Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
The Estimation Of Parameters In Regression Functions Subject To Certain Restraints, Paul D. Minton, Alfred E. Crofts Jr.
The Estimation Of Parameters In Regression Functions Subject To Certain Restraints, Paul D. Minton, Alfred E. Crofts Jr.
Journal of the Graduate Research Center
We consider two types of problems in maximum likelihood estimation of parameters of linear functions subject to certain restraints. One is a family of lines with equal slopes or intercepts; the other is a pair of lines constrained to meet at a predetermined point. In the case of normally distributed errors with equal variances within each set, the solutions are identical with least squares solutions. In addition to linear functions, non-linear functions which are transformable to linearity may be treated under these methods.
A Formula For A Class Of Steady State Solutions, Don E. Edmondson
A Formula For A Class Of Steady State Solutions, Don E. Edmondson
Journal of the Graduate Research Center
An integral representation formula is developed to cope with the problem of determining and studying the steady state solutions of a class of differential equations. The class of differential equations studied is y' + yf = g, where f and g are continuous functions admitting period T > 0. The formula then defines a function admitting period T and serves to allow an analysis of the differential equation above. Theorem I delineates some of the properties of the function and Theorem II provides answers to the steady state questions. An application is made to a capacitance circuit problem.