Generalized Hyperbolic Secant Distributions With Applications to Fin
Among the symmetrical distributions with an infinite domain, the most popular alternative to the normal variant is the logistic distribution as well as the Laplace or the double exponential distribution, which was first introduced in 1774. Occasionally,
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Matthias J. Fischer
Generalized Hyperbolic Secant Distributions With Applications to Finance
SpringerBriefs in Statistics
For further volumes: http://www.springer.com/series/8921
Matthias J. Fischer
Generalized Hyperbolic Secant Distributions With Applications to Finance
123
Matthias J. Fischer Department of Statistics and Econometrics Friedrich-Alexander-Universität Erlangen-Nürnberg Nuremberg Germany
ISSN 2191-544X ISBN 978-3-642-45137-9 DOI 10.1007/978-3-642-45138-6
ISSN 2191-5458 (electronic) ISBN 978-3-642-45138-6 (eBook)
Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013956323 Mathematics Subject Classification (2010): 62E15, 62P20, 91G70, 91B70, 91B84 The Author(s) 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The standard normal distribution dates back to a pamphlet of de Moivre dated 12 November 1733. Further improvements were given by Laplace in 1774. The work of Gauss in 1809 and 1816 established techniques based on the normal distribution, which became standard during the nineteenth century. For both theoretical and practical reasons, the normal distribution is probably the most important distribution, not only in statistics. However, as mentioned by Chew (1968), ‘‘other probability dis
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