Power comparison of the Kolmogorov–Smirnov test under ranked set sampling and simple random sampling

Many studies have been used to compare the power of several goodness-of-fit (GOF) tests under simple random sampling (SRS) and ranked set sampling (RSS). In our study, a different design procedure and ranking process in RSS are thoroughly investigated. A simulation study is conducted to compare the power of the Kolmogorov–Smirnov test under SRS and RSS with different sets and cycle sizes for several distributions. Level-2 sampling design and partially rank-ordered sets are used. Also, we benefited from auxiliary variables in the ranking process. Finally, results are presented with tables and figures. Under these conditions we show that the RSS has better performance against the SRS in finite population.     

Bayesian ratemaking under Dirichlet process mixtures

Experience ratemaking plays a crucial role in general insurance in determining future premiums of individuals in a portfolio by assessing observed claims from the whole portfolio. This paper investigates this problem in which claims can be modeled by certain parametric family of distributions. The Dirichlet process mixtures are employed to model the distributions of the parameters so as to make two advantages: to produce exact Bayesian experience premiums for a class of premium principles generated from generic error functions and, at the same time, provide robust and flexible ways to avoid possible bias caused by traditionally used priors such as non informative priors or conjugate priors. In this paper, the Bayesian experience ratemaking under Dirichlet process mixture models are investigated and due to the lack of analytical forms of the conditional expectations of the quantities concerned, the Gibbs sampling schemes are designed for the purpose of approximations.     

Hypothesis Testing in a Rayleigh Diffusion Model

Applying the large and moderate deviations for the log-likelihood ratio of the Rayleigh diffusion model, we give the negative regions in testing Rayleigh diffusion model and obtain the decay rates of the error probabilities.     

Designing for “touch”, “reach” and “movement” in postwar (1946–1972) English primary and infant school environments

ABSTRACT

This article examines the use and interpretation of the terms “touch”, “reach” and “movement” in Ministry of Education (later, Department of Education) official publications known as Building Bulletins between the years 1949–1972. A close critical reading of Building Bulletins concerned primarily with school design for young children (infant and primary schools) in the English context has been carried out and the results of this exercise are discussed in the wider context of close relationships established between architects designing schools and leading progressive educationalists in Britain. The wider international context, particularly progressive educational design in the USA, is used to further understand the use and interpretation of these terms. The article contributes to a current interest among historians of education in exploring material and sensory histories of schooling.     

An EWMA chart for monitoring process mean

In the statistical process control literature, there exists several improved quality control charts based on cost-effective sampling schemes, including the ranked set sampling (RSS) and median RSS (MRSS). A generalized cost-effective RSS scheme has been recently introduced for efficiently estimating the population mean, namely varied L RSS (VLRSS). In this article, we propose a new exponentially weighted moving average (EWMA) control chart for monitoring the process mean using VLRSS, named the EWMA-VLRSS chart, under both perfect and imperfect rankings. The EWMA-VLRSS chart encompasses the existing EWMA charts based on RSS and MRSS (named the EWMA-RSS and EWMA-MRSS charts). We use extensive Monte Carlo simulations to compute the run length characteristics of the EWMA-VLRSS chart. The proposed chart is then compared with the existing EWMA charts. It is found that, with either perfect or imperfect rankings, the EWMA-VLRSS chart is more sensitive than the EWMA-RSS and EWMA-MRSS charts in detecting small to large shifts in the process mean. A real dataset is also used to explain the working of the EWMA-VLRSS chart.     

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.     

Replication: Revisiting Tversky and Shafir’s (1992) Disjunction Effect with an extension comparing between and within subject designs

Does uncertainty about an outcome influence decisions? The sure-thing principle (Savage, 1954) posits that it should not, but Tversky and Shafir (1992) found that people regularly violate it in hypothetical gambling and vacation decisions, a phenomenon they termed “disjunction effect”. Very close replications and extensions of Tversky and Shafir (1992) were conducted in this paper (N = 890, MTurk). The target article demonstrated the effect using two paradigms in a between-subject design: here, an extension also testing a within-subject design, with design being randomly assigned was added. These results were consistent with the original findings for the “paying to know“ problem (original: Cramer’s V = 0.22, 95% (CI) [0.14, 0.32]; replication: Cramer’s V = 0.30, 95% CI [0.24, 0.37]), yet not for the “choice under risk” problem (original: Cramer’s V = 0.26, 95% CI [0.14, 0.39]; replication: Cramer’s V = 0.11, 95% CI [−0.07, 0.20]). The within-subject extension showed very similar results. Implications for the disjunction effect and judgment and decision-making theory are discussed, and a call for improvements on the statistical understanding of comparisons of between-subject and within-subject designs is introduced. All materials, data, and code are available on https://osf.io/gu58m/.     

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.