This book presents a new research topic in statistics--vertical density representation (VDR). The theory of VDR has been found to be useful for developing new ideas and methodologies in statistics and management science. The first paper related to VDR appeared in 1991. Several others have since been published and work is continuing on the topic. The purpose of this book is to survey the results presented in those papers and provide some new, unpublished results. VDR may be regarded as a special kind of transformation. By assuming that a variate is uniformly distributed on the contours of a...