Pioneering Works on Distribution Theory

This book highlights the forefront of research on statistical distribution theory, with a focus on unconventional random quantities, and on phenomena such as random partitioning. The respective papers reflect the continuing appeal of distribution theory and the lively interest in this classic field, which owes much of its expansion since the 1960s to Professor Masaaki Sibuya, to whom this book is dedicated.
The topics addressed include a test procedure for discriminating the (multivariate) Ewens distribution from the Pitman Sampling Formula, approximation to the length of the Ewens distribution by discrete distributions and the normal distribution, and the distribution of the number of levels in [ s ]-specified random permutations. Also included are distributions associated with orthogonal polynomials with a symmetric matrix argument and the characterization of the Jeffreys prior.

Gathers a wealth of rigorously peer-reviewed contributions, written by respected experts Highlights the latest approaches to statistical distributions Though chiefly focusing on theory, will also appeal to readers interested in applied probabilities

Autorentext

Nobuaki Hoshino, Kanazawa University
Shuhei Mano, The Institute of Statistical Mathematics
Takaaki Shimura, The Institute of Statistical Mathematics

Inhalt

Gibbs Base Random Partitions.- Asymptotic and approximate discrete distributions for length of Ewens sampling formula.- An Error Bound for the Normal Approximation to the Length of a Ewens Partition.- Distribution of Number of Levels in [s]-specified Random Permutation.- Properties of General Systems of Orthogonal Polynomials with Symmetric Matrix Argument.- Conjugate Analysis under Jeffreys' Prior with its Implications to Likelihood Inference.