On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Classification of Texts' Authorship Using a Regression Model on Compressed Data

2010 Mathematics Subject Classification: 68T50,62H30,62J05.

Group Comparisons on Cognitive Attributes Using the Least Squares Distance Model of Cognitive Diagnosis

2010 Mathematics Subject Classification: 62P15.

Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

Lp Microlocal Supercritical Markov Branching Processes with Non-Homogeneous Poisson Immigration

2010 Mathematics Subject Classification: 60J80.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

On Estimation and Testing for Pareto Tails

2010 Mathematics Subject Classification: 62F10, 62F12.

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.

On the Poisson Process of Order k Space

2010 Mathematics Subject Classification: 60E05, 62P05.

Minimum Description Length Principle in Discriminating Marginal Distributions

2010 Mathematics Subject Classification: 94A17, 62B10, 62F03.