A new family of life distributions

Birnbaum, Z. W.; Saunders, Sam C.

doi:10.2307/3212003

Cited by 680 publications

(336 citation statements)

References 5 publications

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“…Figure 1c depicts the probability distribution function (red hollow circles) of the animal's dwelling time t d of continuous swimming along the surface. The Birnbaum-Saunders probability distribution function [29] Figure 1e (red curves) is a polar plot depicting the fraction of time that the nematode swims in a direction u + Du/2 as a function of u. The angle u is measured with respect to the conduit's axis and Du ¼108.…”

Section: Experimental Observations Of Individualmentioning

confidence: 99%

A hydrodynamic mechanism for attraction of undulatory microswimmers to surfaces (bordertaxis)

Yuan

Raizen

Bau

2015

J. R. Soc. Interface.

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ResearchCite this article: Yuan J, Raizen DM, Bau HH. 2015 A hydrodynamic mechanism for attraction of undulatory microswimmers to surfaces (bordertaxis). J. R. Soc. Although small nematodes significantly impact human and animal health, agriculture, and ecology, little is known about the role of hydrodynamics in their life cycles. Using the nematode Caenorhabditis elegans as a model undulatory microswimmer, we have observed that animals are attracted to and swim along surfaces. The attraction to surfaces does not require mechanosensory neuron function. In dilute swarms, swimmers aggregate near surfaces. Using resistive force-based theory, symmetry arguments, and direct hydrodynamic simulations, we demonstrate that forces resulting from the interaction between the swimmer-induced flow field and a nearby surface cause a short-range hydrodynamic torque that stirs the swimmers towards the surface. When combined with steric forces, this causes locomotion along the surface. This surface attraction may affect nematode mate and food finding behaviour and, in the case of parasitic nematodes, may facilitate host penetration. Surface attraction must be accounted for when studying animals' responses to various stimuli, and suggests means of controlling undulatory microswimmers.

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Section: Experimental Observations Of Individualmentioning

confidence: 99%

A hydrodynamic mechanism for attraction of undulatory microswimmers to surfaces (bordertaxis)

Yuan

Raizen

Bau

2015

J. R. Soc. Interface.

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“…For each path, we know that the distribution of the first passage time to its threshold value can be approximated by Birnbaum-Saunders distribution [2]. Pan and Balakrishnan [9] gave the lifetime distribution of product with two dependent performance characteristics using bivariate Birnbaum-Saunders distribution.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…specify the copula family as Gaussian copula with parameters (1) (0,Σ); the rank correlations among the triple degradation paths are (2) τ; the marginal distribution of the increments for (3) i th degradation path is gamma distribution with parameters…”

Section: Simulation Of Datamentioning

confidence: 99%

Lifetime Distribution and Associated Inference of Systems with Multiple Degradation Measurements Based on Gamma Processes

Pan¹,

Feng²,

Sun³

2016

EiN

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Lifetime Distribution anD associateD inference of systems with muLtipLe DegraDation measurements baseD on gamma processes wyznaczanie rozkłaDu czasów życia oraz wnioskowanie DLa systemów wymagających pomiarów współistniejących DegraDacji w oparciu o procesy gamma PAn Z, Feng J, Sun Q. Lifetime distribution and associated inference of systems with multiple degradation measurements based on gamma processes. eksploatacja i niezawodnosc -Maintenance and Reliability 2016; 18 (2): 307-313, http://dx

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“…4, No. 3;2015 33 The data set was used by Cordeiro and Lemonte (2011) to illustrate the application of a four-parameter beta-Birnbaum-Saunders distribution (BBSD) and it was compared to the two-parameter Birnbaum-Saunders distribution (BSD) (Birnbaum and Saunders, 1969). The three-parameter CW{L}, four-parameter CW{L} and flexible Weibull distribution (FWD) (Bebbington et al, 2007) are applied to fit the data.…”

Section: Wwwccsenetorg/ijspmentioning

confidence: 99%

Some Generalized Families of Weibull Distribution: Properties and Applications

AlMheidat¹,

Famoye²,

Lee³

2015

IJSP

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The Weibull distribution has been applied in various fields, especially to fit life time data. Some of these applications are limited partly due to the fact that the distribution has monotonically increasing, monotonically decreasing or constant hazard rate. This limitation undoubtedly inspired researchers to develop generalized Weibull distribution that can exhibit unimodal or bathtub hazard rate. In this article, we introduce six new families of T-Weibull{Y} distributions arising from the quantile function of a random variable Y. These six families are: The T-Weibull{uniform}, T-Weibull{exponential}, T-Weibull{log-logistic}, T-Weibull{Fré chet}, T-Weibull{logistic} and T-Weibull{extreme value}. Some properties of these families are discussed and general expressions for the quantile function, the Shannon's entropy, the non-central moments and the mean deviations are provided. Different new members of the T-Weibull{Y} families are derived and some of their properties are discussed. Two real data sets are used to illustrate the potential usefulness of the T-Weibull{Y} distributions and the results are compared with the results from some existing distributions.

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A new family of life distributions

Cited by 680 publications

References 5 publications

A hydrodynamic mechanism for attraction of undulatory microswimmers to surfaces (bordertaxis)

A hydrodynamic mechanism for attraction of undulatory microswimmers to surfaces (bordertaxis)

Lifetime Distribution and Associated Inference of Systems with Multiple Degradation Measurements Based on Gamma Processes

Some Generalized Families of Weibull Distribution: Properties and Applications

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