Stochastic ordering of medians in samples from normal distributions

In this paper, we discuss some stochastic comparisons for the sample median in a random sample from a normal distribution. Specifically, we establish that the sample median is stochastically farther than the sample mean to the population mean. To verify the result of comparison, we derive an upper bound for some distributional characteristics of the distance between the sample median and the population mean. The stochastic ordering considered here is the likelihood ratio order.     

Shrinkage estimation of P(Y < X) in the exponential distribution mixing with exponential distribution

ABSTRACT

The problem of estimation of R = P(Y < X) have been used in the paper. Let X has exponential distribution mixing with exponential distribution with parameters β and θ and Y independently of X has exponential distribution with parameter λ. By using a prior guess or estimate R₀, different shrinkage estimators of R are derived. Then the performance of the estimators are discussed. Finally, we compare these results with Baklizei and Dayyeh (2003) approaches.     

Economic design of VSI X̄ control chart with correlated non-normal data under multiple assignable causes

It has been recently revealed that the Shewhart control charts with variable sampling interval (VSI) perform better than the traditional Shewhart chart with the fixed sampling interval in detecting shifts in the process. In most of these research works, the normality and independency of the process data or measurements are assumed and that the process is subjected to only one assignable cause. While, in practice, these assumptions usually do not hold, some recent studies are focused on working with only one or two of these violations. In this paper, the situation in which the process data are correlated and follow a non-normal distribution and that there is multiplicity of assignable causes in the process is considered. For this case, a cost model for the economic design of the VSI X? control chart is developed, where the Burr distribution is employed to represent the non-normal distribution of the process data. To obtain the optimal values of the design parameters, a genetic algorithm is employed in which the response surface methodology is applied. A numerical example is presented to show the applicability and effectiveness of the proposed methodology. Sensitivity analysis is also carried out to evaluate the effects of cost and input parameters on the performance of the chart.     

Robust surface estimation in multi-response multistage statistical optimization problems

As the ordinary least squares (OLS) method is very sensitive to outliers as well as to correlated responses, a robust coefficient estimation method is proposed in this paper for multi-response surfaces in multistage processes based on M-estimators. In this approach, experimental designs are used in which the intermediate response variables may act as covariates in the next stages. The performances of both the ordinary multivariate OLS and the proposed robust multi-response surface approach are analyzed and compared through extensive simulation experiments. Sum of the squared errors in estimating the regression coefficients reveals the efficiency of the proposed robust approach.     

Financial Development,Institutional Quality and Poverty Reduction: Worldwide Evidence

Social Indicators Research - There is a burgeoning literature on wealth in the rich world. It mainly focuses on the top. This paper shows that assets can also matter for the analysis of poverty and...     

Modeling the effectiveness of urban agriculture education courses

Urban Ecosystems - Urban agriculture can provide food security that is essential to sustainable development goals. Citizen education plays a vital role in urban agriculture formation. The present...     

The microanatomy of trabecular bone in young normal and osteoporotic elderly males

Normally there is a gradual continual loss of cortical and trabecular bone in both men and women as they age. Osteopenia and osteoporosis are conditions in which the loss results in brittle bones that fracture easily. Males with low testosterone and hypogonadism are predisposed to osteoporosis and prevention tends to be overshadowed by the greater problem in postmenopausal women. The ability of the skeleton to resist external forces depends partly upon the amount of bone present and partly upon other factors including cancellous bone microarchitecture. This is examined in iliac crest bone biopsies from idiopathic osteoporotic men, mean age 60 ± 12 SD years [n = 16]. These were compared with a healthy control group (autopsy samples), mean age 30 ± 8.9 years [n = 28] with the aim of examining the pattern of cancellous atrophy in male idiopathic osteoporosis. Undecalcified specimens were embedded in methylmethacrylate and prepared for histomorphometry. Sections were analysed using an automated trabecular analysis system (TAS), whereby a binary image was created. Area measurements including the trabecular surface and distance measurements including the trabecular width were made. The binary image was thinned to its medial framework and the node and terminus number as indices of trabecular interconnection were recorded, together with the strut length. Results (median (range)) showed a lower percentage bone volume in the elderly osteoporotic male, 10.2% (5.4–23.1) compared to young normals 25.2% (14.6–43.9), p < 0.001. The trabeculae tended to be thinner, 95.7 µm (66.7–170.7) c.f. 120.8 µm (75.8–208.6) and considerably fewer in number, 11.1 (2.1–31.4) c.f. 48.3 (25.4–66.9), p < 0.001 per field and in particular the number of nodes, 2.1 (0.15–14) c.f. 40.6 (10.3–74.1) per field and the node: terminus ratio fell to 0.13 (0.01–1.19) c.f. controls 0.98 (0.24–6.69), p < 0.001. It was concluded that the pattern of cancellous atrophy in male idiopathic osteoporosis differs from normal aging and resembles that in postmenopausal women. Results using the automated TAS confirm previous observations made manually.     

Statistical Monitoring of Autocorrelated Simple Linear Profiles Based on Principal Components Analysis

In this article, a transformation method using the principal component analysis approach is first applied to remove the existing autocorrelation within each profile in Phase I monitoring of autocorrelated simple linear profiles. This easy-to-use approach is independent of the autocorrelation coefficient. Moreover, since it is a model-free method, it can be used for Phase I monitoring procedures. Then, five control schemes are proposed to monitor the parameters of the profile with uncorrelated error terms. The performances of the proposed control charts are evaluated and are compared through simulation experiments based on different values of autocorrelation coefficient as well as different shift scenarios in the parameters of the profile in terms of probability of receiving an out-of-control signal.     

Quantitative Risk Assessment for Developmental Neurotoxic Effects

Developmental neurotoxicity concerns the adverse health effects of exogenous agents acting on neurodevelopment. Because human brain development is a delicate process involving many cellular events, the developing fetus is rather susceptible to compounds that can alter the structure and function of the brain. Today, there is clear evidence that early exposure to many neurotoxicants can severely damage the developing nervous system. Although in recent years, there has been much attention given to model development and risk assessment procedures for developmental toxicants, the area of developmental neurotoxicity has been largely ignored. Here, we consider the problem of risk estimation for developmental neurotoxicants from animal bioassay data. Since most responses from developmental neurotoxicity experiments are nonquantal in nature, an adverse health effect will be defined as a response that occurs with very small probability in unexposed animals. Using a two-stage hierarchical normal dose-response model, upper confidence limits on the excess risk due to a given level of added exposure are derived. Equivalently, the model is used to obtain lower confidence limits on dose for a small negligible level of risk. Our method is based on the asymptotic distribution of the likelihood ratio statistic (cf. Crump, 1995). An example is used to provide further illustration.