Applications in Statistics

Mathai, A. M.; Saxena, R. K.; Haubold, Hans J.

doi:10.1007/978-1-4419-0916-9_4

Cited by 5 publications

(9 citation statements)

References 6 publications

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“…Such an issue was also commented on by Zaghloul [37]. Pagnini and Saxena also proposed to express the Voigt function in terms of Fox functions [38][39][40]:…”

Section: Representations Of the Voigt Function: A Non-exhaustive Mini...mentioning

confidence: 99%

Extracting Physical Information from the Voigt Profile Using the Lambert W Function

Pain

2024

Plasma

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Spectral line shapes are a key ingredient of hot-plasma opacity calculations. Since resorting to elaborate line-shape models remains prohibitive for intensive opacity calculations involving ions in different excitation states, with L, M, etc., shells are populated, and Voigt profiles often represent a reliable alternative. The corresponding profiles result from the convolution of a Gaussian function (for Doppler and sometimes ionic Stark broadening) and a Lorentzian function, for radiative decay (sometimes referred to as “natural” width) and electron-impact broadening. However, their far-wing behavior is incorrect, which can lead to an overestimation of the opacity. The main goal of the present work was to determine the energy (or frequency) at which the Lorentz wings of a Voigt profile intersect with the underlying Gaussian part of the profile. It turns out that such an energy cut-off, which provides us information about the dominant line-broadening process in a given energy range, can be expressed in terms of the Lambert W function, which finds many applications in physics. We also review a number of representations of the Voigt profile, with an emphasis on the pseudo-Voigt decomposition, which lends itself particularly well to cut-off determination.

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“…Such an issue was also commented on by Zaghloul [37]. Pagnini and Saxena also proposed to express the Voigt function in terms of Fox functions [38][39][40]:…”

Section: Representations Of the Voigt Function: A Non-exhaustive Mini...mentioning

confidence: 99%

Extracting Physical Information from the Voigt Profile Using the Lambert W Function

Pain

2024

Plasma

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“…Similar to the previous section, substituting the value of () in (), applying the identity from Mathai and Saxena 58 to transform

{(1 + Cγ)}^{italic- italic1}

into

G_{italic1 italic, italic1}^{italic1 italic, italic1} ([], {italicCγ|}_{0}^{0})

and

Γ ((),, m italic, ((), \frac{italicmγ}{Ҩ}))

G_{1 italic, 2}^{2 italic, 0} ([], {\frac{mγ}{Ҩ}|}_{italic0 italic, m}^{1})

C^{'} italic= \frac{1}{italicln italic2} \int_{0}^{\infty} \frac{F_{c}^{γ} ((), γ)}{italic1 italic+ italicCγ} italicdγ

C^{'} italic= \frac{1}{italicln italic2} \int_{0}^{\infty} \frac{(1 + \frac{Γ (m, \frac{italicmγ}{Ҩ})}{Γ (m)} [\frac{italicLX}{ϐ_{ϖ}} G_{ϖ + 1, 3 ϖ + 1}^{3 ϖ, 1} [{(|, \frac{italicXγ}{ϐ_{ϖ}})}_{v_{italic2}, 0}^{1, v_{italic1}}] - 1])}{italic1 italic+ italicCγ} italicdγ

…”

Section: Asymmetric Nakagami‐m/gamma–gamma Distribution Mixed Rf‐fso ...mentioning

confidence: 99%

“…Similar to the previous section, substituting the value of ( 29) in (23), applying the identity from Mathai and Saxena 58…”

Section: Ergodic Capacitymentioning

confidence: 99%

Performance of orthogonal frequency division multiplexing based M‐ary quadrature amplitude modulation in asymmetrical dual‐hop mixed RF‐FSO transmission system

Hemanth

Sangeetha

Jaiswal

2023

Int J Communication

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Summary This paper investigates the performance of a dual‐hop mixed relay system with radio frequency (RF) and free‐space optics (FSO) communication under the effect of pointing error (PE) and atmospheric turbulence (AT). This paper considers a system where RF and FSO links are cascaded. The RF link is modeled by Nakagami‐m fading, and the FSO link is modeled as gamma–gamma (G‐G) fading channel. Both the channel models use orthogonal frequency division multiplexing (OFDM) with M‐ary quadrature amplitude modulation (QAM). The expressions for probability density function, cumulative distribution function, signal‐to‐noise ratio, and ergodic capacity are derived. The moment generating function (MGF) of fading and the bit error rate (BER) of the OFDM‐based M‐ary QAM scheme is derived in terms of Meijer's G‐function. It has been observed that, in fixed gain relay systems, the modulation scheme's BER is dominated by the SNR of the RF link. While in a variable gain relay system, the turbulence conditions of the FSO system affect the SNR and the BER of the modulation method. The feasibility of heterodyne detection and intensity modulation direct detection (IM/DD) is analyzed in terms of outage probability and ergodic capacity. The results can be used to choose the optimal modulation order and relay system for QAM‐OFDM‐based optical wireless systems.

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“…The investigation into the t − x space form of the PDF begins with the Montroll-Weiss equation (equation ( 5)), which can be expressed in the form of an H function [38] (for more detail see appendix A) as,…”

Section: Probability Density Functionmentioning

confidence: 99%

“…The definition of the Fox H-function appears in terms of the Mellin-Barnes type integral as follows [38],…”

Section: Data Availability Statementmentioning

confidence: 99%

A generalised diffusion equation corresponding to continuous time random walks with coupling between the waiting time and jump length distributions

Cleland¹,

Williams²

2023

J. Phys. A: Math. Theor.

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This work outlines a transiently coupled continuous time random walk framework. The coupling is between the displacement probability density function and the elapsed waiting time, and is of the form 1 − exp (−αt) coupling of this kind generates larger displacements for longer waiting times, however, decouples on longer timescales. Such coupling is proposed to be physically relevant to systems in which diffusion is driven by the development of internal stresses which release and develop cyclically. This article outlines the associated generalised diffusion equation (GDE), which describes the time evolution of the position probability density function, P(x, t). The solution for P(x, t) is obtained using the properties of the Fox H function, both in terms of its transform properties but also its expansion theorems. The second moment and the asymptotic features of the solution are extracted. The relaxation of P(x, t) back to the solution of a decoupled-type GDE is highlighted.

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Applications in Statistics

Cited by 5 publications

References 6 publications

Extracting Physical Information from the Voigt Profile Using the Lambert W Function

Extracting Physical Information from the Voigt Profile Using the Lambert W Function

Performance of orthogonal frequency division multiplexing based M‐ary quadrature amplitude modulation in asymmetrical dual‐hop mixed RF‐FSO transmission system

A generalised diffusion equation corresponding to continuous time random walks with coupling between the waiting time and jump length distributions

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