Title: Estimating parameters of directional distributions
Abstract: Data related to spread of disease bacteria, wind directions, seasonal variations etc. can be represented by directional distributions. Langevin distribution is one of most commonly used directional distributions. We unify the results on admissibility, minimaxity and best equivariance of MLE of direction parameter. Various other estimators of direction parameter are compared with respect to robustness and asymptotic efficiency. Methods of improving estimators for spherical location are developed. Special applications to problems in restricted parameter spaces are given.
Title: Study of a nonlinear renewal equation with diffusion
Abstract: We consider a nonlinear age structured McKendrick-von Foerster
population model with diffusion term (MV-D). We prove the existence and
uniqueness of solution of the MV-D equation. We also prove the convergence
of the solution to its steady state as time tends to infinity using the generalized relative entropy inequality and Poincare Writinger type inequality.
We propose a numerical scheme for the linear MV-D equation. We discretize
the time variable to get a system of second order ordinary differential
equations. Convergence of the scheme is established using the stability
estimates by introducing Rothe’s function.
4:00pm
5:00pm
6:00pm
Time:
3:00pm-4:00pm
Location:
Room No. 216
Description:
Title: Estimating parameters of directional distributions
Abstract: Data related to spread of disease bacteria, wind directions, seasonal variations etc. can be represented by directional distributions. Langevin distribution is one of most commonly used directional distributions. We unify the results on admissibility, minimaxity and best equivariance of MLE of direction parameter. Various other estimators of direction parameter are compared with respect to robustness and asymptotic efficiency. Methods of improving estimators for spherical location are developed. Special applications to problems in restricted parameter spaces are given.
Time:
3:30pm-4:30pm
Location:
Mini conference room, Mathematics department
Description:
Title: Study of a nonlinear renewal equation with diffusion
Abstract: We consider a nonlinear age structured McKendrick-von Foerster
population model with diffusion term (MV-D). We prove the existence and
uniqueness of solution of the MV-D equation. We also prove the convergence
of the solution to its steady state as time tends to infinity using the generalized relative entropy inequality and Poincare Writinger type inequality.
We propose a numerical scheme for the linear MV-D equation. We discretize
the time variable to get a system of second order ordinary differential
equations. Convergence of the scheme is established using the stability
estimates by introducing Rothe’s function.