On the rate of convergence of maxima for the generalized Maxwell distribution

Huang, Jianwen; Wang, Jianjun; Luo, Guowang

doi:10.1080/02331888.2017.1307376

Cited by 4 publications

(5 citation statements)

References 9 publications

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“…However, lemma 6 (appendix D.1) suggests that for Gaussian and sub-Gaussian eccenticity distributions, err 2 is exceedingly fast decreasing in n for a given tolerance T . Given that EVT error convergence rates are usually slow [21,25], this suggests an optimal region of m >> n. This is inline with the 1-medoid algorithms RAND, TOPRANK, trimed and meddit And differs from the K-medoid algorithms PAM, CLARA, PAMAE (m = n) & CLARANS (m << n). We propose a novel K-medoid algorithm MCPAM in the m >> n regime.…”

Section: Faster Large Scale K-medoidsmentioning

confidence: 84%

Scalable K-Medoids via True Error Bound and Familywise Bandits

Babu¹,

Agarwal²,

Babu³

et al. 2019

Preprint

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K-Medoids(KM) is a standard clustering method, used extensively on semi-metric data. Error analyses of KM have traditionally used an in-sample notion of error, which can be far from the true error and suffer from generalization error. We formalize the true K-Medoid error based on the underlying data distribution, by decomposing it into fundamental statistical problems of: minimum estimation (ME) and minimum mean estimation (MME). We provide a convergence result for MME and bound the true KM error for iid data. Inspired by this bound, we propose a computationally efficient, distributed KM algorithm namely MCPAM. MCPAM has expected runtime O(km) and provides massive computational savings for a small tradeoff in accuracy. We verify the quality and scaling properties of MCPAM on various datasets. And achieve the hitherto unachieved feat of calculating the KM of 1 billion points on semi-metric spaces.

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Section: Faster Large Scale K-medoidsmentioning

confidence: 84%

Scalable K-Medoids via True Error Bound and Familywise Bandits

Babu¹,

Agarwal²,

Babu³

et al. 2019

Preprint

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“…This distribution has been used to study the two types of reliability functions. Huang and Wang (2017) [15] have studied the GMD to compute an exact uniform convergence rate. Further (Huang and Wang, 2018) [14] also used GMD distribution to study the asymptotic of extremes and the asymptotic extension of the moment of maximum.…”

Section: Introductionmentioning

confidence: 99%

Inverse Power Generalized Maxwell Distribution with Applications in Industry

Alsahangiti

Gemeay

Sapkota

et al. 2023

Preprint

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Employing the inverse power transformation technique, we have proposed a new continuous three-parameter probability distribution and named it inverse power generalized Maxwell distribution. This distribution is the generalized version of the generalized Maxwell distribution. For this model, we have derived some functions related to survival analysis. Several statistical properties of the model are provided. This study also focused on the estimation of the unknown model parameters. Six different parameter estimation methods are employed and studied extensively through numerical simulation. To investigate the applications of the suggested model, two real engineering data sets are considered and empirically found that the suggested model can provide a superior fit as compared to some candidate models under study.\\ \\ \textbf{Keywords:} Generalize Maxwell distribution, Moments, Estimation, Inverse power, Entropy.

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“…Related work concerning properties of GMD(k) can be found in [3] [4] [5] and [6]. GMD(k) has received applications in a variety of areas, see, e.g., establishing the discretized equilibrium distributions of the lattice Boltzmann method [7], describing the stress relaxation behavior of food matrices [8], being used to derive a different class of multiple relaxation-time lattice Boltzmann models [9], and modeling the linear viscoelastic fluids [10].…”

Section: Introductionmentioning

confidence: 99%

Expansions of maximum and minimum from Generalized Maxwell distribution

Huang

2020

Preprint

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Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic expansions of joint distribution and density for normalized partial maxima and minima are established. These expansions are used to educe speeds of convergence of joint distribution and density of normalized maxima and minima tending to its corresponding ultimate limits. Numerical analysis are provided to support our results.

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On the rate of convergence of maxima for the generalized Maxwell distribution

Cited by 4 publications

References 9 publications

Scalable K-Medoids via True Error Bound and Familywise Bandits

Scalable K-Medoids via True Error Bound and Familywise Bandits

Inverse Power Generalized Maxwell Distribution with Applications in Industry

Expansions of maximum and minimum from Generalized Maxwell distribution

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