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Dissertation Information for Javier Cabrera

NAME:
- Javier Cabrera
- (Alias) Javier Fernandez Cabrera

DEGREE:
- Ph.D.

DISCIPLINE:
- Statistics

SCHOOL:
- Princeton University (USA) (1983)

ADVISORS:
- None

COMMITTEE MEMBERS:
- None

MPACT Status: Incomplete - Inspected

Title: STATISTICS ON THE HYPERBOLOID

Abstract: "This Thesis studies random variables x = (x(,1),..,xq) which are points on the hyperboloid x(,1)('2)-x(,2)('2)-..-x(,q)('2) = 1, x(,1) > 0. Statistical methods are developed for the class of distributions with densities of the form f(x(,1)(mu)(,1)-x(,2)(mu)(,2)-(.)(.)(.)-x(,q)(mu)(,q)) which have a rotationally symmetric feature. Two particular distributions are examined in detail. The Jensen distribution, with density proportional to exp{-(kappa)(x(,1)(mu)(,1)-x(,2)(mu)(,2)-..-x(,q)(mu)(,q)} and the density proportional to exp{-(kappa)(x(,1)(mu)(,1)-x(,2)(mu)(,2)-..-x(,q)(mu)(,q))('2)}.

The theory and methods parallel those used on the sphere x(,1)('2)+..+x(,q)('2) = 1. The two particular distributions above are the hyperbolic analogues of the Langevin-Fisher and the Scheiddegger-Watson distributions on the sphere. The hyperbolic analogues are studied as the sample size and as (kappa) tends to infinity. Many of the results found are closely related to spherical results.

In studying data from any hyperbolic distribution we were lead to study the effects of changing the signs of columns in the matrix of second order moments on the eigenvalues and eigenvectors of the matrix."

MPACT Scores for Javier Cabrera

A = 0
C = 1
A+C = 1
T = 0
G = 0
W = 0
TD = 0
TA = 0
calculated 2008-01-31 06:29:18

Advisors and Advisees Graph

Directed Graph

Students under Javier Cabrera

ADVISEES:
- None

COMMITTEESHIPS:
- Chukwuemeka Akaezuwa - Rutgers University (1994)