Entropy estimation and goodness-of-fit tests for the inverse Gaussian and Laplace distributions using paired ranked set sampling

ABSTRACT

In this paper, Vasicek [A test for normality based on sample entropy. J R Stat Soc Ser B. 1976;38:54–59] entropy estimator is modified using paired ranked set sampling (PRSS) method. Also, two goodness-of-fit tests using PRSS are suggested for the inverse Gaussian and Laplace distributions. The new suggested entropy estimator and goodness-of-fit tests using PRSS are compared with their counterparts using simple random sampling (SRS) via Monte Carlo simulations. The critical values of the suggested tests are obtained, and the powers of the tests based on several alternatives hypotheses using SRS and PRSS are calculated. It turns out that the proposed PRSS entropy estimator is more efficient than the SRS counterpart in terms of root mean square error. Also, the proposed PRSS goodness-of-fit tests have higher powers than their counterparts using SRS for all alternative considered in this study.     

A Class of Normalized Random Measures with an Exact Predictive Sampling Scheme

Abstract. In this article, we define and investigate a novel class of non‐parametric prior distributions, termed the class . Such class of priors is dense with respect to the homogeneous normalized random measures with independent increments and it is characterized by a richer predictive structure than those arising from other widely used priors. Our interest in the class is mainly motivated by Bayesian non‐parametric analysis of some species sampling problems concerning the evaluation of the species relative abundances in a population. We study both the probability distribution of the number of species present in a sample and the probability of discovering a new species conditionally on an observed sample. Finally, by using the coupling from the past method, we provide an exact sampling scheme for the system of predictive distributions characterizing the class .     

Irreversible random sequential filling of lattices by monte carlo simulation

By means of Monte Carlo simulations we study the irreversible, random, sequential filling of small clusters (e.g., pairs, triples,...) on linear, square, and cubic lattices. In particular, we are interested in the fraction of sites filled at saturation (the point at which further filling is not possible without rearrangement of the filled and empty sites). The results obtained show good agreement with those of previously developed analytic techniques.

We present the first extensive results for filling linear strings of lattice sites by use of the end-on mechanism (where the ends of the string are chosen sequentially rather than simultaneously as in conventional filling). For end-on filling we find that the saturation coverage increases, relative to conventional filling, for short strings, but decreases as we go to the limit of infinitely long strings (the car-parking problem).

An examination of the Palasti conjecture (and its extension to discrete lattices) is also made.     

期货市场有效性理论与实证检验

本文以我国期货市场选取的六种期货的价格行为为对象,利用单位根检验与自相关检验的结合,并同时利用方差比检验和多重方差比检验来随机游走假设进行实证研究,目的在于探讨国内铜、大豆、小麦等六大期货市场是否呈有效态势。结果显示:各种检验方法得出的结论不尽一致,除上天胶外,各大期货市场的对数期货价格序列不能拒绝弱式有效市场假设。     

无定形橡木陈酿白兰地的机理研究

研究了橡木桶陈酿白兰地的机理，阐明了桶板自然风干三年的作用，提出了白兰地陈酿质量的控制指标，为工艺设计奠定了基础．     

A likelihood based approach for joint modeling of longitudinal trajectories and informative censoring process

We propose a joint modeling likelihood-based approach for studies with repeated measures and informative right censoring. Joint modeling of longitudinal and survival data are common approaches but could result in biased estimates if proportionality of hazards is violated. To overcome this issue, and given that the exact time of dropout is typically unknown, we modeled the censoring time as the number of follow-up visits and extended it to be dependent on selected covariates. Longitudinal trajectories for each subject were modeled to provide insight into disease progression and incorporated with the number follow-up visits in one likelihood function.     

Modelling ordinal assessments: fit is not sufficient

Assessments in ordered categories are ubiquitous in the social sciences. These assessments are assigned ordinal counts and analyzed with probabilistic models. If the counts fit the model, it is assumed that no unaccounted for factors govern the distribution and that it is a random error distribution. However, because tests of fit utilize parameter estimates from the data, the data may fit the model even when the modeled distributions cannot be random error distributions. This paper applies the additional criterion of strict unimodality, common to all random error distributions, to decide if a modeled distribution is not a random error distribution. However, not only are common random error distributions strictly unimodal, they are also strictly log-concave, a stronger form of unimodality which ensures smooth transitions between probabilities of adjacent counts. The paper shows that the operation for determining the strict unimodality also ensures that the distribution is locally strictly log-concave around the measure of the entity of assessment.     

Joint (k,l)-hurdle random effects models for mixed longitudinal power series and normal outcomes

A random effects model for analyzing mixed longitudinal normal and count outcomes with and without the possibility of non ignorable missing outcomes is presented. The count response is inflated in two points (k and l) and the (k, l)-Hurdle power series is used as its distribution. The new distribution contains, as special submodels, several important distributions which are discussed, such as (k, l)-Hurdle Poisson and (k, l)-Hurdle negative binomial and (k, l)-Hurdle binomial distributions among others. Random effects are used to take into account the correlation between longitudinal outcomes and inflation parameters. A full likelihood-based approach is used to yield maximum likelihood estimates of the model parameters. A simulation study is performed in which for count outcome (k, l)-Hurdle Poisson, (k, l)-Hurdle negative binomial and (k, l)-Hurdle binomial distributions are considered. To illustrate the application of such modelling the longitudinal data of body mass index and the number of joint damage are analyzed.     

A note on the almost sure central limit theorem for the product of partial sums of m-dependent random variables

We present an almost sure central limit theorem for the product of the partial sums of m-dependent random variables. In order to obtain the main result, we prove a corresponding almost sure central limit theorem for a triangular array.     

Optimal stratification in stratified designs using weibull-distributed auxiliary information

Sampling has evolved into a universally accepted approach for gathering information and data mining as it is widely accepted that a reasonably modest-sized sample can sufficiently characterize a much larger population. In stratified sampling designs, the whole population is divided into homogeneous strata in order to achieve higher precision in the estimation. This paper proposes an efficient method of constructing optimum stratum boundaries (OSB) and determining optimum sample size (OSS) for the survey variable. The survey variable may not be available in practice since the variable of interest is unavailable prior to conducting the survey. Thus, the method is based on the auxiliary variable which is usually readily available from past surveys. To illustrate the application as an example using a real data, the auxiliary variable considered for this problem follows Weibull distribution. The stratification problem is formulated as a Mathematical Programming Problem (MPP) that seeks minimization of the variance of the estimated population parameter under Neyman allocation. The solution procedure employs the dynamic programming technique, which results in substantial gains in the precision of the estimates of the population characteristics.