-spline to compromise between parametric and non-parametric approaches. Data sets from wheat and barley trials, designed as randomized complete block design and row-column, are analyzed. We set out a simple strategy of choosing between additive model and two-dimensional setting. We explore different estimation methods and offer some generalizations. The results show importance of the P-spline in modelling trend and the need to choose between additive and two-dimensional settings.     

Estimation of the Mean and Standard Deviation of the Logistic Distribution Based on Multiply Type-II Censored Samples

In this paper, we discuss the problem of estimating the mean and standard deviation of a logistic population based on multiply Type-II censored samples. First, we discuss the best linear unbiased estimation and the maximum likelihood estimation methods. Next, by appropriately approximating the likelihood equations we derive approximate maximum likelihood estimators for the two parameters and show that these estimators are quite useful as they do not need the construction of any special tables (as required for the best linear unbiased estimators) and are explicit estimators (unlike the maximum likelihood estimators which need to be determined by numerical methods). We show that these estimators are also quite efficient, and derive the asymptotic variances and covariance of the estimators. Finally, we present an example to illustrate the methods of estimation discussed in this paper.     

Distance Mean and Variance Functions and Sphere Fitting

Motivated by circle fitting to spatial distributions, this paper looks at the relationship between the expected distance function and the radial density. Inversion of this relationship is given simply in dimensions 1 and 3 and generally by using Mellin transforms. Examples of variance function behaviour are given and calculations of the coefficient of sphericity shown.     

Reliability and Some Characteristics of Circular Consecutive-k-Within-m-Out-of-n:F System

A system can be classified with respect to the physical arrangement of its components and the functioning principle. A circular consecutive k-within-m-out-of-n:F system consists of n circularly ordered components and fails if and only if there are m consecutive components that include among them at least k failed components. A circular consecutive k-within-m-out-of-n:F system turns into circular consecutive k-out-of-n:F for m = k and k-out-of-n:F system for m = n. In this study, signature-based analysis of circular consecutive k-within-m-out-of-n:F system is performed. A new approximation to this system is provided based on maximum number of failed components and an illustrative example is given for different values of n, m, k to compare the approximate results with simulated and exact results.     

Reliabilities for (n,f, k (i,j)) and ⟨n,f, k (i,j)⟩ Systems

The (n,f,k(i,j)):F(? n,f,k(i,j)?:F) system consists of n components ordered in a line or circle, while the system fails if, and only if, there exist at least f failed components OR (AND) at least k consecutive failed components among components i,i + 1,…,j ? 1,j. In this article, we present the system reliability formulae for these systems with product of matrices by means of a two-stage finite Markov chain imbedding approach, a technique first used by Cui et al. (2002 Cui , L. R. , Kuo , W. , Xie , M. ( 2002 ). On (f,g)-out-of-((i,j),n) systems and its reliability . In: Third International Conference on Mathematical Methods in Reliability Methodology and Practice , June 17–20 , Norway , Trondheim , pp. 173 – 176 . [Google Scholar]). In addition, their dual systems, denoted by (n,f,k(i,j)):G and ? n,f,k(i,j)?:G, are also introduced. Two numerical examples are given to illustrate the results.     

Two-stage tests of hypotheses in the general linear model

Two-stage (double sample) tests of hypotheses are presented for testing linear hypotheses in the general linear model. General and one-sided alternatives are considered. Computational techniques for computing critical points are discussed. Tables of critical points are presented. An example suggests that two-stage tests can achieve the same power as a fixed sample size test while reducing considerably the expected number of observations required for the test     

Statistical Gambler's Ruin Problem

Abstract

The gambler's ruin problem is one of the most important problems in the emergence of probability. The problem has been long considered “solved” from a probabilistic viewpoint. However, we do not find the solution satisfactory. In this paper, the problem is recast as a statistical problem. Bounds of the estimate are derived over wide classes of priors. Interestingly, the probabilistic estimates ω(1/2) are identified as the most conservative solutions while the plug-in estimates are found to be out of range of the bounds. It implies that, although conservative, the probabilistic estimates ω(1/2) are justified by our analysis while the plug-in estimates are too extreme for estimating the ruin probability of gambler.