VDR may be regarded as a special kind of transformation. By assuming that a variate is uniformly distributed on the contours of a given function in real n-dimensional space, and considering the density of the ordinate of the given function, the density of the original variate can be represented. The book discusses basic results and extensions. In particular, the uniform assumption on contours is relaxed to the general case. Applications are presented in Monte Carlo simulation, chaos-based uniform random number generation, and what may be called behavioral estimation. In addition, the authors include a new result in analyzing correlation into two separate components, which provides flexibility in modeling correlated phenomena, such as when combining expert estimates.

Contents:

• Vertical Density Representation
• Applications of Vertical Density Representation
• Multivariate Vertical Density Representation
• Applications of Multivariate VDR
• VDR and Chaos
• Management Science Applications of VDR–I
• Management Science Applications of VDR–II
• Management Science Applications of VDR–III
• Open Questions and Future Research

“This book is the first comprehensive presentation of the theory of vertical density representation ... The text is illustrated with many original and surprising examples.”

“This text is recommended for statisticians who need to analyze multivariate data; especially in the field of management science.”

“I found the book interesting and easy reading ... Connections with Khinchine's theorem and with the distribution of an inverse CDF are enlightening.”