New approximations to the exact distribution of the kruskal-wallis test statistic

Several approximations to the exact distribution of the Kruskal-Wallis test' statistic presently exist. There approximations can roughly be grouped into two classes: (i) computationally difficult with good accuracy, and (ii) easy to compute but not as accurate as the first class. The purpose of this paper is to introduce two nev approximations (one in the latter class and one which is computationally more involved)y and to compare these with other popular approximations. These comparisons use exact probabilities where available and Monte Carlo simulation otherwise.     

A Methodology for Grouping Source Terms for Consequence Calculations in Probabilistic Risk Assessments

The individual plant analyses in the U.S. Nuclear Regulatory Commission's reassessment of the risk from commercial nuclear power plants (NUREG-1150) consist of four parts: systems analysis, accident-progression analysis, source-term analysis, and consequence analysis. Careful definition of the interfaces between these parts is necessary for both information flow and computational efficiency. This paper describes the procedure used to define the interface between the source-term analysis and the consequence analysis. This interface is accomplished by forming groups of source terms with similar properties and then performing one set of MACCS calculations for each group.     

An approximation to the exact distribution of the wilcoxon-mann-whitney rank sum test statistic

An approximation to the exact distribution of the Wilcoxon rank sum test (Mann-Whitney U-test) and the Siegel-Tukey test based on a linear combination of the two-sample t-test applied to ranks and the normal approximation is compared with the usual normal approximation. The normal approximation results in a conservative test in the tails while the linear combination of the test statistics provides a test that has a very high percentage of agreement with tables of the exact distribution. Sample sizes 3≤m, n≤50 were considered.     

On some alternative procedures using ranks for the analysis of experimental designs

The analysis of data from eseperisental designs is often hampered by the lack of more than one procedure available for the analysis, especially when that procedure is based on assumptions which do not apply in the situation at hand. In this paper tvo classes of alternative procedures are discussed and compared, One is the aligned ranks procedure which first standardises the data by subtracting an appropriate estimate of location, then replaces the data with ranks t and finally uses an appropriate test statistic which has asymptotically a chi-square distribution The second procedure is the rank transform which first replaces all of the data with the ranks, and then employs the usual parametric methods, but computed on the ranks instead of the data Some Monte Carlo simulations for a test of interaction in a two way layout with replication enable the robustness and pover of these tvo methods to be compared with the usual analysis of variancs.     

On the Solution Approach for Bayesian Modeling of Initiating Event Frequencies and Failure Rates

There is a need for plant-specific distributions of incidence and failure rates rather than distributions from pooled data which are based on the "common incidence rate" assumption. The so-called superpopulation model satisfies this need through a practically appealing approach that accounts for the variability over the population of plants. Unfortunately, the chosen order in which the integrals with respect to the individual plant rates λ_i, ( i = 0, 1…, m ) and the parameters a , β of the Γ-population distribution are solved seems to drive the solution close to the common incidence rate distribution. It is shown that the solution obtained from interchanging the order and solving the integrals with respect to the individual plant rates by Monte Carlo simulation very quickly provides the plant specific distribution. This differing solution behaviour may be due to the lack of uniform convergence over (α, β, λ_I, ( i = 1,…, m ))-space. Examples illustrate the difference that may be observed.     

Perceptions and Experiences of Marriage Preparation Among U.S. Muslims: Multiple Voices from the Community

Although Muslims in the United States are a growing population, there is limited research on their relational patterns and how they prepare for marriage. We conducted in‐depth interviews with 32 members of the Muslim community in Southeast Michigan including married individuals, divorced individuals, therapists, and imams (Muslim religious leaders) to explore their perceptions and experiences of marriage preparation. Our analysis revealed that marriage preparation varies but is less likely to involve a requirement of premarital counseling, with imams being the primary providers, not therapists. Barriers to participation include stigma, lack of awareness, logistical and financial challenges, and parental influence. Partnerships between imams and therapists, and family and community efforts are necessary to address barriers and increase participation in premarital education programs.     

A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis

The analysis of probabilistic fault trees often involves the investigation of events that contribute both to the frequency of the top event and to the uncertainty in this frequency. This paper provides a discussion of three measures of the contribution of an event to the total uncertainty in the top event. These measures are known as uncertainty importance measures. Two of these measures are new developments. Each of the measures is shown to have unique advantages and disadvantages. The three measures are based on, respectively, the expected reduction in the variance of the top-event frequency should the uncertainty in an event be resolved, the same measure based on the log frequency, and a measure based on shifts in the quantiles of the distribution of top-event frequency.     

Rank correlation plots for use with correlated input variables

A method for inducing a desired rank correlation matrix on multivariate input vectors for simulation studies has recently been developed by Iman and Conover (1982). The primary intention of this procedure is to produce correlated input variables for use with computer models. Since this procedure is distribution free and allows the exact marginal distributions to remain intact it can be used with any marginal distributions for which it is reasonable to think in terms of correlation. In this paper we present a series of rank correlation plots based on this procedure when the marginal distributions are normal, lognormal, uniform and loguniform. These plots provide a convenient tool both for aiding the modeler in determining the degree of dependence among input variables (rather than guessing) and for communicating with the modeler the effect of different correlation assumptions. In addition this procedure can be used with sample multivariate data by sampling directly from the respective marginal empirical distribution functions.     

Why Do Neighbors Have Different Environmental Priorities? Analysis of Environmental Risk Perception in a Beirut Neighborhood

Differences in environmental priorities within an urban neighborhood of Beirut are analyzed. The explanatory capabilities of five categories of contextual variables are compared: socioeconomic status, locality, health, behavior, and environmental beliefs. Semi-structured interviews with key individuals in the community and residents were first conducted. Four environmental issues of concern were identified. A survey was carried out to identify the relative priority accorded by respondents to these four issues, and to measure variables likely to explain differences of opinion. Bivariate and multivariate logistic regression analyses were conducted for each of the four problems. The 99% confidence interval (CI) of the odds ratio (OR) was used as a test of significance. Respondents suffering from a respiratory disease (OR = 6.94, 99%CI = 1.54-31.25), those living in less crowded houses (OR = 4.88, 99%CI = 1.38-17.24), and those not living close to the neighborhood's industrial street (OR=5.26, 99%CI = 1.01-27.78) are significantly more likely to rank poor air quality first. Significant associations are found between poor water quality as first priority and nonpresence of a smoker in the household (OR = 6.12, 99%CI = 1.84-20.32) and perception of water salinity as a problem (OR = 7.46, 99%CI = 1.50-37.03). Males (OR = 6.94, 99%CI = 1.02-47.62) and tenants versus owners (OR = 10.49, 99%CI = 1.36-80.61) are significantly more likely to rank the residential-industrial mix first. Socioeconomic variables retain their explanatory capability in the studied neighborhood, despite relatively small income disparities. Behavioral variables, such as smoking, may be causative factors of priorities. Analyzing relative priorities, rather than "concern" or lack of it, reveals more complex patterns of association. Identifying environmental-perception divide lines can help develop a more inclusive and effective participatory environmental management.     

Bayesian Modeling of Initiating Event Frequencies at Nuclear Power Plants1

Probabilistic risk assessments (PRAs) of nuclear power plants proceed by modeling potential accident sequences at the plant of interest. These hypothesized accident sequences begin with initiating events. A very important initiating event phenomenon is the loss of off-site power (LOSP). This is the interruption of the preferred power supply to the essential and nonessential switchgear buses resulting in the use of emergency power supplies. If off-site power is not restored in a reasonable period of time, emergency backup sources of AC and DC power may subsequently fail, resulting in a possible core meltdown. Industry data show 63 LOSP incidents in the operating history of nuclear plants in the United States. Two Bayesian models for the frequency of incidents of LOSP are presented. One model assumes that all nuclear power generating stations share a common incidence rate for LOSP, and a posterior distribution is found for the mean incidence rate for all plants. The second model assumes that the incidence rates for individual plants belong to a superpopulation of incidence rates. Under this model the incidence rate for each plant is unique, but related to the incident rate of all other plants through the superpopulation. These models provide a vehicle for incorporating initiating event uncertainty into PRAs.