Search

This paper introduces a generalization of the so-called space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form. It turns out that this generalization can be put in relation to a specific subordination of a homogeneous Poisson process by means of a subordinator for which it is possible to express the characterizing L\'evy measure explicitly. Moreover, the law of this subordinator solves a one-sided first-order differential equation in which a particular convolution-type integral operator appears, called Prabhakar derivative. In the last section of the paper, a similar model is introduced in which the Prabhakar derivative also acts in time. In this case, too, the probability generating function of the corresponding process and the probability distribution are determined.

Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper, a class of random sequences, called Generalized Species Sampling Sequences, is defined and a condition to have conditional identity in distribution is given. Moreover, a class of generalized species sampling sequences that are conditionally identically distributed is introduced and studied: the Generalized Ottawa sequences (GOS). This class contains a '`randomly reinforced'' version of the P\'olya urn and of the Blackwell-MacQueen urn scheme. For the empirical means and the predictive means of a GOS, we prove two convergence results toward suitable mixtures of Gaussian distributions. The first one is in the sense of stable convergence and the second one in the sense of almost sure conditional convergence. In the last part of the paper we study the length of the partition induced by a GOS at time $n$, i.e. the random number of distinct values of a GOS until time $n$. Under suitable conditions, we prove a strong law of large numbers and a central limit theorem in the sense of stable convergence. All the given results in the paper are accompanied by some examples.

Riassunto Melchior Cesarotti è stato uno dei protagonisti illustri che si sono occupati della Questione della Lingua nel tempo dell’Illuminismo Italiano. Facendo una lettura attenta di tipo close reading utilizzando il metodo dell’analisi del discorso, questo articolo ricalca le tesi centrali e le motivazioni di Cesarotti e dimostra la loro importanza nel processo dello sviluppo di una lingua nazionale italiana. Il merito del Cesarotti non è di avere superato il linguaggio delle tre corone fiorentine come modello di lingua scritta, ma di avere introdotto la libertà di arricchirlo con termini nuovi, derivanti dalla parte nobile di tutti gli idiomi italiani e stranieri. Resumo Melchior Cesarotti foi um dos protagonistas ilustres que trataram da chamada Questione della Lingua no tempo do Iluminismo Italiano. Realizando uma leitura atenta do tipo close reading e utilizando o método da análise do discurso, este artigo resume as teses centrais e as motivações de Cesarotti e demonstra a sua importância no processo do desenvolvimento de uma língua nacional italiana. O mérito de Cesarotti não é de ter superado a linguagem das tre corone fiorentine como modelo da língua escrita, mas sim de ter introduzido a liberdade de enriquecê-la com novos termos que derivassem das partes nobres de todos os idiomas italianos e estrangeiros. Abstract Melchior Cesarotti was among the most famous protagonists who contributed to the Questione della Lingua during the Italian Enlightenment. Through a close reading process, using the method of discourse analysis, this paper aims to retrace the central theses and the motivations of Cesarotti, and to show their importance within the process of the development of a national italian language. The merit of Cesarotti was not to have excelled the language of the tre corone fiorentine as model of written language, but to have come up with the freedom to enrich the italian language with new terms, deriving from the noble part of all idioms spoken in the Italian territory.

Monitoring the coefficient of variation (CV) is an effective approach to monitor a process when both the process mean and the standard deviation are not constant but, nevertheless, proportional. Until now, few contributions have investigated the monitoring of the CV for short production runs. This paper proposes an adaptive Shewhart control chart implementing a variable sample size (VSS) strategy in order to monitor the coefficient of variation in a short production run context. Formulas for the truncated average run length are derived. Moreover, a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV in order to evaluate the performance of each chart in a short run context. An example illustrates the use of this chart on real data.