Testing dominance of biometric functions

The hazard rate (HR) and mean residual lifetime are two of the most practical and best-known functions in biometry, reliability, statistics and life testing. Recently, the reversed HR function is found to have interesting properties useful in additional areas such as censored data and forensic science. For these three biometric functions, we propose testing methods that they take on a known functional form against that they dominate or are dominated by this known form. This goodness-of-fit-type testing is wider in applications and more interesting than the long-standing testing procedures for exponentiality against the monotonicity of these functions or even the change point problems. This is so since we can test against any choice of the survival distribution and not just exponentiality. For this general testing, we present easy to implement tests and generalize them into classes of statistics that could lead to more powerful and efficient testing.     

A bootstrap control chart for inverse Gaussian percentiles

The conventional Shewhart-type control chart is developed essentially on the central limit theorem. Thus, the Shewhart-type control chart performs particularly well when the observed process data come from a near-normal distribution. On the other hand, when the underlying distribution is unknown or non-normal, the sampling distribution of a parameter estimator may not be available theoretically. In this case, the Shewhart-type charts are not available. Thus, in this paper, we propose a parametric bootstrap control chart for monitoring percentiles when process measurements have an inverse Gaussian distribution. Through extensive Monte Carlo simulations, we investigate the behaviour and performance of the proposed bootstrap percentile charts. The average run lengths of the proposed percentage charts are investigated.     

中国企业储蓄率变动原因探析

我国国民储蓄率一直居高不下,其中企业部门的储蓄率变动逐渐引起人们的关注。研究发现,国民储蓄率自2008年增势减缓,主要因为企业部门储蓄率出现下降,企业支付的劳动者报酬、财产支出以及融资渠道的变化是企业储蓄变动的主要原因。进一步通过E-G协整法探究企业储蓄率对国民经济、投资率的影响,发现企业部门对经济发展和投资水平起到积极作用。最后,根据企业部门的国民地位和储蓄率变动趋势给出密切关注企业储蓄率、合理降低居民储蓄率的相关建议。     

A new two-parameter lifetime distribution with decreasing,increasing or upside-down bathtub-shaped failure rate

In this paper, we introduce a generalization of the Bilal distribution, where a new two-parameter distribution is presented. We show that its failure rate function can be upside-down bathtub shaped. The failure rate can also be decreasing or increasing. A comprehensive mathematical treatment of the new distribution is provided. The estimation by maximum likelihood is discussed, and a closed-form expression for Fisher’s information matrix is obtained. Asymptotic interval estimators for both of the two unknown parameters are also given. A simulation study is conducted and applications to real data sets are presented.     

Confidence distributions applied to propagating uncertainty to inference based on estimating the local false discovery rate: A fiducial continuum from confidence sets to empirical Bayes set estimates as the number of comparisons increases

Empirical Bayes estimates of the local false discovery rate can reflect uncertainty about the estimated prior by supplementing their Bayesian posterior probabilities with confidence levels as posterior probabilities. This use of coherent fiducial inference with hierarchical models generates set estimators that propagate uncertainty to varying degrees. Some of the set estimates approach estimates from plug-in empirical Bayes methods for high numbers of comparisons and can come close to the usual confidence sets given a sufficiently low number of comparisons.     

The almost sure convergence rate of the estimator of optimized certainty equivalent risk measure under α-mixing sequences

Conditional value-at-risk (CVaR) model is a kind of financial risk measure that is extensively supported and accepted by international financial community. Its optimized form can be regarded as an optimized certainty equivalent (OCE) risk measurement. In this paper, we mainly discuss and analyze the strong laws of large numbers and the convergence rate of OCE's estimator under α-mixing sequences. The result shows that the almost sure convergence rate of CVaR estimator is given by the results of OCE estimator. Its convergence rate is inversely proportional to the square root of the sample size under certain conditions. Its effectiveness is verified by simulation experiments for two classical α-mixing sequences.     

An improved two-stage procedure to compare hazard curves

Qiu and Sheng has proposed a powerful and robust two-stage procedure to compare two hazard rate functions. In this paper we improve their method by using the Fisher test to combine the asymptotically independent p-values obtained from the two stages of their procedure. In addition, we extend the procedure to situations with multiple hazard rate functions. Our comprehensive simulation study shows that the proposed method has a good performance in terms of controlling the type I error rate and of detecting power. Three real data applications are considered for illustrating the use of the new method.     

Daily Inhalation Rate and Time‐Activity/Location Pattern in Japanese Preschool Children

Lack of data on daily inhalation rate and activity of children has been an issue in health risk assessment of air pollutants. This study aimed to obtain the daily inhalation rate and intensity and frequency of physical activity in relation to the environment in Japanese preschool children. Children aged four–six years (n= 138) in the suburbs of Tokyo participated in this study, which involved three days' continuous monitoring of physical activity using a tri‐axial accelerometer and parent's completion of a time/location diary during daily life. The estimated three‐day mean daily inhalation rate (body temperature, pressure, saturated with water vapor) was 9.9 ± 1.6 m³/day (0.52 ± 0.09 m³/kg/day). The current daily inhalation rate value of 0.580 m³/kg/day proposed for use in health risk assessment in Japan is confirmed to be valid to calculate central value of inhaled dose of air pollutants in five‐ to six‐year‐old children. However, the 95th percentile daily inhalation rate of 0.83 m³/kg/day based on measurement for five‐year‐old children is recommended to be used to provide an upper bound estimate of exposure that ensure the protection of all five‐ to six‐year‐old children from the health risk of air pollutants. Children spent the majority of their time in sedentary and light level of physical activity (LPA) when indoors, while 85% of their time when outdoors was spent in LPA and moderate‐to‐vigorous physical activity. The results suggest the need to consider variability of minute respiratory ventilation rate according to the environment for more refined short‐term health risk assessment.     

Elasticity function of a discrete random variable and its properties

Elasticity (or elasticity function) is a new concept that allows us to characterize the probability distribution of any random variable in the same way as characteristic functions and hazard and reverse hazard functions do. Initially defined for continuous variables, it was necessary to extend the definition of elasticity and study its properties in the case of discrete variables. A first attempt to define discrete elasticity is seen in Veres-Ferrer and Pavía (2014a). This paper develops this definition and makes a comparative study of its properties, relating them to the properties shown by discrete hazard and reverse hazard, as both defined in Chechile (2011). Similar to continuous elasticity, one of the most interesting properties of discrete elasticity focuses on the rate of change that this undergoes throughout its support. This paper centers on the study of the rate of change and develops a set of properties that allows us to carry out a detailed analysis. Finally, it addresses the calculation of the elasticity for the resulting variable obtained from discretizing a continuous random variable, distinguishing whether its domain is in real positives or negatives.     

Empirical Bayes estimation in continuous one-parameter exponential families under associated samples

In this paper, we study the empirical Bayes (EB) estimation in continuous one-parameter exponential families under negatively associated (NA) samples and positively associated (PA) samples. Under certain regularity conditions, it is shown that the convergence rates of proposed EB estimators under NA or PA samples are the same as those of EB estimators under independent observations, which significantly improve the existing results in EB estimation under associated samples.