Arcsine Distribution | ScienceGate

Some Properties of the Arcsine Distribution

Journal of the American Statistical Association ◽

10.1080/01621459.1980.10477449 ◽

1980 ◽

Vol 75 (369) ◽

pp. 173-175 ◽

Cited By ~ 9

Author(s):

Barry C. Arnold ◽

Richard A. Groeneveld

Keyword(s):

Arcsine Distribution

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INTERPOLATION OF CHEBYSHEV POLYNOMIALS AND INTERACTING FOCK SPACES

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025706002421 ◽

2006 ◽

Vol 09 (03) ◽

pp. 361-371 ◽

Cited By ~ 7

Author(s):

IZUMI KUBO ◽

HUI-HSIUNG KUO ◽

SUAT NAMLI

Keyword(s):

Orthogonal Polynomials ◽

Anderson Model ◽

Chebyshev Polynomials ◽

Field Operator ◽

Parameter Family ◽

Probability Measures ◽

Fock Spaces ◽

Arcsine Distribution ◽

Multiplicative Renormalization ◽

Renormalization Method

We discover a family of probability measures μa, 0 < a ≤ 1, [Formula: see text] which contains the arcsine distribution (a = 1) and semi-circle distribution (a = 1/2). We show that the multiplicative renormalization method can be used to produce orthogonal polynomials, called Chebyshev polynomials with one parameter a, which reduce to Chebyshev polynomials of the first and second kinds when a = 1 and 1/2 respectively. Moreover, we derive the associated Jacobi–Szegö parameters. This one-parameter family of probability measures coincides with the vacuum distribution of the field operator of the interacting Fock spaces related to the Anderson model.

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Jackknife Parametric Estimation in a Truncated Arcsine Distribution

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319990309 ◽

1999 ◽

Vol 49 (3-4) ◽

pp. 225-230

Author(s):

M. Masoom Ali ◽

Jungsoo Woo ◽

Changsoo Lee

Keyword(s):

Parametric Estimation ◽

Arcsine Distribution

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A characterization of the arcsine distribution

Statistics & Probability Letters ◽

10.1016/j.spl.2009.08.018 ◽

2009 ◽

Vol 79 (24) ◽

pp. 2451-2455 ◽

Cited By ~ 2

Author(s):

Karl Michael Schmidt ◽

Anatoly Zhigljavsky

Keyword(s):

Arcsine Distribution

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Some characterizations of Arcsine distribution

Moroccan Journal of Pure and Applied Analysis ◽

10.7603/s40956-015-0005-6 ◽

2015 ◽

Vol 1 (2) ◽

pp. 70-75

Author(s):

M. Ahsanullah

Keyword(s):

Arcsine Distribution ◽

Distributional Properties

Abstract Some distributional properties of the symmetric arcsine distribution on (−1, 1) is presented. Based on the distributional properties, several characterizations of the arcsine distribution are given.

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Skew Arcsine Distribution

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v15i330355 ◽

2021 ◽

pp. 26-34

Author(s):

Nuri Celik

Keyword(s):

Brownian Motion ◽

Simulation Study ◽

Real Data ◽

Statistical Modelling ◽

Data Sets ◽

Underlying Distribution ◽

Arcsine Distribution ◽

Motion Studies ◽

New Distribution

The arcsine distribution is very important tool in statistics literature especially in Brownian motion studies. However, modelling real data sets, even when the potential underlying distribution is pre-defined, is very complicated and difficult in statistical modelling. For this reason, we desire some flexibility on the underlying distribution. In this study, we propose a new distribution obtained by arcsine distribution with Azzalini’s skewness procedure. The main characteristics of the proposed distribution are determined both with theoretically and simulation study.

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Arcsine laws for random walks generated from random permutations with applications to genomics

Journal of Applied Probability ◽

10.1017/jpr.2021.14 ◽

2021 ◽

Vol 58 (4) ◽

pp. 851-867

Author(s):

Xiao Fang ◽

Han L. Gan ◽

Susan Holmes ◽

Haiyan Huang ◽

Erol Peköz ◽

...

Keyword(s):

Random Walk ◽

Limit Theorems ◽

Simple Random Walk ◽

Random Permutation ◽

Asymptotic Distributions ◽

Maximum Height ◽

Strong Embedding ◽

Arcsine Distribution ◽

Special Cases ◽

Functional Central Limit Theorems

AbstractA classical result for the simple symmetric random walk with 2n steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the maximum height all have exactly the same distribution and converge when scaled to the arcsine law. Motivated by applications in genomics, we study the distributions of these statistics for the non-Markovian random walk generated from the ascents and descents of a uniform random permutation and a Mallows(q) permutation and show that they have the same asymptotic distributions as for the simple random walk. We also give an unexpected conjecture, along with numerical evidence and a partial proof in special cases, for the result that the number of steps above the origin by step 2n for the uniform permutation generated walk has exactly the same discrete arcsine distribution as for the simple random walk, even though the other statistics for these walks have very different laws. We also give explicit error bounds to the limit theorems using Stein’s method for the arcsine distribution, as well as functional central limit theorems and a strong embedding of the Mallows(q) permutation which is of independent interest.

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