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In this paper, we focus on Pitman closeness probabilities when the estimators are symmetrically distributed about the unknown parameter θ. We first consider two symmetric estimators θˆ1 and θˆ2 and obtain necessary and sufficient conditions for θˆ1 to be Pitman closer to the common median θ than θˆ2. We then establish some properties in the context of estimation under the Pitman closeness criterion. We define Pitman closeness probability which measures the frequency with which an individual order statistic is Pitman closer to θ than some symmetric estimator. We show that, for symmetric populations, the sample median is Pitman closer to the population median than any other independent and symmetrically distributed estimator of θ. Finally, we discuss the use of Pitman closeness probabilities in the determination of an optimal ranked set sampling scheme (denoted by RSS) for the estimation of the population median when the underlying distribution is symmetric. We show that the best RSS scheme from symmetric p...

In this work, we extend prior results concerning the simultaneous Pitman closeness of order statistics (OS) to population quantiles. By considering progressively type-II right-censored samples, we derive expressions for the simultaneous closeness probabilities of the progressively censored OS to population quantiles. Explicit expressions are deduced for the cases when the underlying distribution has bounded and unbounded supports. Illustrations are provided for the cases of exponential, uniform and normal distributions for various progressive type-II right-censoring schemes and different quantiles. Finally, an extension to the case of generalized OS is outlined.

We first compare the ranked set sampling (RSS) and simple random sampling schemes for the estimation of the population median through Pitman’s measure of closeness. Then, by using Banks’ criterion, we determine the frequency with which an individual order statistic is closer to the median than some symmetric estimator in an ϵ -neighbourhood of the median. Finally, we consider the simultaneous Pitman closeness criterion and identify the median RSS as the optimal RSS scheme for estimating the population median.

Selecting the optimal progressive censoring scheme for the exponential distribution according to Pitman closeness criterion is discussed. For small sample sizes the Pitman closeness probabilities are calculated explicitly, and it is shown that the optimal progressive censoring scheme is the usual Type-II right censoring case. It is conjectured that this to be the case for all sample sizes. A general algorithm is also presented for the numerical computation of the Pitman closeness probabilities between any two progressive censoring schemes of the same size.

We recently described an iterative synthesis of oligo-vinyl ethers, followed by a radical cascade to provide a family of hexahydro-2H-furo[3,4-b]pyrans. Our results for the radical cascade were consistent with either a direct 6-endo-trig addition of a vinyl radical onto the first vinyl ether function or an initial 5-exo-trig addition, followed by rearrangement to the more stable anomeric radical intermediate. In this report, we describe our further mechanistic studies aimed at distinguishing between these two possibilities and conclude that the 5-exo/3-exo/retro-3-exo pathway is dominant.

Prediction of censored order statistics from a Type-II censored sample can be done with trivial bounds having perfect confidence. However, given independent samples from the same absolutely continuous distribution, improved bounds can be attained. In this regard, we develop here point prediction based on L-statistics for predicting order statistics (OS) from a future sample as well as for predicting censored OS from a Type-II censored sample. An example is taken to illustrate these ideas, and the limiting case wherein a single independent sample is arbitrarily large is also discussed.

Plotting points of order statistics are often used in the determination of goodness-of-fit of observed data to theoretical percentiles. Plotting points are usually determined by using nonparametric methods which produce, for example, the mean- and median-ranks. Here, we use a distribution-based approach which selects plotting points (quantiles) based on the simultaneous-closeness of order statistics to population quantiles. We show that the plotting points so determined are robust over a multitude of symmetric distributions and then demonstrate their usefulness by examining the power properties of a correlation goodness-of-fit test for normality.

Best linear unbiased, best linear invariant, and maximum likelihood predictors are commonly used in reliability studies for predicting either censored failure times or lifetimes from a future life-test. In this article, by assuming a Type-II right-censored sample from an exponential distribution, we compare best linear unbiased (BLUP) and best linear invariant (BLIP) predictors of the censored order statistics in the one-sample case and order statistics from a future sample in the two-sample case, in terms of Pitman closeness criterion. Some specific conclusions are drawn and supporting numerical results are presented.

Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last 50 years since the ground breaking work of Lloyd [E.H. Lloyd, Least squares estimation of location and scale parameters using order statistics, Biometrika 39 (1952), pp. 88–95]. These comparisons have been made under many different criteria across different parametric families of distributions. A noteworthy one is by Nagaraja [H.N. Nagaraja, Comparison of estimators and predictors from two-parameter exponential distribution, Sankhyā Ser. B 48 (1986), pp. 10–18], who made a comparison of best linear unbiased (BLUE) and best linear invariant (BLIE) estimators in the case of exponential distribution. In this paper, continuing along the same lines by assuming a Type II right censored sample from a scaled-exponential distribution, we first compare BLUE and BLIE of the exponential mean parameter in terms of Pitman closeness (nearness) criterion. We show that the BLUE is always Pitman closer th...

In reliability studies, one typically would assume a lifetime distribution for the units under study and then carry out the required analysis. One popular choice for the lifetime distribution is the family of two-parameter Weibull distributions (with scale and shape parameters) which, through a logarithmic transformation, can be transformed to the family of two-parameter extreme value distributions (with location and scale parameters). In carrying out a parametric analysis of this type, it is highly desirable to be able to test the validity of such a model assumption. A basic tool that is useful for this purpose is a quantile–quantile (QQ) plot, but in its use, the issue of the choice of plotting position arises. Here, by adopting the optimal plotting points based on Pitman closeness criterion proposed recently by Balakrishnan et al. (2010b), and referred to as simultaneous closeness probability (SCP) plotting points, we propose a correlation-type goodness of fit test for the extreme value distribution. W...

Juvenile hormone III (JH-III) controls several aspects of insect development, and analogues of JH-III are widely used as insect control agents. Recent reports suggest that these compounds may also perturb the normal development of crustaceans, and perhaps other aquatic species. In an attempt to prepare more highly degradable (and thus less environmentally persistent) mimics of JH-III, we prepared a series of analogues incorporating vinyl ether functionality. The stability of these compounds in water or warm, moist air was evaluated, revealing two distinct decomposition pathways.

This paper presents an extension to the the Ivanoff–Merzbach renewal process. The Ivanoff–Merzbach process is a natural analogue to the one-dimensional renewal process. Restricting our attention to two dimensions, the focus of the current paper will be formation of this extension, which we will refer to as a Markov renewal process, as well as simulation, estimation and applications to data sets in ecology and forestry. Copyright © 2010 John Wiley & Sons, Ltd.

We derive expressions for the probability that an individual order statistic is closest to the target parameter among the order statistics from a complete random sample. Results are given for random variables with bounded and complete support. We then apply these general results to location-scale parameter families of distributions with specific applications to estimation of percentiles. In this case, simultaneous-closeness probabilities depend upon the parameters through the value of p in the percentile and the sample size, n. Results are finally illustrated with the estimation of percentiles for normal and exponential distributions.

"There has never been a less political being."1 Such was the way in which Gabriel Marcel described his close friend and fellow convert, the French Catholic literary critic, Charles Du Bos (1882-1939). Marcel attributed Du Bos's "radical disinterest in all that occurred in the public realm" to a certain "spiritual agoraphobia," which suggests an overt avoidance of political or social engagement on account of his Catholicism.2 But as Marcel himself conceded, this "agoraphobia" was not absolute, for political matters could impress themselves upon him when they became strictly ethical problems. This article goes further and explores how Charles Du Bos's intellectual and spiritual sensibilities provide an insight into the construction of a particular Catholic intellectual form of engagement during the interwar period, one that can be broadly defined as "third way."Multiple Catholic intellectual identities competed for space at this time, ranging from the right-wing actors of Action Francaise and the Jeune droite, through to the Christian democrats grouped around the Dominican journals and press engines La Vie Intellectuelle (1928) and Sept (1934), the daily L'Aube (1932), and the left-leaning personalism of Emmanuel Mounier and those progressives around the Communist review Terre Nouvelle. A particular strain of political Catholicism shared an ideological minimum with thirdway discourse in France. In the late 1920s and early 1930s, a young generation of intellectuals, whom Zeev Sternhell famously defined as "neither right nor left," occupied a middle ground or third way precisely because they sought to overhaul traditional political forms and ideologies.3 This third way, composed of "neo-socialists, "young turks," non-conformists, and neosyndicalists," is striking for the sheer variety of ideological positions it embraced, but these positions were nevertheless characterized by a shared ethical imperative in terms of a certain degree of rejection of parliamentary liberalism and capitalist disorder, a disavowal of the extremes of Fascism and Communism, and by a desire to rehabilitate spiritual values through the person.4 During the interwar years, Jacques Maritain, the neo-Thomist philosopher and commandeer of Christian humanism, dominated Catholic third-way discourse in his attempt to forge a viable alternative to totalitarian statism and laissez-faire individualism. Certainly Du Bos did not elaborate any clear political vision based on a refusal of extreme ideological positions and radical renewal of society as Maritain did with the publication of his seminal work, Integral Humanism (1936). Rather this paper focuses on the ways in which Du Bos is representative of the necessary intellectual disposition underpinning a third way. It argues that this disposition rests fundamentally upon a notion of the "tragic." For Du Bos, the tragic animated a certain agnostic attitude. This agnosticism was integral to his Catholicism and his political position: it signalled the importance of recognizing the insufficiency of human understanding in faith and the uncertainty of absolute truth -claims in political engagement. This submission to ambiguity finds its theological counterpoint in the uncertainty of Jesus on the soteriological significance of his death.5 Du Bos's third-way disposition is explored through an examination of the role of the tragic, firstly, through a consideration of his personal spiritual journey both before, and beyond his conversion in 1927; secondly, by suggesting that his accommodation of the tragic was central to his embrace of an "ethic of responsibility;" and thirdly, by a discussion of his meditations on the Munich Agreement of 1938, in which this ethic and the tragic converge.I. CHARLES DU BOS: THE MAN AND PERSONAL TRAGEDYCharles Du Bos was born in Paris in 1882 into an extraordinarily rich familial and educational European heritage. An easy affinity for English, German, and Russian as well as French writers, and a natural appreciation for the variety of creative impulses, bestowed upon Du Bos the reputation of a "literary cosmopolitan. …

In this paper, we consider joint distributions of order statistics generated by two simulation methods. By using these distributions, we study the nature of dependence and exceedence probabilities between them.

A sample of 111 12-year-old children in Salford, UK was examined in 1988, and the findings compared with those of a survey carried out in 1960 of 12-year-old children in the same city. Between 1960 and 1988, the mean DMFT of the boys fell from 6.04 to 2.34 and that of the girls from 6.54 to 3.40. All types of teeth were affected by caries in 1960 but in 1988 none of the canines and mandibular lateral incisors were affected. In 1960 the permanent first molars contributed 57% of the boys' and 54% of the girls' total DMFT while in 1988 they contributed 87% of the boys' and 73% of the girls' DMFT. Jackson's Treatment Index showed that the dental services were making a greater impact in 1988; for the boys it rose from 29.5 to 63.2 and for the girls from 27.8 to 62.3.

Benzyl chlorides and bromides are shown to undergo copper-promoted coupling with a variety of terminal alkynes including, for the first time, electron-poor acetylenes such as methyl propiolate. The reaction permits easy access to a wide range of (functionalized) benzyl-substituted propiolates (as well as several related alkynes) from commercially available benzyl halides. These products should in turn function as useful building blocks for the synthesis of previously inaccessible (functionalized) benzyl-substituted heterocycles.

In this article, Pitman closeness of sample order statistics to population quantiles of a location-scale family of distributions is discussed. Explicit expressions are derived for some specific families such as uniform, exponential, and power function. Numerical results are then presented for these families for sample sizes n = 10,15, and for the choices of p = 0.10, 0.25, 0.75, 0.90. The Pitman-closest order statistic is also determined in these cases and presented.

Redox-active metals in the brain mediate numerous biochemical processes and are also implicated in a number of neurodegenerative diseases. A number of different approaches are available for quantitatively measuring the spatial distribution of biometals at an image resolution approaching the subcellular level. Measured biometal levels obtained using laser ablation-inductively coupled plasma mass spectrometry (LA-ICPMS; spatial resolution 15 μm × 15 μm) were within the range of those obtained using X-ray fluorescence microscopy (XFM; spatial resolution 2 μm × 7 μm) and regional changes in metal concentration across discrete brain regions were replicated to the same degree. Both techniques are well suited to profiling changes in regional biometal distribution between healthy and diseased brain tissues, but absolute quantitation of metal levels varied significantly between methods, depending on the metal of interest. Where all possible variables affect metal levels, independent of a treatment/phenotype are controlled, either method is suitable for examining differences between experimental groups, though, as with any method for imaging post mortem brain tissue, care should be taken when interpreting the total metal levels with regard to physiological concentrations.

Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last six decades since the ground breaking work of Lloyd [13]; see Arnold et al. [1] and David and Nagaraja [9] for elaborate details in this regard. Recently, Pitman closeness comparison of order statistics as estimators for population parameters, such as medians and quantiles, and their applications have been carried out by Balakrishnan et al. [3, 4, 5, 7]. In this paper, we discuss the Pitman closest estimators based on convex linear combinations of two contiguous order statistics, which sheds additional insight with regard to the estimation of the population median in the case of even sample sizes. We finally demonstrate the proposed method for the uniform, exponential, power function and Pareto distributions.

Synchrotron-based x-ray fluorescence microscopy, immunofluorescence, and Western blotting were used to investigate changes in copper (Cu) and Cu-associated pathways in the vulnerable substantia nigra (SN) and locus coeruleus (LC) and in nondegenerating brain regions in cases of Parkinson's disease (PD) and appropriate healthy and disease controls. In PD and incidental Lewy body disease, levels of Cu and Cu transporter protein 1, were significantly reduced in surviving neurons in the SN and LC. Specific activity of the cuproprotein superoxide dismutase 1 was unchanged in the SN in PD but was enhanced in the parkinsonian anterior cingulate cortex, a region with α-synuclein pathology, normal Cu, and limited cell loss. These data suggest that regions affected by α-synuclein pathology may display enhanced vulnerability and cell loss if Cu-dependent protective mechanisms are compromised. Additional investigation of copper pathology in PD may identify novel targets for the development of protective therapies for this disorder. © 2014 Elsevier Inc.

Disturbances in brain copper result in rare and severe neurological disorders and may play a role in the pathogenesis and progression of multiple neurodegenerative diseases. Our current understanding of mammalian brain copper transport is based on model systems outside the central nervous system and no data are available regarding copper transport systems in the human brain. To address this deficit, we quantified regional copper concentrations and examined the distribution and cellular localization of the copper transport proteins Copper transporter 1, Atox1, ATP7A, and ATP7B in multiple regions of the human brain using inductively coupled plasma-mass spectrometry, Western blot and immunohistochemistry. We identified significant relationships between copper transporter levels and brain copper concentrations, supporting a role for these proteins in copper transport in the human brain. Interestingly, the substantia nigra contained twice as much copper than that in other brain regions, suggesting an important role for copper in this brain region. Furthermore, ATP7A levels were significantly greater in the cerebellum, compared with other brain regions, supporting an important role for ATP7A in cerebellar neuronal health. This study provides novel data regarding copper regulation in the human brain, critical to understand the mechanisms by which brain copper levels can be altered, leading to neurological disease. © 2013 The Royal Society of Chemistry.

This paper introduces nonparametric estimation methods for spatial point processes satisfying a particular renewal property. Martingale methods yield a unified approach for renewal processes in both one and two dimensions, and can be used for both synchronous and asynchronous data. In each case, we obtain martingale estimators of the avoidance probabilities that characterize the renewal process. Asymptotic properties of the estimators are studied analytically and empirically.

Benzyl chlorides and bromides are shown to undergo copper-promoted coupling with a variety of terminal alkynes including, for the first time, electron-poor acetylenes such as methyl propiolate. The reaction permits easy access to a wide range of (functionalized) benzyl-substituted propiolates (as well as several related alkynes) from commercially available benzyl halides. These products should in turn function as useful building blocks for the synthesis of previously inaccessible (functionalized) benzyl-substituted heterocycles.

This paper demonstrates how to apply the Ivanoff–Merzbach renewal process (Ivanoff and Merzbach, 2006; Ivanoff, 2008) to the modelling of environmental and other forms of point process data. The model is explored via simulation, focusing on two special cases. Maximum likelihood estimation of model parameters is described and demonstrated for these cases. The methods are applied to a point pattern related to human settlement patterns and to a point pattern describing the locations of a species of pine. Copyright © 2009 John Wiley & Sons, Ltd.

The configuration and dynamics of six Bathyergus suillus and one Cryptomys hottentotus burrow systems in coastal fynbos vegetation was studied for a year by monitoring mound production and excavating burrows. Bathyergus suillus is a large solitary mole-rat and C. hottentotus is smaller and social. Our results are compared with those for other subterranean rodents. Most B. suillus burrows (15–22 cm in diameter) were 40–65 cm below ground to prevent their collapse in the seasonally softer and drier surface sand; the burrows were consequently situated deeper than most food plants. Cryptomus hottentotus burrows were narrower (5–7 cm) and shallower (

This thesis explores British reactions to the Amritsar Massacre 1919 and the Croke Park Massacre 1920. It centres on the British Government’s response to these massacres, and the perspectives of two opposed political groups: the British and Irish Unionists, and the Labour Party. Connections and comparisons are drawn between the Government response to both cases and the official representations of the events. Right-wing criticism of the Government's management of the Amritsar crisis is discussed. How the right-wing response connected to the Croke Park Massacre is evaluated. Notions of 'Britishness' and how these were used to bolster the arguments presented by the Government and the right wing are also considered. The right-wing defence of Amritsar is contrasted with the reaction of the Labour Party. This thesis demonstrates how Labour objected to both massacres and challenged the official portrayals of the shootings. The Labour Party's support for Indian and Irish nationalists and preferred approach to imperial rule in India and Ireland in 1920 is illustrated. The reactions of the right wing and the Labour Party are continuously juxtaposed with the official responses. How British reactions to the Amritsar Massacre and the Croke Park Massacre were connected by the overriding context of 'imperial crisis' is highlighted throughout. This thesis contributes to existing comparative and connected studies on India, Ireland and imperial violence in the interwar period, as well as general studies on the Amritsar Massacre and the Croke Park Massacre. It draws attention to similarities, differences, and connections between both cases, which are absent from existing historiography. This thesis employs several primary sources that have been under-utilised by historians, and gives sufficient focus to the left-wing response which has previously received limited scholarly attention.