John Panaretos

Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.

On Some Distributions Arising from Certain Generalized Sampling Schemes

With the notion of success in a series of trials extended to refer to a run of like outcomes, several new distributions are obtained as the result of sampling from an urn without replacement or with additional replacements. In this context, the hypergeometric, negative hypergeometric, logarithmic series, generalized Waring, Polya and inverse Polya distributions are extended and their properties are studied

On generalized binomial and multinomial distributions and their relation to generalized Poisson distributions

SummaryThe binomial and multinomial distributions are, probably, the best known distributions because of their vast number of applications. The present paper examines some generalizations of these distributions with many practical applications. Properties of these generalizations are studied and models giving rise to them are developed. Finally, their relationship to generalized Poisson distributions is examined and limiting cases are given.

On some distributions arising in inverse cluster sampling

In this paper, distributions of items sampled inversely in clusters are derived. In particular, negative binomial type of distributions are obtained and their properties are studied. A logarithmic series, type of distribution is also defined as limiting form of the obtained generalized negative binomial distribution

Extreme Value Index Estimators and Smoothing Alternatives: Review and Simulation Comparison

Extreme-value theory and corresponding analysis is an issue extensively applied in many different fields. The central point of this theory is the estimation of a parameter γ, known as extreme-value index. In this paper we review several extreme-value index estimators, ranging from the oldest ones to the most recent developments. Moreover, some smoothing and robustifying procedures of these estimators are presented. A simulation study is conducted in order to compare the behaviour of the estimators and their smoothed alternatives. Maybe, the most prominent result of this study is that no uniformly best estimator exists and that the behaviour of estimators depends on the value of the parameter γ itself

Identifiability of compound poisson distributions

Compound Poisson distributions (CPDs) are frequently used as alternatives in studying situations where a simple Poisson model is found inadequate to describe. In this paper an attempt is made to identify compound Poisson distributions when it is known that the conditional distribution of two random variables (r.v.s) is compound binomial. Some interesting special cases and their application to accident theory are discussed.

A Generating Model Involving Pascal and Logarithmic Series Distributions

This paper considers a model where an original observation from a discrete distribution generates, according to a certain mechanism, another observation. A special case with the logarithmic series distribution as the original distribution and the Pascal distribution as the generating mechanism is examined. The interpretation, implications and applications of the results are discussed

An Extension of the Damage Model

The damage model was introduced byRao [1963] and is based on the assumption that an original observation is subjected to a destructive process. Rao, examined in detail the case where the distribution of the original observation and the destructive process were Poisson and Binomial respectively with fixed parameters.In this paper we extend the damage model to the case where either the parameter of the Poisson or the parameter of the Binomial is a random variable with a given distribution function (d.f.).

The Correlated Gamma-Ratio Distribution in Model Evaluation and Selection

The paper considers the problem of selecting one of two not necessarily nested competing regression models based on comparative evaluations of their abilities in each of two different issues: The first pertains to viewing the problem as a “best-fitting” model determination problem in the sense that a model is sought which is closest to the observed data, and utilizes some measure of the adequacy of the models to describe existing observations. The second is entirely different from the first in that it takes account of the predictive adequacy of the models. It is shown that certain test statistics can be constructed which within each of the above settings can lead to appropriate model selection procedures based on sequential comparisons of the competing models in their abilities to describe the data or to predict future observations. The null distribution of these statistics, termed as the “Correlated Gamma Ratio Distribution”, is obtained as the distribution of the ratio of two correlated gamma variates. Applications are given as well as some simulation results revealing the behaviour of the model selection procedures developed. Potential extensions of the proposed procedures are described.

On the Joint Distribution of Two Discrete Random Variables

SummaryLetX, Y be two discrete random variables with finite support andX≧Y. Suppose that the conditional distribution ofY givenX can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution ofX (and hence the joint distribution of (X, Y)) when partial independence only is assumed forY andX−Y.