Summary

It is known that the set $$\left\{ {E\left( {X_{k_n ,n} } \right)\left| {n = 1,2, \cdots } \right.} \right\}, where 1 \leqq k_n \leqq n,$$ of expectations of order statistics of samples from a distributionF which has a finite expectation determinesF. In this note, we show that each of the sets $$\begin{gathered} \left\{ {E\left( {X_{k_j ,n_j } } \right)\left| {j = 1,2, \cdots } \right.} \right\}, \hfill \\ where \left\{ {\left( {{{k_j } \mathord{\left/ {\vphantom {{k_j } {n_j }}} \right. \kern-\nulldelimiterspace} {n_j }}} \right)\left| {j = 1,2, \ldots } \right.} \right\} is dense in \left[ {0,1} \right], \hfill \\ \end{gathered} $$ $$\begin{gathered} \left\{ {E\left( {X_{1,1} } \right)} \right\} \cup \left\{ {E\left( {X_{k_j ,2j + 1} } \right)\left| {j = 1,2, \cdots } \right.} \right\} \cup \hfill \\ \left\{ {E\left( {X_{k'j,2j + 1} } \right)\left| {j = 1,2, \cdots } \right.} \right\},where 1 \leqq k_j< k'_j \leqq 2j + 1, \hfill \\ \end{gathered} $$ also determinesF.

In this chapter we consider several superpopulation models of victimization and derive an estimate of θ on the basis of each. The fit of each model is tested using a X² goodness of fit statistic for each of the years 1973 though 1975. We find that a correlated Bernoulli model is an inappropriate model of crime, while a homogeneous Bernoulli model and a Markov model provide better fits to the data. None of these models fits the data as well as the model under which the modified ad hoc estimator is consistent.

Resumen

Se introduce el concepto general de medida de inquietud (o medida de incertidumbre cualitativo-cuantitativa) sobre una clase de esquemas dobles de probabilidades y utilidades; y se estudian algunas de sus propiedades: invariancia, componibilidad, etc. Finaliza el trabajo con la caracterización de una clase particular de medidas.

Cross-cultural survey data for Japan and France were analyzed in various aspects by a quantification method of response pattern, equivalent to Benzécri’s analyse des correspondances. New findings regarding consistencies and differences in ways of thinking between the two peoples emerged. Methodological suggestions are given throughout the data analysis.

Consensus among experts in the technological forecasting by the Delphi method is here shown to be interpretable as a leading indicator or rather an antecedent factor of a national consensus and therefore as an intersubjective probability of choosing a particular policy among prospective policies when experts are properly selected. The condition under which this interpretation is valid is shown to hold in several Delphi surveys. Hence a logical foundation is obtained to fill two gaps: one gap between subjective opinions and an objective event of technological breakthroughs, and the other gap between the distributed opinions and a single event. Thus the statistical analysis of consensus is now given a meaning and the statistical methods are discussed to measure the consensus among experts in terms of, e.g., distribution matchings of their opinions. Experiences in technological and social forecastings and assessments are reported.

An optimal Inspection and replacement problem for a discrete-time Markovian deterioration system is investigated. It is assumed that the system is monitored incompletely by a certain mechanism which gives the decision-maker some Information about the exact state of the system. The problem is to obtain an optimal inspection and replacement policy minimizing the expected average cost per unit time over the infinite horizon and formulated as a partially observable Markov decision process. Under some reasonable conditions reflecting the practical meaning of the deterioration, it is shown that there exists an optimal Inspection and replacement policy in the class of monotonic four region-policies.

Zusammenfassung

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