Estimating the distribution of a sum of independent lognormal random variables

Beaulieu, N.C.; Abu-Dayya, Adnan; McLane, P.J.

doi:10.1109/26.477480

Cited by 289 publications

(156 citation statements)

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“…If the K lognormal RVs are identically distributed, then the approximating lognormal moments µ Y and σ Y can even be expressed in closed-form. While the F-W method accurately models the tail portion (large values of X) of the lognormal sum pdf, it is quite inaccurate near the head portion (small values of X) of the sum pdf, especially for large values of σ Y i [10]. The mean square error in µ Y and σ Y increases with a decrease in the spread of the mean values or an increase in the spread of the standard deviations of the summands [13].…”

Section: Comparison Of Various Lognormal Sum Approximation Methodsmentioning

confidence: 99%

“…Beaulieu et al [6], [10] have studied in detail the accuracy of several of the above methods, and shown that each method has its own advantages and disadvantages; none is unquestionably better than the others. Farley's method and, more generally, the formulae derived in [7] are strict bounds that can be quite loose for certain typical parameters.…”

Section: Introductionmentioning

confidence: 99%

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Flexible lognormal sum approximation method

Mehta

Zhang

2005

GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.

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A simple and novel method is presented to approximate the distribution of the sum of independent, but not necessarily identical, lognormal random variables, by the lognormal distribution. It is shown that matching a short GaussHermite approximation of the moment generating function of the lognormal sum with that of the lognormal distribution leads to an accurate lognormal sum approximation. The advantage of the proposed method over the ones in the literature, such as the Fenton-Wilkinson method, Schwartz-Yeh method, and the recently proposed BeaulieuXie method, is that it provides the parametric flexibility to handle the inevitable trade-off that needs to be made in approximating different regions of the probability distribution function. The accuracy is verified using extensive simulations based on a cellular layout. IEEE Globecom 2005This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-A simple and novel method is presented to approximate the distribution of the sum of independent, but not necessarily identical, lognormal random variables, by the lognormal distribution. It is shown that matching a short GaussHermite approximation of the moment generating function of the lognormal sum with that of the lognormal distribution leads to an accurate lognormal sum approximation. The advantage of the proposed method over the ones in the literature, such as the Fenton-Wilkinson method, Schwartz-Yeh method, and the recently proposed Beaulieu-Xie method, is that it provides the parametric flexibility to handle the inevitable trade-off that needs to be made in approximating different regions of the probability distribution function. The accuracy is verified using extensive simulations based on a cellular layout.

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Section: Comparison Of Various Lognormal Sum Approximation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Flexible lognormal sum approximation method

Mehta

Zhang

2005

GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.

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“…This function has been proposed by Farley [22] for analysing the SLN distribution in the independent and identically distributed case. We then have…”

Section: B Historical Motivationmentioning

confidence: 99%

“…We use the 3-parameter Modified-Power-Lognormal (MPLN) distribution as our approximating function, which has been previously proposed for approximating the SLN cdf in various ways [3], [5], [13], [16], [22]. In Section II, we summarise the many arguments, some novel, for the choice of this particular distribution.…”

Section: Introductionmentioning

confidence: 99%

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Fitting the Modified-Power-Lognormal to the Sum of Independent Lognormals Distribution

Szyszkowicz

Yanıkömeroğlu

2009

GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference

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Abstract-We propose a new method for calculating a tight approximation to the distribution of the sum of independent lognormal random variables. We make use of a three-parameter modified-power-lognormal distribution function as the approximating distribution. We use theoretical results from our previous work on the tails of the distribution of the sum of lognormals to match the slope of the modified-power-lognormal function at both tails. This would not have been possible with many of the recently-proposed distribution functions, which do not behave properly in the tails. We then also use moment-matching to find the best curve match. Our method is mostly closed-form, requiring only one simple numerical integral.We compare our method with those in literature in terms of complexity and accuracy. We conclude that our method is more accurate than the simple (closed-form) methods, and much simpler to understand and implement than the more accurate methods which rely heavily on numerical integration.Index Terms-sum of lognormals, interference analysis

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Visible Light Communications

Nakagawa

2017

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Estimating the distribution of a sum of independent lognormal random variables

Cited by 289 publications

References 10 publications

Flexible lognormal sum approximation method

Flexible lognormal sum approximation method

Fitting the Modified-Power-Lognormal to the Sum of Independent Lognormals Distribution

Visible Light Communications

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