Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings

It is known that the normal approximation is applicable for sums of non negative random variables, W, with the commonly employed couplings. In this work, we use the Stein’s method to obtain a general theorem of non uniform exponential bound on normal approximation base on monotone size bias couplings of W. Applications of the main result to give the bound on normal approximation for binomial random variable, the number of bulbs on at the terminal time in the lightbulb process, and the number of m runs are also provided.     

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.     

Multivariate normal mean–variance mixture distribution based on Birnbaum–Saunders distribution

A multivariate normal mean–variance mixture based on a Birnbaum–Saunders (NMVMBS) distribution is introduced and several properties of this new distribution are discussed. A new robust non-Gaussian ARCH-type model is proposed in which there exists a relation between the variance of the observations, and the marginal distributions are NMVMBS. A simple EM-based maximum likelihood estimation procedure to estimate the parameters of this normal mean–variance mixture distribution is given. A simulation study and some real data are used to demonstrate the modelling strength of this new model.     

Production systems and supplier selection: a multi-phase process model

Abstract

Purpose: This paper presents a combined multi-phase supplier selection model. The process repeatedly revisits the criteria and sourcing decision as the development process continues. This enables a structured adoption of product and production system innovation from strategic suppliers, where previously the literature purely focuses on product innovation or cost reduction. Design/methodology/approach: The authors adopted an embedded researcher style, inductive, qualitative case study of an industrial supply cluster comprising a focal automotive company and its interaction with three different strategic stamping suppliers. Findings: Our contribution is the multi-phased production and product innovation process. This is an advance from traditional supplier selection and also an extension of ideas of supplier-located product development as it includes production system development, and complements the literature on working with strategic suppliers. Specifically, we explicitly articulate the previously unreported issue of whether a supplier chosen for its innovation capabilities at the start of the new product development process will also be the most appropriate supplier during the production system development phase, when an ability to work collaboratively may be the most important attribute, or in the large-scale production phase when an ability to manufacture at low unit cost may be most important. Originality/value: The paper identifies a multi-phase approach to tendering within a fixed body of strategic suppliers which seeks to identify the optimum technological and process decisions as well as the traditional supplier sourcing choice. These areas have not been combined before and generate a valuable approach for firms to adopt as well as for researchers to extend our understanding of a highly complex process.     

Tail asymptotic of discounted aggregate claims with compound dependence under risky investment

This paper considers the tail asymptotic of discounted aggregate claims with compound dependence under risky investment. The price of risky investment is modeled by a geometric Lévy process, while claims are modeled by a one-sided linear process whose innovations further obeying a so-called upper tail asymptotic independence. When the innovations are heavy tailed, we derive some uniform asymptotic formulas. The results show that the linear dependence has significant impact on the tail asymptotic of discounted aggregate claims but the upper tail asymptotic independence is negligible.     

Sample size re‐estimation incorporating prior information on a nuisance parameter

Prior information is often incorporated informally when planning a clinical trial. Here, we present an approach on how to incorporate prior information, such as data from historical clinical trials, into the nuisance parameter–based sample size re‐estimation in a design with an internal pilot study. We focus on trials with continuous endpoints in which the outcome variance is the nuisance parameter. For planning and analyzing the trial, frequentist methods are considered. Moreover, the external information on the variance is summarized by the Bayesian meta‐analytic‐predictive approach. To incorporate external information into the sample size re‐estimation, we propose to update the meta‐analytic‐predictive prior based on the results of the internal pilot study and to re‐estimate the sample size using an estimator from the posterior. By means of a simulation study, we compare the operating characteristics such as power and sample size distribution of the proposed procedure with the traditional sample size re‐estimation approach that uses the pooled variance estimator. The simulation study shows that, if no prior‐data conflict is present, incorporating external information into the sample size re‐estimation improves the operating characteristics compared to the traditional approach. In the case of a prior‐data conflict, that is, when the variance of the ongoing clinical trial is unequal to the prior location, the performance of the traditional sample size re‐estimation procedure is in general superior, even when the prior information is robustified. When considering to include prior information in sample size re‐estimation, the potential gains should be balanced against the risks.     

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.     

Local asymptotic normality for long-memory process with strong mixing noises

Abstract

We will establish the local asymptotic normality (LAN) for fractional autoregressive long memory model in the case of strong mixing noises. This opens the way in future work to construct an adaptive estimator and construct optimal tests for the parameters. To check the feasibility and validity of our theoretical results a simulations study is considered.     

Control Chart for Monitoring Autocorrelated Process with Multiple Exogenous Inputs

We propose to use AR-Sieve Bootstrap in the construction of a control chart of an autocorrelated process influenced by multiple exogenous inputs. The control charts are compared with Exponentially Weighted Moving Average (EWMA) control chart through a simulation study. AR-Sieve bootstrap control limits are narrower than EWMA control limits. While the proposed method yields a higher rate of false alarms, it is quick in detecting even minimal structural changes.