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.

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 function.