We develop and evaluate analytic and bootstrap bias-corrected maximum likelihood estimators for the shape parameter in the Nakagami distribution. This distribution is widely used in a variety of disciplines, and the corresponding estimator of its scale parameter is trivially unbiased. We find that both “corrective” and “preventive” analytic approaches to eliminating the bias, to O(n), are equal...

In this paper we provide a complete analytic solution to a particular separable convex quadratic programming problem with bound and equality constraints. This study constitutes the generalization of prior papers in which additional simplifications were considered. We present an algorithm that leads to determination of the analytic optimal solution. We demonstrate that our algorithm is able to d...

The evolution of cosmic string networks is an interesting dynamical problem. The equations governing these networks are classical and fully specified, but the length scale at which cosmic string loops form has been uncertain to tens of orders of magnitude. Numerical simulations are limited in the range of length and time scales they can reach, while analytic methods have been limited by the non...

We present an analytic expression for the axis ratio distributions of triaxial dark matter halos. The ellipticity of a dark halo develops as a consequence of the filamentary nature of the cosmic web induced by the initial coherent tidal interactions. Adopting the picture, we derive both the minor-to-major and the conditional intermediate-to-major axis ratio distributions, and examine how they d...

A self-contained derivation of the IPESD models [Majda, A.J., Klein, R., 2003. Systematic multi-scale models for the tropics. J. Atmos. Sci. 60, 393–408] governing synoptic and planetary scale tropical flows is provided. This derivation demonstrates the analytic tractability of the model and the effect of zonally and meridionally tilted synoptic scale heating on the forcing of planetary scale f...

Abstract We update Halo Zeldovich Perturbation Theory (HZPT, [1]), an analytic model for the two-point statistics of dark matter, to describe halo and galaxy clustering, galaxy-matter cross-correlation on nonlinear scales. The correcting has Fourier transform, therefore is valid in both configuration space space. accurate at 2%-level or less P_mm (k< 1 h/Mpc), P_hm P_hh 2 P gm gg ξ mm (r>...