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 Physics , 2007, DOI: 10.1209/0295-5075/79/66006 Abstract: We address the role of community structure of an interaction network in ordering dynamics, as well as associated forms of metastability. We consider the voter and AB model dynamics in a network model which mimics social interactions. The AB model includes an intermediate state between the two excluding options of the voter model. For the voter model we find dynamical metastable disordered states with a characteristic mean lifetime. However, for the AB dynamics we find a power law distribution of the lifetime of metastable states, so that the mean lifetime is not representative of the dynamics. These trapped metastable states, which can order at all time scales, originate in the mesoscopic network structure.
 Quantitative Biology , 2012, DOI: 10.1209/0295-5075/99/18004 Abstract: Correlated velocity patterns and associated large length-scale transmission of traction forces have been observed in collective live cell migration as a response to a "wound". We argue that a simple physical model of a force-driven heterogeneous elastic membrane sliding over a viscous substrate can qualitatively explain a few experimentally observed facts: (i) the growth of velocity ordering which spreads from the wound boundary to the interior, (ii) the exponential tails of the traction force distributions, and (iii) the swirling pattern of velocities in the interior of the tissue.
 Journal of Quality and Reliability Engineering , 2012, DOI: 10.1155/2012/760687 Abstract: A four-parameter family of Weibull distributions is introduced, as an example of a more general class created along the lines of Marshall and Olkin, 1997. Various properties of the distribution are explored and its usefulness in modelling real data is demonstrated using maximum likelihood estimates. 1. Introduction Probability distributions are often used in survival analysis for modeling data, because they offer insight into the nature of various parameters and functions, particularly the failure rate (or hazard) function. Throughout the last decades, a considerable amount of research was devoted to the creation of lifetime models with more than the classical increasing and decreasing hazard rates; apparently, the motivation for this trend was to provide with more freedom of choice in the description of complex practical situations (see e.g., [1–9], and the references therein). In this paper a general class of models is introduced, by adding an extra parameter to a distribution in the sense of Marshall and Olkin [10], and subsequently used in developing a four-parameter modified Weibull extension distribution, with various failure rate curves that compete well with other alternatives in fitting real data. Specifically, Xie et al. [11] generalized the Chen [12] distribution by adding the lacking scale parameter, thus creating a three-parameter Weibull distribution; although the variety of shapes of the reliability curves was not enriched, the resulting model provided better fit to real data. The proposed distribution extends the Xie et al. [11] distribution by adding a shape parameter; it will be seen that compared to the previous and other models, the cost of the addition is balanced by the improvement in fitting real data. The paper is organized as follows. Section 2 includes the general class of models and some properties. The proposed four-parameter Weibull model is introduced in Section 3 and some properties and reliability aspects are studied. The parameters are estimated by the method of maximum likelihood and the observed information matrix is obtained; the fit of the proposed distribution to two sets of real data is examined against three and two parameter competitors. 2. The Class of Distributions It is possible to generalize a distribution by adding a shape parameter, in the sense of Marshall and Olkin [10]. Thus, starting with a distribution with survival function , the survival function of the proposed family with the additional parameter is given by and when , then . The probability density and hazard functions are readily found to be
 International Journal of Quality, Statistics, and Reliability , 2012, DOI: 10.1155/2012/760687 Abstract: A four-parameter family of Weibull distributions is introduced, as an example of a more general class created along the lines of Marshall and Olkin, 1997. Various properties of the distribution are explored and its usefulness in modelling real data is demonstrated using maximum likelihood estimates.
 Pakistan Journal of Statistics and Operation Research , 2005, DOI: 10.1234/pjsor.v1i1.109 Abstract: We construct a sampling algorithm to generate ordered statistics from conditional lifetime distributions by expressing the conditional distribution of ordered statistics in terms of cumulative hazard function. We use uniform spacing algorithm to generate uniform (0,1) ordered statistics in the proposed algorithm.
 Said Hofan Alkarni Open Journal of Statistics (OJS) , 2013, DOI: 10.4236/ojs.2013.35036 Abstract: In this paper, a new lifetime class with decreasing failure rate is introduced by compounding truncated binomial distribution with any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of its probability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived in order to obtain the asymptotic covariance matrix. This new class of distributions generalizes several distributions which have been introduced and studied in the literature.
 Physics , 2011, DOI: 10.1103/PhysRevB.85.085120 Abstract: At ambient temperatures, CeRuSn exhibits an extraordinary structure with a coexistence of two types of Ce ions in a metallic environment, namely trivalent Ce3+ and intermediate valent Ce(4-x)+. Charge ordering produces a doubling of the unit cell along the c-axis with respect to the basic monoclinic CeCoAl type structure. Below room temperature, a phase transition with very broad hysteresis has been observed in various bulk properties like electrical resistivity, magnetic susceptibility, and specific heat. The present x-ray diffraction results show that at low temperatures the doubling of the CeCoAl type structure is replaced by an ill-defined modulated ground state. In this state, at least three different modulation periods compete, with the dominant mode close to a tripling of the basic cell. The transition is accompanied by a significant contraction of the c axis. XANES data suggest that the average Ce valence remains constant, thus the observed c axis contraction is not due to any valence transition. We propose a qualitative structure model with modified stacking sequences of Ce3+ and Ce(4-x)+ layers in the various modulated phases. Surprisingly, far below 100 K the modulated state is sensitive to x-ray irradiation at photon fluxes available at a synchrotron. With photon fluxes of order 10E12/s, the modulated ground state can be destroyed on a timescale of minutes and the doubling of the CeCoAl cell observed at room temperature is recovered. The final state is metastable at 10 K. Heating the sample above 60 K again leads to a recovery of the modulated state. Thus, CeRuSn exhibits both thermally and x-ray induced reversible transformations of the Ce3+/Ce(4-x)+ charge ordering pattern. Such a behavior is unique among any know intermetallic compound.
 Mathematics , 2009, Abstract: For several pairs $(P,Q)$ of classical distributions on $\N_0$, we show that their stochastic ordering $P\leq_{st} Q$ can be characterized by their extreme tail ordering equivalent to $P(\{k_\ast \})/Q(\{k_\ast\}) \le 1 \le \lim_{k\to k^\ast} P(\{k\})/Q(\{k\})$, with $k_\ast$ and $k^\ast$ denoting the minimum and the supremum of the support of $P+Q$, and with the limit to be read as $P(\{k^\ast\})/Q(\{k^\ast\})$ for $k^\ast$ finite. This includes in particular all pairs where $P$ and $Q$ are both binomial ($b_{n_1,p_1} \leq_{st} b_{n_2,p_2}$ if and only if $n_1\le n_2$ and $(1-p_1)^{n_1}\ge(1-p_2)^{n_2}$, or $p_1=0$), both negative binomial ($b^-_{r_1,p_1}\leq_{st} b^-_{r_2,p_2}$ if and only if $p_1\geq p_2$ and $p_1^{r_1}\geq p_2^{r_2}$), or both hypergeometric with the same sample size parameter. The binomial case is contained in a known result about Bernoulli convolutions, the other two cases appear to be new. The emphasis of this paper is on providing a variety of different methods of proofs: (i) half monotone likelihood ratios, (ii) explicit coupling, (iii) Markov chain comparison, (iv) analytic calculation, and (v) comparison of Levy measures. We give four proofs in the binomial case (methods (i)-(iv)) and three in the negative binomial case (methods (i), (iv) and (v)). The statement for hypergeometric distributions is proved via method (i).
 Physics , 1998, DOI: 10.1016/S0370-2693(98)00439-0 Abstract: We investigate the relevance of time ordering in the definition of off-diagonal parton distributions in terms of products of fields. The method we use easily allows determination of their support properties and provides a link to their interpretation from a parton point of view. It can also readily be applied to meson distribution amplitudes.}
 International Journal of Statistics and Probability , 2013, DOI: 10.5539/ijsp.v2n2p42 Abstract: The main purpose of this note is to provide further properties of discrete lifetime distributions based on variance residual lifetimes (VRL). New discrete aging classes are introduced in terms of discrete version of VRL. We demonstrate closure of discrete variance residual lifetime under convolution and mixing.
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