The probability density function is a fundamental concept in statistics. Specifying the density function f of a random variable X on Ω gives a natural description of the distribution of X on the universe Ω. When it cannot be specified, an estimate of this density may be performed by using a sample of n observations independent and identically distributed (X1, ..., Xn) of X . Histogram is the ol...

denote the order statistics, and let (1) Fn(x) 1 n-L l[xiSx) for-00 < x < 00 n i=l denote the empirical df; here 1.4 denotes the indicator function of the set A. Then (2) is called the empirical process.

This paper reviews the method of model-fitting via the empirical characteristic function. The advantage of using this procedure is that one can avoid difficulties inherent in calculating or maximizing the likelihood function. Thus it is a desirable estimation method when the maximum likelihood approach encounters difficulties but the characteristic function has a tractable expression. The basic...

We propose a novel method for blind separation of statistically independent sources. The objective function used in the separation is based on the fact that the joint characteristic function factors to a product of the characteristic functions of the independent marginals. New algorithm for minimizing the above criterion is derived as well. It estimates the separating matrix by ensuring that th...

We introduce two nonparametric independent component analysis (ICA) criteria based on factorization of characteristic functions. This approach has potential to separate wide class of distributions because characteristic function always exists. A simple criterion allowing for efficient search of the separating matrix and a more advanced criterion possessing desirable consistency property are pre...

Let M be the interior of a compact 3–manifold with boundary, and let T be an ideal triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures, semi–angle structures and generalised angle structures on (M ;T ) respectively in terms of a generalised Euler characteristic function on the solution space of the normal surface theory of (M ; T )....

The reliability and validity of standard and qualitative scores for the Ruff Figural Fluency Test (RFFT; Ruff, 1988) was examined in 102 healthy undergraduates. Participants (M age = 21.79; SD = 3.7; age = 80% Caucasian) were administered the RFFT and measures assessing executive functions (EF) and other cognitive domains. Inter-scorer reliability was excellent (0.9 range) for most RFFT indices...

We review the most recent developments in the area of testing by the empirical characteristic function. Our main focus is on goodness-of-fit tests based on i.i.d. observations, but we also refer to testing for symmetry and testing for independence.

Jiang, Dickey, and Kuo [12] gave the multivariate c-characteristic function and showed that it has properties similar to those of the multivariate Fourier transformation. We first give the multivariate c-characteristic function of a random functional of a Ferguson-Dirichlet process over the unit sphere. We then find out its probability density function using properties of the multivariate c-cha...

The paper investigates vanishing conditions on the first cohomology module of a normalized rank 2 vector bundle F on P which force F to split. The present vanishing conditions improve other conditions known in the literature and are obtained with simple computations on the Euler characteristic function, avoiding the speciality lemma and other heavy tools.