Lagrangian Probability Distributions
Birkhäuser-Verlag eBooks · 2006
Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.Printed in the United States of America.(KeS/MP) 9 8 7 6 5 4 3 2 1 www.birkhauser.comJoseph Louis Lagrange (1736-1813) Joseph Louis Lagrange was one of the two great mathematicians of the eighteenth century.He was born in France and was appointed professor at the age of 19.He helped in founding the Royal Academy of Sciences at the Royal Artillery School in 1757.He was very close to the famous mathematician Euler, who appreciated his work immensely.When Euler left the Berlin Academy of Science in 1766, Lagrange succeeded him as director of mathematics.He left Berlin in 1787 and became a member of the Paris Academy of Science and remained there for the rest of his career.He helped in the establishment of École Polytechnique and taught there for some time.He survived the French revolution, and Napoleon appointed him to the Legion of Honour and Count of the Empire.Lagrange had given two formulae for the expansion of the function f (z) in a power series of u when z = ug(z) (mémoires de l'Acad.Roy.des Sci.Berlin, 24, 1768, 251) which have been extensively used by various researchers for developing the class of Lagrangian probability models and its families described in this book.Lagrange developed the calculus of variations, which was very effective in dealing with mechanics.His work Mécanique Analytique (1788), summarizing all the work done earlier in mechanics, contained unique methods using differential equations and mathematical analysis.He created Lagrangian mechanics, provided many new solutions and theorems in number theory, the method of Lagrangian multipliers, and numerous other results which were found to be extremely useful. To Shakuntla Consul and Busola Famoyeviii Foreword A multivariate extension was developed by I. J. Good in 1955, but the definition and basic properties of the Lagrangian distributions are due to P. C. Consul, who in collaboration with R. L. Shenton wrote in the early 1970s in a number of pioneering papers with detailed discussion of these distributions.This book is a welcome addition to the literature on discrete univariate and multivariate distributions and is an important source of information on numerous topics associated with powerful new tools and probabilistic models.The wealth of materials is overwhelming and the well-organized, lucid presentation is highly commendable.Our thanks go to the authors for their labor of love, which will serve for many years as a textbook, as well as an up-to-date handbook of the results scattered in the periodical literature and as an inspiration for further research in an only partially explored field.