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.

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

Betrachten Sie folgende Merkmale: Haarfarbe, Einkommen, Zugehörigkeit zu einer sozialen Schicht, Körpergröße, Geschlecht, Beruf, Vermögen, Religionsbekenntnis, Zahl der Kontobewegungen pro Monat, Abiturnote in Deutsch, Abweichung von der Norm bei Fertigungsprozessen.

Zusammenfassung

Wir greifen die Fragestellung vom Abschnitt 1.3 auf und stellen uns die Aufgabe, die Häufigkeitsverteilungen der Merkmale

„Unterrichtsstunden“ (Item 6, dessen Werte in den Lochkartenspalten 5–6 erfaßt sind),

„Hausaufgaben“ (Item 7 mit den Werten in Spalte 7),

„Abschalten“ (Item 10 mit den Werten in Spalte lo) und

„Schulleistung“ (Item 14 mit den Werten in Spalte 14)

Tiago de Oliveira presented the first paper in a series on statistical choice of univariate extreme models. This paper is a second one in that series. We present formulae for the general mean values and variances and some computer results. We investigated for how small values of the sample size the proposed test statistics may be useful by computer simulations applying the chisquare and Stephens’goodness of fit tests for normality. Some concrete data are further analysed in more detail. We conclude the paper with a general discussion.