An empirical study on gamma shadow fading based localization

Büyükçorak, Saliha; Kurt, Güneş Karabulut; Yongaçoğlu, Abbas

doi:10.23919/eusipco.2017.8081703

Cited by 1 publication

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References 13 publications

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“…Modeling fading channels, shadowing effects [1,2,3,4,5,6,7,8,9,10,11] and attenuation in wireless networks [12]; Other forms of modeling such as: binary error modeling [13], beamforming [14], spatial deployment modeling [15], delay [16], source localization [17], line of sight interference power [18], atmospheric turbulence [19,20] and color texture characterization [21]. Modeling by the direct use of gamma distribution fit via parameter estimation [22,23,24].…”

Section: Introductionmentioning

confidence: 99%

Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication

Okagbue

Adamu

Anake

2020

Heliyon

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The use of quantile functions of probability distributions whose cumulative distribution is intractable is often limited in Monte Carlo simulation, modeling, and random number generation. Gamma distribution is one of such distributions, and that has placed limitations on the use of gamma distribution in modeling fading channels and systems described by the gamma distribution. This is due to the inability to find a suitable closed-form expression for the inverse cumulative distribution function, commonly known as the quantile function (QF). This paper adopted the Quantile mechanics approach to transform the probability density function of the gamma distribution to second-order nonlinear ordinary differential equations (ODEs) whose solution leads to quantile approximation. Closed-form expressions, although complex of the QF, were obtained from the solution of the ODEs for degrees of freedom from one to five. The cases where the degree of freedom is not an integer were obtained, which yielded values closed to the R software values via Monte Carlo simulation. This paper provides an alternative for simulating gamma random variables when the degree of freedom is not an integer. The results obtained are fast, computationally efficient and compare favorably with the machine (R software) values using absolute error and Kullback-Leibler divergence as performance metrics.

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