S. H. Ong

Image analysis by Tchebichef moments

This paper introduces a new set of orthogonal moment functions based on the discrete Tchebichef polynomials. The Tchebichef moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain of the image coordinate space. This property makes Tchebichef moments superior to the conventional orthogonal moments such as Legendre moments and Zernike moments, in terms of preserving the analytical properties needed to ensure information redundancy in a moment set. The paper also details the various computational aspects of Tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction.

Image analysis by Krawtchouk moments

In this paper, a new set of orthogonal moments based on the discrete classical Krawtchouk polynomials is introduced. The Krawtchouk polynomials are scaled to ensure numerical stability, thus creating a set of weighted Krawtchouk polynomials. The set of proposed Krawtchouk moments is then derived from the weighted Krawtchouk polynomials. The orthogonality of the proposed moments ensures minimal information redundancy. No numerical approximation is involved in deriving the moments, since the weighted Krawtchouk polynomials are discrete. These properties make the Krawtchouk moments well suited as pattern features in the analysis of two-dimensional images. It is shown that the Krawtchouk moments can be employed to extract local features of an image, unlike other orthogonal moments, which generally capture the global features. The computational aspects of the moments using the recursive and symmetry properties are discussed. The theoretical framework is validated by an experiment on image reconstruction using Krawtchouk moments and the results are compared to that of Zernike, pseudo-Zernike, Legendre, and Tchebyscheff moments. Krawtchouk moment invariants are constructed using a linear combination of geometric moment invariants; an object recognition experiment shows Krawtchouk moment invariants perform significantly better than Hus moment invariants in both noise-free and noisy conditions.

Image Analysis Using Hahn Moments

This paper shows how Hahn moments provide a unified understanding of the recently introduced Chebyshev and Krawtchouk moments. The two latter moments can be obtained as particular cases of Hahn moments with the appropriate parameter settings and this fact implies that Hahn moments encompass all their properties. The aim of this paper is twofold: (1) To show how Hahn moments, as a generalization of Chebyshev and Krawtchouk moments, can be used for global and local feature extraction and (2) to show how Hahn moments can be incorporated into the framework of normalized convolution to analyze local structures of irregularly sampled signals.

A class of Hurwitz–Lerch Zeta distributions and their applications in reliability

Abstract In this paper, we revisit the study of the Hurwitz–Lerch Zeta (HLZ) distribution by investigating its structural properties, reliability properties and statistical inference. More specifically, we explore the reliability properties of the HLZ distribution and investigate the monotonic structure of its failure rate, mean residual life function and the reversed hazard rate. It is shown that the HLZ distribution is log-convex and hence that it is infinitely divisible. Both the hazard rate and the reversed hazard rate are found to be decreasing. The maximum likelihood estimation of the parameters is discussed and an example is provided in which the HLZ distribution fits the data remarkably well.

Analysis of Long-Tailed Count Data by Poisson Mixtures

Abstract This article deals with various mixed Poisson distributions in order to analyze count data characterized by their long tails and over dispersion when the Poisson distribution and negative binomial distribution are found to be inadequate. Several mixed Poisson distributions are presented and their structural properties are investigated. Three well-known data sets, having long tails, are analyzed and the results of fitting by various models are provided.

A model for the prediction of Oncomelania hupensis in the lake and marshland regions, China

A model has been developed for predicting the density of Oncomelania hupensis, the intermediate host snail of Schistosoma japonicum. The model takes into account different environmental factors, including elevation, air and soil temperature, type of vegetation, mean height of preponderant vegetation and soil humidity. Deviance and Akaike information criteria were used to determine the best model fits. Model diagnostics and internal and external validations of model efficiency were also performed. From the final prediction model, two important results emerge. First, air temperature should be used with care to study the distribution of O. hupensis and to predict its potential survival because the impact is indirect, and it is weaker and more unstable than soil temperature. Second, the more important environmental factor for O. hupensis prediction at the microscale is soil humidity, but the more important macroscale environmental factor is soil temperature. This finding might help in selecting different environmental features for studying O. hupensis at different spatial scales. Our model is promising for predicting the density of O. hupensis, and hence can provide more objective information about snail dispersal, which might eventually replace the tedious and imprecise field work for annual surveillance of O. hupensis.

Krawtchouk moments as a new set of discrete orthogonal moments for image reconstruction

Krawtchouk polynomials can be used to form the basis of a set of discrete orthogonal moments. In this paper, Krawtchouk moments are used to analytically reconstruct binary images. Their performance is compared to that of Zernike, Legendre (continuous) and Chebyshev (discrete) moments.

On a generalized non-central negative binomial distribution

On considere une generalisation de la loi binomiale negative non centree qui est une convolution des variables binomiales negatives et pseudo-binomiales

The computer generation of bivariate binomial variables with given marginals and correlation

In this paper simple mixture models are proposed for generating bivariate binomial variables when the marginal distributions and correlation coefficient are specified. The methods of Loukas and Kemp (1986, Commun. Statist. B) are also considered and comparative timings are given. Analogous models for the bivariate negative binomial and gamma distributions are also examined.

Parameter Estimation for Discrete Distributions by Generalized Hellinger-Type Divergence Based on Probability Generating Function

This article considers a probability generating function-based divergence statistic for parameter estimation. The performance and robustness of the proposed statistic in parameter estimation is studied for the negative binomial distribution by Monte Carlo simulation, especially in comparison with the maximum likelihood and minimum Hellinger distance estimation. Numerical examples are given as illustration of goodness of fit.