Characterization of the Geometric Distribution Via Linear Combinations of Observations and of Records

In a sequence of independent identically distributed geometric random variables, the sum of the first two record values is distributed as a simple linear combination of geometric variables. It is verified that this distributional property characterizes the geometric distribution. A related characterization conjecture is also discussed. Related discussion in the context of weak records is also provided.

Stationarity as a path property

Traditionally, stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of paths, denoted by A, which corresponds to the notion of stationarity. On one hand, the set A is shown to be large enough, so that for any stationary process, almost all of its paths are in A. On the other hand, we prove that any path in A will behave in the optimal way under any stationarity test satisfying some mild conditions.

BROWNIAN SEMISTATIONARY PROCESSES AND CONDITIONAL FULL SUPPORT

In this note, we study the infinite-dimensional conditional laws of Brownian semistationary processes. Motivated by the fact that these processes are typically not semimartingales, we present sufficient conditions ensuring that a Brownian semistationary process has conditional full support, a distributional property that has two important implications. It ensures, firstly, that the process admits no free lunches under proportional transaction costs, and secondly, that it can be approximated pathwise (in the sup norm) by semimartingales that admit equivalent martingale measures.

THE DEVIATIONS OF MORPHOSYNTAX OF GRAMMATICAL CATEGORIES IN THE ESSAYS OF THE ENGLISH GRADUATE STUDENTS OF STATE UNIVERSITY OF PADANG

This research dealt with deviations or errors of morphosyntax of grammatical categories which consist of structural properties and distributional properties of nouns, verbs, adjectives and adverbs made by the first semester English graduate students of State University of Padang (UNP) in writing their essays. It aimed at explaining what errors of morphosyntax of grammatical categories committed by those students in writing their essays. The subjects of this research were the first semester English graduate students of 2008/ 2009 academic year of UNP. There were 15 randomly selected students who took the course of Academic Writing as the subjects of the research. The instrument used was through a test with one administration where the lecturer asked the students to construct essays based on the topics given. The analysis of data was based on theories proposed by Payne (1997) describing morphosyntax, error analysis method by James (1998) and Scovel (2001). It was found out that deviations of morphosyntax of grammatical categories mostly occurred. First, in the mis-formation of verbs (54.45%) as a structural property that exhibits subject agreement and in the omission of verbs which serves as predicates of clauses as a distributional property. Second, in the misformation of nouns (32.07%) exhibiting number as structural property and in the omission of nouns as a distributional property which serves as heads of noun phrases. Third, in the misformation of adjective (8.33%) which exhibits predicative function; and fourth in the errors of omission suffix –ly in adverbs (5.05%) modifying verbs. The findings reveal that the use of correct morphosyntax of grammatical categories of the first semester English graduate students of 2008/ 2009 academic year of UNP in writing essays is low implication?

Le groupe nominal épithète

Summary This paper explores the syntactic structure of those French constructions where an NP directly follows another. Examples are provided by Monsieur le Professeur, Mes amis les linguistes, Les linguistes mes amis, the later being equivalent to the English cases My Brother the fool and The fool my brother. Following an analysis of their distributional property, the syntactic structure of the groups is shown to involve the modification of the first noun by the following DP. While therefore structurally comparable to an adjectival modifier, these DPs impose a condition of coreference between the two nouns. A further interpretative constraint is shown to hold concerning the referentially anchored status of either of the DPs. Thus, the form of the complement can determine the behaviour of the head, as demonstrated by this atypical nominal group.

Characterizations of the geometric distribution by distributional properties

Some new characterizations of the geometric distribution are studied. A generalization of the characterization by the well-known ‘lack-of-memory' property is given together with some closely related characterizations. Furthermore the modified geometric distribution is characterized by a distributional property of the difference of two successive order statistics. The latter result extends work of Puri and Rubin (1970). Finally the geometric distribution is characterized by a conditional distribution property of the difference of two arbitrary order statistics, which generalizes a result by Arnold (1980). Some of the results given answer open questions put in earlier papers.

Characterizations of the geometric distribution by distributional properties

Some new characterizations of the geometric distribution are studied. A generalization of the characterization by the well-known ‘lack-of-memory' property is given together with some closely related characterizations. Furthermore the modified geometric distribution is characterized by a distributional property of the difference of two successive order statistics. The latter result extends work of Puri and Rubin (1970). Finally the geometric distribution is characterized by a conditional distribution property of the difference of two arbitrary order statistics, which generalizes a result by Arnold (1980). Some of the results given answer open questions put in earlier papers.