In the context of the appearance-based paradigm for object recognition, it is generally believed that algorithms based on LDA (Linear Discriminant Analysis) are superior to those based on PCA (Principal Components Analysis). In this communication we show that this is not always the case. We present our case (cid:12)rst by using intuitively plausible arguments and then by showing actual results on a face database. Our overall conclusion is that when the training dataset is small, PCA can outperform LDA, and also that PCA is less sensitive to di(cid:11)erent training datasets.

IEEE Transactions on Pattern Analysis and Machine Intelligence

A new algorithm is presented for simulating stable random variables on a digital computer for arbitrary characteristic exponent α(0 < α ≤ 2) and skewness parameter β(-1 ≤ β ≤ 1). The algorithm involves a nonlinear transformation of two independent uniform random variables into one stable random variable. This stable random variable is a continuous function of each of the uniform random variables, and of α and a modified skewness parameter β' throughout their respective permissible ranges.

https://www.jstor.org/stable/pdfplus/2285309.pdf

A Method for Simulating Stable Random Variables

Non-Gaussian statistical signal processing is important when signals and/or noise deviate from the ideal Gaussian model. Stable distributions are among the most important non-Gaussian models. They share defining characteristics with the Gaussian distribution, such as the stability property and central limit theorems, and in fact include the Gaussian distribution as a limiting case. To help engineers better understand the stable models and develop methodologies for their applications in signal processing. A tutorial review of the basic characteristics of stable distributions and stable signal processing is presented. The emphasis is on the differences and similarities between stable signal processing methods based on fractional lower-order moments and Gaussian signal processing methods based on second-order moments. >

Signal processing with fractional lower order moments: stable processes and their applications

A comprehensive account of economic size distributions around the world and throughout the years In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions. Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include: Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.

Statistical Size Distributions in Economics and Actuarial Sciences

The four parameters of a stable distribution may be estimated consistently from five pre-determined sample quantiles with the aid of the accompanying tables, for a in the range [0.6, 2.0] and g in the range [-1, 1]. The problem of the discontinuity of the traditional location parameter in the asymmetrical cases as a passes unity is resolved. The proposed estimators of a and c are similar to those of Fama and Roll, except that the small asymptotic bias in their estimators has been eliminated, and their restrictions that a be no less than 1.0 and that the distribution be symmetrical have been relaxed. The proposed estimators can provide good initialization values for other more efficient, but computer-intensive, methods.

Simple consistent estimators of stable distribution parameters

SUMMARY Estimation of the parameters of the stable laws is considered for samples of size at least 50. The modulus of the difference between the empirical and theoretical characteristic functions is weighted and integrated over the real line; this function of the sample values and the parameters is then minimized with respect to the parameters via a gradient search routine nested within a sequential search. Extensive simulation experiments validate the effectiveness of the estimation procedure over the entire parameter space. Application of the procedure to stock market price behaviour is made.

R. A. Leitch

Papers

The estimation of the parameters of the stable laws