The non-central negative binomial distribution: Further properties and applications

Abstract

The non-central negative binomial distribution is both a mixed and compound Poisson distribution with applications in photon and neural counting, statistical optics, astronomy and a stochastic reversible counter system. In this paper various important probabilistic properties of the non-central negative binomial distribution in practical applications like log-concavity, discrete self-decomposability, unimodality, asymptotic behavior and tail length of the probability distribution have been derived. The construction as a mixed Poisson process by specifying a joint distribution for the inter-arrival times and its application is illustrated by a fit to real life data set.     

Cluster-based multivariate outlier identification and re-weighted regression in linear models

A cluster methodology, motivated by a robust similarity matrix is proposed for identifying likely multivariate outlier structure and to estimate weighted least-square (WLS) regression parameters in linear models. The proposed method is an agglomeration of procedures that begins from clustering the n-observations through a test of ‘no-outlier hypothesis’ (TONH) to a weighted least-square regression estimation. The cluster phase partition the n-observations into h-set called main cluster and a minor cluster of size n?h. A robust distance emerge from the main cluster upon which a test of no outlier hypothesis’ is conducted. An initial WLS regression estimation is computed from the robust distance obtained from the main cluster. Until convergence, a re-weighted least-squares (RLS) regression estimate is updated with weights based on the normalized residuals. The proposed procedure blends an agglomerative hierarchical cluster analysis of a complete linkage through the TONH to the Re-weighted regression estimation phase. Hence, we propose to call it cluster-based re-weighted regression (CBRR). The CBRR is compared with three existing procedures using two data sets known to exhibit masking and swamping. The performance of CBRR is further examined through simulation experiment. The results obtained from the data set illustration and the Monte Carlo study shows that the CBRR is effective in detecting multivariate outliers where other methods are susceptible to it. The CBRR does not require enormous computation and is substantially not susceptible to masking and swamping.     

Two-sided Bayesian and frequentist tolerance intervals: general asymptotic results with applications

It is well known that that the construction of two-sided tolerance intervals is far more challenging than that of their one-sided counterparts. In a general framework of parametric models, we derive asymptotic results leading to explicit formulae for two-sided Bayesian and frequentist tolerance intervals. In the process, probability matching priors for such intervals are characterized and their role in finding frequentist tolerance intervals via a Bayesian route is indicated. Furthermore, in situations where matching priors are hard to obtain, we develop purely frequentist tolerance intervals as well. The findings are applied to real data. Simulation studies are seen to lend support to the asymptotic results in finite samples.     

Canonical expansions,correlation structure,and conditional distributions of bivariate distributions generated by mixtures

A simple result concerning the canonical expansions of mixed bivariate distributions is considered. This result is then applied to analyze the correlation structures of the Bates-Neyman accident proneness model and its generalization, to derive probability inequalities based on the concept of positive dependence, and to construct a bivariate beta distribution with positive correlation coefficient applicable in computer simulation experiments. The mixture formulation of the conditional distribution of this class of mixed bivariate distributions is used to define and generate first-order autoregressive gamma and negative binomial sequences.     

Dual chain migration: post-1965 Filipino immigration to the United States

In analyzing Filipino migration to the United States since 1965, the authors identify two distinct chains of immigrants. One derives from the Filipinos who entered the country prior to 1965; the other comes from the flow of highly trained professionals who immigrated during the late 1960s and early 1970s. "To establish the historical basis for the two patterns of immigration that unfolded in the post-1965 period, the article begins with a brief examination of Filipino immigration to the United States. An analysis of the modes of entry used in both chains follows this overview. The study concludes with a discussion of the degree of convergence in these two chains and the consequences of each for contemporary Filipino-American community development." Data are from published U.S. census material and from Immigration and Naturalization Service reports and tapes dating from 1972 to 1985.     

A modified Conway–Maxwell–Poisson type binomial distribution and its applications

This article proposes a generalized binomial distribution, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional Conway–Maxwell–Poisson (CMP) distribution given a sum of two CMP variables. In this article, we consider the properties of the probability mass function, indices of dispersion, skewness and kurtosis, and give applications of the proposed distribution. The estimation method and simulation study are also considered.     

Medical students' exposure to formaldehyde in a gross anatomy dissection laboratory.

The authors studied 150 first-year medical students exposed to formaldehyde during the dissection of cadavers in a gross anatomy laboratory. As a reference group, they used 189 third- and fourth-year medical students matched for sex, ethnic group, and age. Environmental and personal samples were collected to determine the exposure to formaldehyde among the first-year students. The mean concentration of formaldehyde in parts per million (ppm) in the area was 0.50 ppm (range = 0.40-0.60 ppm) and the personal sample was 0.74 ppm (range = 0.41-1.20 ppm). No significant differences were noted in the pre- and post-exposure mean FEV1 (forced expiratory volume in 1 second) and FVC (forced vital capacity) among the 22 randomly selected exposed male and female subjects. Significant differences, however, were observed in the exposed group for symptoms of decreased ability to smell, eye irritation, throat irritation, and dry mouth in comparison with the reference group. These symptoms were also significantly related to the time and place of occurrence. Medical schools should take more concrete measures to reduce students' exposure to formaldehyde. Meanwhile, although it is not now the practice in most medical schools, students should have ready access to goggles and respirators when working in dissection laboratories.     

Estimation of frequencies of sinusoids in the presence of noise

A method is proposed and developed for estimating the frequencies of K sinusoids given the sum of these sinusoids in Gaussian noise. Attention is focused on the properties of these estimators when the observation time is short, the separation between frequencies is small, and the signal-to-noise ratio is high. The estimators are shown to be approximately unbiased and approximately normally distributed. The covariance matrix is also calculated. Relatively simple bounds on the variance of the estimators are found.