Bounded risk estimation of a linear combination of location parameters in negative exponential distributions via three-stage sampling

The paper deals with the problem of bounded risk point estimation for a linear combination of location parameters of two negative exponential distributions. Isogai and Futschik considered the situation when the location and scale parameters are all unknown. They proposed purely sequential procedures and gave second order expansions of the average sample sizes and risks. In this paper we propose three-stage procedures and derive second order expansions of the average sample sizes and risks. Further, we compare the results with those from previous work.     

Interspecific competition between two species of Trichogrammatidae III The analytical study on the competition

Summary The experiment was carried out in order to analyze the results of interspecific competition which were mentioned in the previous reports (Sasaba 1964, 1965). The following definite tendencies were obtained and an account was given with regard to the process of competition. (1)T. minutum had a higher reproductive rate thanT. japonicum at a lower density of the parent wasps. (2) The parasitic efficiency ofT. minutum was high as compared withT. japonicum. (3)T. japonicum was consistently superior toT. minutum in the interspecific competition at larval stage. Contribution from the Entomological Laboratory, College of Agriculture, Kyoto University, No. 384.     

A systems model and computer simulation of the green rice leafhopper populations in control programmes

Summary A simulation model of the green rice leafhopper-spiders system was presented. The validity of this model for simulation purpose was tested by comparing the calculated values with observed ones (Fig. 4). The effectiveness of various control measures against leafhoppers was evaluated by computer simulations. The computer simulation demonstrated that the wrong use of selective insecticide, contrary to expectation, brought an increase in the pest density, i. e., that the egg densities of leafhoppers in the 2nd and 3rd generations are increased by the insecticidal application in February, while they are decreased by the July application (Table 2). To obtain satisfactory control by sterile-male release, 320,000 sterile-male per square kilometer should be released even in the combined use with insecticides (Fig. 5). The escape of leafhoppers from predation by spiders was demonstrated by the simulation. It is suggested that spiders are able to suppress the leafhopper populations at a low density when there is a very favorable balance between spiders and leafhoppers, and this condition may be realized by sophisticated use of selective insecticides (Fig. 6). Factors and/or processes which have to be involved in a more improved systems model are discussed. A part of this research was supported by science research fund from the Ministry of Education.     

Power transformation of the F distribution and a power normal family

To transform the F distribution to a normal distribution, two types of formula for power transformation of the F variable are introduced. One formula is an extension of the Wilson-Hilferty transformation for the chi 2 variable, and the other type is based on the median of the F distribution. Combining those two formulas, a simple formula for the median of the F distribution is derived, and its numerical accuracy is evaluated. Simplification of the formula of the Wilson-Hilferty transformation, through the median formula, leads us to construct a power normal family from the generalized F distribution. Unlike the Box-Cox power normal family, our family has a property that the covariance structure of the maximum-likelihood estimates of the parameters is invariant under a scale transformation of the response variable. Numerical examples are given to show the diff erence between two power normal families.     

Sequential estimation of a linear function of location parameters of two negative exponential distributions

The paper considers the problem of bounded risk point estimation for a linear function of location parameters of two negative exponential distributions, including the difference in a special case, when two scale parameters are unknown. Purely sequential procedures are proposed and second order expansions of the average sample sizes and risk are given. Furthermore some simulation results are provided.     

Nonparametric recursive estimation in stationary markov processes

This paper deals with a class of recursive kernel estimators of the transition probability density function t(y|x) of a stationary Markov process. A sufficient condition for such estimators to be weakly and strongly 2 consistent for almost all (x,y)∈R² is given. Further an L, convergence result is obtained. No continuity conditions are imposed on t(y|x).     

Applications of a new power normal family

The main purpose of this paper is to give an algorithm to attain joint normality of non-normal multivariate observations through a new power normal family introduced by the author (Isogai, 1999). The algorithm tries to transform each marginal variable simultaneously to joint normality, but due to a large number of parameters it repeats a maximization process with respect to the conditional normal density of one transformed variable given the other transformed variables. A non-normal data set is used to examine performance of the algorithm, and the degree of achievement of joint normality is evaluated by measures of multivariate skewness and kurtosis. Besides the above topic, making use of properties of our power normal family, we discuss not only a normal approximation formula of non-central F distributions in the frame of regression analysis but also some decomposition formulas of a power parameter, which appear in a Wilson-Hilferty power transformation setting.