The first method we shall study for solving differential equations is called Euler's method, it serves to illustrate the concepts involved in the advanced methods. It has limited use because of the larger error that is accumulated with each successive step. However, it is important to study Euler's method because the remainder term and error analysis is easier to understand. Theorem (Euler's Me...

Abstract: This survey article discusses the main concepts and techniques of Stein’s method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and also its relation to concentration of measure inequalities. The material is presented at a level accessible to beginning graduate students studying probability with the main emphasis on the themes that a...

Assouad’s method provides a somewhat different technique for proving lower bounds. Instead of reducing the estimation problem to a multiple hypothesis test or simpler estimation problem, as with Le Cam’s method and Fano’s method from the preceding lectures, here we transform the original estimation problem into multiple binary hypothesis testing problems, using the structure of the problem in a...

Introduction. Whitham's averaged equations [1] for a nonlinear evolution system describe slow modulations of parameters on a family of periodic traveling wave solutions (or on families of multiphase quasiperiodic solutions, which are so far knows to exist only for integrable equations) and are a system of hydrodynamic type [2, 3], that is, of the form

aging declines abilities and leads to increased risk of falling and subsequently poorer quality of life. the objective of this study was to identify a proper assessment for risk of falling among institutionalized elderly. in order to accomplish this aim, two functional assessment methods, berg scale and tinetti scale, were used and the validity indices of these methods were calculated. prospect...

Abstract. This study introduces a new approach to problem of estimating parameter(s) of a given copula. More precisely, using the concept of the generalized linear models (GLM) accompanied with least square method, we introduce an estimation method, say GLM-method. A simulation study has been conducted to provide a omparison among the inversion of Kendal’s tau, the inversion of Spearman’s rho,...