Davenport's Value and Distribution

Value distribution and potential theory

We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: extensions of Picard’s theorems to quasiregular maps between Riemannian manifolds, a version of the Second Main Theorem of Nevanlinna for curves in projective space and non-linear divisors, description of extremal function...

Value Distribution Of

Normal Distribution, "p" Value and Confidence Intervals.

W data is col lected, in order to make sense of it, the data needs to be organised in a manner which shows the various values and the frequencies at which these values have occurred, that is the “pattern that the values form after they are organised” and this is called a distribution. A distribution guides how raw data can be converted into meaningful information and also influences the choice ...

Some results on value distribution of the difference operator

In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

Generalized Extreme Value Distribution and Extreme Economic Value at Risk (EE-VaR) October 2007 Generalized Extreme Value Distribution and Extreme Economic Value at Risk (EE-VaR)

Ait-Sahalia and Lo (2000) and Panigirtzoglou and Skiadopoulos (2004) have argued that Economic VaR (E-VaR), calculated under the option market implied risk neutral density is a more relevant measure of risk than historically based VaR. As industry practice requires VaR at high confidence level of 99%, we propose Extreme Economic Value at Risk (EE-VaR) as a new risk measure, based on the General...