Distributions of certain variables in samples from two-parameter exponential distribution

Cumulative distribution function of the variable Y=(U+c)/(Z/2ν)) is given. Here U and Z are independent random variables, U has the exponential distribution (1.1) with θ=0, σ=1, Z has the distribution χ² (2ν) and c is a real quantity. The variable Y with U and Z given by (2.2) and (2.3) is used for inference about the parametric functions ?=θ?kσ of a two-parameter exponential distribution (1.1) with k or ? known. Special cases of ? or k are: the parameter θ, the Pth quantile Xp, the mean θ+σ and the value of the cumulative distribution function or of the reliability function at given point a. Also one-sided tolerance limits for a two-parameter exponential distribution can be derived from the distribution of the variable Y. The results are also applied to the Pareto distribution.     

Analysis of environmental flow requirements for macroinvertebrates in a creek affected by urban drainage (Prague metropolitan area,Czech Republic)

The habitat suitability index and environmental flow requirements were assessed for ten species of macroinvertebrates in a 2 km length section of the urban Boti? creek (average flow 0.4 m³ s^?1) in Prague. Boti? creek has been affected by two combined sewer overflows (CSO). Spring, summer and fall seasonal environmental flow requirements were identified using the Physical HABitat SIMulation System (PHABSIM) approach for the whole macroinvertebrate community: Spring – optimal flow 0.32–0.38 m³ s^?1, minimal flow 0.20–0.21 m³ s^?1 and maximal acceptable flow 0.91–0.93 m³ s^?1; Summer - optimal flow 0.42–0.45 m³ s^?1, minimal flow 0.19–0.21 m³ s^?1 and maximal acceptable flow 0.95–1.00 m³ s^?1; Fall - optimal flow 0.38–0.48 m³ s^?1, minimal flow 0.22–0.23 m³ s^?1 and maximal acceptable flow 0.95–0.98 m³ s^?1. The seasonal variability of environmental flow for all three categories is approximately 10%. Environmental flow requirements of the studied species and their life stages vary with depth, velocity and bottom substratum. Due to inflow from the CSOs, the optimal and maximal acceptable flow are not maintained and the maximal flow is exceeded by more than twice its value. Although the Instream Flow Incremental Methodology (IFIM) was primarily designed for large impounded rivers, the study proved its applicability in small streams affected by urbanization and urban drainage.     

Young,anchored and free? Examining the dynamics of early housing pathways in Australia

Young people are remaining in the parental home for longer, and returning there more often, before attaining residential independence. In Australia, these patterns have prompted concerns about a ‘boomerang generation’ whose housing aspirations and decisions have either been directly questioned, or viewed as symptomatic of broader affordability issues. Employing a longitudinal perspective, we argue that early residential pathways reflect a mix of stable and dynamic influences involving individuals, their families, and their broader relationships. Using data from a large cohort (n = 2082) of young Australians participating in the ‘Our Lives’ research project, we examine housing pathway formation between the ages of 12/13 and 21/22. Events such as parental union dissolution or partnership formation were found to encourage home leaving, whilst being employed at a younger age and having grown up rurally predicted both leaving and remaining out of home. Close, supportive relationships with family and friends served to ‘anchor’ respondents at home for longer, and parental socioeconomic resources enabled respondents to leave home and return if needed. The findings suggest that early residential independence reflects various factors, not all of which are in young people’s control, and some of which may hinder the longer term sustainability of their living arrangements.     

Cystatin C as a predictor of mortality in elderly patients with chronic kidney disease

Background: The prevalence of chronic kidney disease (CKD) in the elderly is high. Serum cystatin C is an accurate marker of kidney function and it also has prognostic utility in CKD patients. The aim of our study was to determine the prediction of serum cystatin C and other markers of kidney function on long-term survival in elderly CKD patients.

Methods: Fifty eight adult Caucasian patients, older than 65 years, without known malignancy, thyroid disease and/or not on steroid therapy were enrolled in the study. In each patient, ⁵¹CrEDTA clearance, serum creatinine, serum cystatin C, and estimated glomerular filtration rate using different equations were determined on the same day and patients were then followed for 11 years or until their death.

Results: The means are as follows: ⁵¹CrEDTA clearance 53.3?±?17.4?ml/min/1.73?m², serum creatinine 1.62?±?0.5?mg/dl, serum cystatin C 1.79?±?0.5?mg/l, Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) creatinine equation 40.1?±?14?ml/min/1.73?m², Berlin Initiative Study 2 (BIS2) equation 38.9?±?10.7?ml/min/1.73?m², full age spectrum (FAS) creatinine equation 43.8?±?13.8?ml/min/1.73?m², FAS cystatin C equation 40.1?±?11.7?ml/min/1.73?m². In the follow up period, 47 (81%) patients died. Cox regression analysis showed different hazard ratios (HRs) for death: for ⁵¹CrEDTA clearance HR 1.022 (95% CI 1.004–1.042; p?=?.015), serum creatinine HR 1.013 (95% CI 1.006–1.019; p?=?.001), serum cystatin C HR 2.028 (95% CI 1.267–3.241; p?=?.003), CKD-EPI creatinine equation HR 1.048 (95% CI 1.019–1.076; p?=?.001), BIS2 equation HR 1.055 (95% CI 1.021–1.088; p?=?.001), FAS creatinine equation HR 1.046 (95% CI 1.017–1.074; p?=?.001), FAS cystatin C equation HR 1.039 (95% CI 1.010–1.071; p?=?.009).

Conclusions: Our results showed the highest HR for serum cystatin C among kidney function markers for prediction of outcome in elderly CKD patients.     

A simple algorithm for the adaptation of scores and power behavior of the corresponding rank test

The purpose of this paper is twofold:On one hand we want to give a very simple algorithm for evaluating a special rank estimator of the type given in Behnen, Neuhaus, and Ruymgaart (1983) for the approximate optimal choice of the scores-generating function of a two-sample linear rank test for the general testing problem H_o:F=G versus H₁:F ≤ G, F ≠ G, in order to demonstrate that the corresponding adaptive rank statistic is simple enough for practical applications. On the other hand we prove the asymptotic normality of the adaptive rank statistic under H (leading to approximate critical values) and demonstrate the adaptive behavior of the corresponding rank test by a Monte Carlo power simulation for sample sizes as low as m=10, n=10.     

Solving,Estimating, and Selecting Nonlinear Dynamic Models Without the Curse of Dimensionality

We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids to overcome the curse of dimensionality for approximations. We apply sparse grids to a global polynomial approximation of the model solution, to the quadrature of integrals arising as rational expectations, and to three new nonlinear state space filters which speed up the sequential importance resampling particle filter. The posterior of the structural parameters is estimated by a new Metropolis–Hastings algorithm with mixing parallel sequences. The parallel extension improves the global maximization property of the algorithm, simplifies the parameterization for an appropriate acceptance ratio, and allows a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge for the solution and estimation of a general class of models.     

On the Ghoudi,Khoudraji, and Rivest test for extreme‐value dependence

Ghoudi, Khoudraji & Rivest [The Canadian Journal of Statistics 1998;26:187–197] showed how to test whether the dependence structure of a pair of continuous random variables is characterized by an extreme‐value copula. The test is based on a U‐statistic whose finite‐ and large‐sample variance are determined by the present authors. They propose estimates of this variance which they compare to the jackknife estimate of Ghoudi, Khoudraji & Rivest ( 1998 ) through simulations. They study the finite‐sample and asymptotic power of the test under various alternatives. They illustrate their approach using financial and geological data. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

On vertex-parity edge-colorings

A vertex signature \(\pi \) of a finite graph G is any mapping \(\pi \,{:}\,V(G)\rightarrow \{0,1\}\). An edge-coloring of G is said to be vertex-parity for the pair \((G,\pi )\) if for every vertex v each color used on the edges incident to v appears in parity accordance with \(\pi \), i.e. an even or odd number of times depending on whether \(\pi (v)\) equals 0 or 1, respectively. The minimum number of colors for which \((G,\pi )\) admits such an edge-coloring is denoted by \(\chi '_p(G,\pi )\). We characterize the existence and prove that \(\chi '_p(G,\pi )\) is at most 6. Furthermore, we give a structural characterization of the pairs \((G,\pi )\) for which \(\chi '_p(G,\pi )=5\) and \(\chi '_p(G,\pi )=6\). In the last part of the paper, we consider a weaker version of the coloring, where it suffices that at every vertex, at least one color appears in parity accordance with \(\pi \). We show that the corresponding chromatic index is at most 3 and give a complete characterization for it.     

Broadcasting multiple messages in the 1-in port model in optimal time

In the 1-in port model, every vertex of a synchronous network can receive at most one message in each time unit. We consider simultaneous broadcasting of multiple messages from the same source or from distinct sources in such networks with an additional restriction that every received message can be sent out to neighbors only in the next time unit and never to already informed vertex. We use a general concept of level-disjoint partitions developed for this scenario. Here we introduce a subgraph extension technique for efficient spreading information within this concept. Surprisingly, this approach with so called biwheels leads to simultaneous broadcasting of optimal number of messages on a wide class of graphs in optimal time. In particular, we provide tight results for bipartite tori, meshes, hypercubes, Knödel graphs, circulant graphs. We also propose several open problems and conjectures.