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Here we compute approximations to the density of a sum of N mutualiy independent and identically distributed lognormal rvs. As is weli known, the density of a sum of independent, iqentically distributed rvs is given by the inverse Fourier (or laplace) transform of the Nth power hf the charaeteristic function, so we begin by studying the characteristic function of a lognormal density. We perform an asymptotic anafysis of it in its various regions for N and var(xi) 02 large and compute approximatipns to the density of the sum by transforming back.
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On Sums of Lognormal Random Variables (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book explores the fascinating world of the lognormal distribution, a mathematical model widely used in fields ranging from finance to geology. The author delves into the complex behavior of sums of lognormal random variables, a topic of great significance in areas like portfolio analysis and the study of mineral resource deposition. The book provides a detailed examination of the characteristic function of the lognormal distribution, employing a variety of analytical techniques to illuminate its properties and derive approximations for the density of sums of lognormal random variables. The author meticulously dissects the intricacies of the lognormal distribution, revealing its unique features and the challenges of approximating its behavior, particularly in the context of sums of independent variables. The book's insights into the lognormal distribution are particularly valuable as they provide a framework for understanding and predicting the behavior of complex systems where individual components exhibit lognormal characteristics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332976348_0
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