The entire text has been revised, word by word, and terminology and proofs modernised. Chapters 5 and 6 - the central chapters on distribution - have been greatly enlarged, the former in particular being extensively restructured, with new tables and diagrams to emphasise the relations between different distributions and systems of distributions. Chapters 7 and 8 have been rewritten to give a modern presentation of the fundamentals of probability, and permit a more extended treatment of elementary Bayesianinference. Chapter 9 has an extensive new treatment of the computer-generation of pseudo-random numbers and its application to sampling experiments (Monte Carlo methods). The theoretical treatments elsewhere in the book have been extended to include coverage of important topics in current research - for example, smoothing, kernel estimators, density estimation, the exponential family, saddle-point approximations, fractional and negative moments, and robustness.