Weak convergence of the least concave majorant of estimators for a concave distribution function

The Concave Majorant of Brownian Motion

The distribution of the maximal difference between Brownian bridge and its concave majorant

We provide a representation of the maximal difference between a standard Brownian bridge and its concave majorant on the unit interval, from which we deduce expressions for the distribution and density functions and moments of this difference. This maximal difference has an application in nonparametric statistics where it arises in testing monotonicity of a density or regression curve.

CFD Study of Concave Turbine

Computational fluid dynamics (CFD) is a powerful numerical tool that is becoming widely used to simulate many processes in the industry. In this work study of the stirred tank with 7 types of concave blade with CFD was presented. In the modeling of the impeller rotation, sliding mesh (SM) technique was used and RNG-k-ε model was selected for turbulence. Power consumption in various speeds in th...

The Sugeno fuzzy integral of concave functions

The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES BY CHARLES

R d is log-concave if p = e where φ :Rd → [−∞,∞) is concave. We denote the class of all such densities p on R by Pd,0. Log-concave densities are always unimodal and have convex level sets. Furthermore, log-concavity is preserved under marginalization and convolution. Thus, the classes of log-concave densities can be viewed as natural nonparametric extensions of the class of Gaussian densities. ...