Bias correction for parameter estimates of spatial point process models

When a spatial point process model is fitted to spatial point pattern data using standard software, the parameter estimates are typically biased. Contrary to folklore, the bias does not reflect weaknesses of the underlying mathematical methods, but is mainly due to the effects of discretization of the spatial domain. We investigate two approaches to correcting the bias: a Newton–Raphson-type correction and Richardson extrapolation. In simulation experiments, Richardson extrapolation performs best.     

Construction of closed interval for process capability indices Cpu,Cpl, and Spk based on Boole’s inequality and de Morgan’s laws

ABSTRACT

Considerable effort has been spent on the development of confidence intervals for process capability indices (PCIs) based on the sampling distribution of the PCI or the transferred PCI. However, there is still no definitive way to construct a closed interval for a PCI. The aim of this study is to develop closed intervals for the PCIs C_pu, C_pl, and S_pk based on Boole's inequality and de Morgan's laws. The relationships between different sample sizes, the significance levels, and the confidence intervals of the PCIs C_pu, C_pl, and S_pk are investigated. Then, a testing model for interval estimation for the PCIs C_pu, C_pl, and S_pk is built as a powerful tool for measuring the quality performance of a product. Finally, an applied example is given to demonstrate the effectiveness and applicability of the proposed method and the testing model.     

Monte carlo estimates of the distributions of the random polygons of the voronoi tessellation with respect to a poisson process

A large-scale study, in which two million random Voronoi polygons (with respect to a homogeneous Poisson point process) were generated and mensurated, is described. The polygon characteristics recorded are number of sides (or vertices), perimeter, area and interior angles. A feature is the efficient “quantile” method of replicating Poisson-type random structures, which it is hoped may find useful application elsewhere.     

The Poisson-X family of distributions

ABSTRACT

Recently, Risti? and Nadarajah [A new lifetime distribution. J Stat Comput Simul. 2014;84:135–150] introduced the Poisson generated family of distributions and investigated the properties of a special case named the exponentiated-exponential Poisson distribution. In this paper, we study general mathematical properties of the Poisson-X family in the context of the T-X family of distributions pioneered by Alzaatreh et al. [A new method for generating families of continuous distributions. Metron. 2013;71:63–79], which include quantile, shapes of the density and hazard rate functions, asymptotics and Shannon entropy. We obtain a useful linear representation of the family density and explicit expressions for the ordinary and incomplete moments, mean deviations and generating function. One special lifetime model called the Poisson power-Cauchy is defined and some of its properties are investigated. This model can have flexible hazard rate shapes such as increasing, decreasing, bathtub and upside-down bathtub. The method of maximum likelihood is used to estimate the model parameters. We illustrate the flexibility of the new distribution by means of three applications to real life data sets.     

Bayesian estimation of rare sensitive attribute

Randomized response models have been used to estimate a population proportion of a sensitive attribute. A randomized device is typically employed to protect respondent's privacy in a survey. In addition, an unrelated question is asked to improve the statistical efficiency. In this article, we propose Bayesian estimation of rare sensitive attribute using randomized response technique, which includes a rare unrelated attribute. Two cases are considered, the proportion of a rare unrelated attribute is known and unknown. A simulation study is conducted to assess the performance of the models using mean absolute error and coverage probability. The results show that the performance depends on the parameters and is robust to priors.     

A discrete-time risk model with Poisson ARCH claim-number process

Abstract

In this paper, we propose a discrete-time risk model with the claim number following an integer-valued autoregressive conditional heteroscedasticity (ARCH) process with Poisson deviates. In this model, the current claim number depends on the previous observations. Within this framework, the equation for finding the adjustment coefficient is derived. Numerical studies are also carried out to examine the impact of the Poisson ARCH dependence structure on the ruin probability.     

20 years of Bologna - a story of success,a story of failure

The Bologna Process is a unique harmonisation process taking place outside the policy-making framework of the European Union. It aims at enhancing the comparability and compatibility of higher education structures and degrees across Europe, as well as to institutionalise quality assurance mechanisms. The aim of this article is to provide a condensed, up-to-date overview of the Bologna Process with regard to structural characteristics, before embedding it into a discussion on processes on voluntary policy convergence and to which extent we should be able to find this kind of policy harmonisation in the realm of the Bologna Process. Related to this are questions why this, in principle, completely voluntary process of policy harmonisation, has appealed to so many countries and why they might or might not feel committed to the implementation of its policies and tools.     

A surplus process involving a compound Poisson counting process and applications

Abstract

In this paper, we introduce a surplus process involving a compound Poisson counting process, which is a generalization of the classical ruin model where the claim-counting process is a homogeneous Poisson process. The incentive is to model batch arrival of claims using a counting process that is based on a compound distribution. This reduces the difficulty of modeling claim amounts and is consistent with industrial data. Recursive formula, some properties and relevant main ruin theory results are provided. Further, we consider applications involving zero-truncated negative binomial and zero-truncated binomial batch arrivals when the claim amounts follow exponential or Erlang distribution.     

Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects

Focusing on the model selection problems in the family of Poisson mixture models (including the Poisson mixture regression model with random effects and zero‐inflated Poisson regression model with random effects), the current paper derives two conditional Akaike information criteria. The criteria are the unbiased estimators of the conditional Akaike information based on the conditional log‐likelihood and the conditional Akaike information based on the joint log‐likelihood, respectively. The derivation is free from the specific parametric assumptions about the conditional mean of the true data‐generating model and applies to different types of estimation methods. Additionally, the derivation is not based on the asymptotic argument. Simulations show that the proposed criteria have promising estimation accuracy. In addition, it is found that the criterion based on the conditional log‐likelihood demonstrates good model selection performance under different scenarios. Two sets of real data are used to illustrate the proposed method.     

The effect of autocorrelation on the ewma maxmin tolerance limits

Amin et al. (1999) developed an exponentially weighted moving average (EWMA) control chart, based on the smallest and largest observations in each sample. The resulting plot of the extremes suggests that the MaxMin EWMA may also be viewed as smoothed tolerance limits. Tolerance limits are limits that include a specific proportion of the population at a given confidence level. In the context of process control, they are used to make sure that production will not be outside specifications. Amin and Li (2000) provided the coverages of the MaxMin EWMA tolerance limits for independent data. In this article, it is shown how autocorrelation affects the confidence level of MaxMin tolerance limits, for a specified level of coverage of the population, and modified smoothed tolerance limits are suggested for autocorrelated processes.