Arcsine Distribution | ScienceGate

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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