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Efficient Computation of Distribution Function for Sum of Large Number of Lognormal Random Variables

  • Research Article - Electrical Engineering
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Abstract

This paper presents efficient and convenient methods for computing the sum of large number of lognormal (LN) random variables (RVs) while utilizing the unexpanded form for the characteristic function of the sum obtained previously. These methods are (1) the application of appropriate quadrature rules to the integral involving the characteristic function for the sum after a proper change of variables, and (2) the application of the Epsilon algorithm to reduce the number of needed computations. The Epsilon algorithm is also used to compute the distribution for the sum of correlated LN RVs. Results indicate that while (1) presents a simple to evaluate sum in terms of the weights and nodes of the chosen quadrature rule, it may require 100 to 1,000s of terms to arrive at a reasonable approximation of the target cumulative distribution function. The second method reduces the needed evaluations to as little as 10 and improves the accuracy for both the lower end and higher end of the approximated cdf.

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Authors and Affiliations

  1. Department of Computer Engineering, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Ashraf S. Hasan Mahmoud & Abdallah Hasan Rashed

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  1. Ashraf S. Hasan Mahmoud
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  2. Abdallah Hasan Rashed
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Correspondence to Ashraf S. Hasan Mahmoud.

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Mahmoud, A.S.H., Rashed, A.H. Efficient Computation of Distribution Function for Sum of Large Number of Lognormal Random Variables. Arab J Sci Eng 39, 3953–3961 (2014). https://doi.org/10.1007/s13369-014-0993-y

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  • DOI: https://doi.org/10.1007/s13369-014-0993-y

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