Two New Estimators of Entropy for Testing Normality

We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the existing entropy estimators. Also, we propose two new tests for normality based on the introduced entropy estimators and compare their powers with the powers of other tests for normality. The results show that the proposed estimators and test statistics perform very well in estimating entropy and testing normality. A real example is presented and analyzed.Comment: 28 page

Numerical Computing and Graphics for the Power Method Transformation Using Mathematica

This paper provides the requisite information and description of software that perform numerical computations and graphics for the power method polynomial transformation. The software developed is written in the Mathematica 5.2 package PowerMethod.m and is associated with fifth-order polynomials that are used for simulating univariate and multivariate non-normal distributions. The package is flexible enough to allow a user the choice to model theoretical pdfs, empirical data, or a user's own selected distribution(s). The primary functions perform the following (a) compute standardized cumulants and polynomial coefficients, (b) ensure that polynomial transformations yield valid pdfs, and (c) graph power method pdfs and cdfs. Other functions compute cumulative probabilities, modes, trimmed means, intermediate correlations, or perform the graphics associated with fitting power method pdfs to either empirical or theoretical distributions. Numerical examples and Monte Carlo results are provided to demonstrate and validate the use of the software package. The notebook Demo.nb is also provided as a guide for user of the power method.

A test of the predictive validity of non-linear QALY models using time trade-off utilities

This paper presents a test of the predictive validity of various classes of QALY models (i.e., linear, power and exponential models). We first estimated TTO utilities for 43 EQ-5D chronic health states and next these states were embedded in health profiles. The chronic TTO utilities were then used to predict the responses to TTO questions with health profiles. We find that the power QALY model clearly outperforms linear and exponential QALY models. Optimal power coefficient is 0.65. Our results suggest that TTO-based QALY calculations may be biased. This bias can be avoided using a power QALY model.Cost-utility analysis, QALYs, power QALY model, predictive validity, time tradeoff, Leex

Commercial real estate return distributions: a review of literature and empirical evidence

This paper review the literature on the distribution of commercial real estate returns. There is growing evidence that the assumption of normality in returns is not safe. Distributions are found to be peaked, fat-tailed and, tentatively, skewed. There is some evidence of compound distributions and non-linearity. Public traded real estate assets (such as property company or REIT shares) behave in a fashion more similar to other common stocks. However, as in equity markets, it would be unwise to assume normality uncritically. Empirical evidence for UK real estate markets is obtained by applying distribution fitting routines to IPD Monthly Index data for the aggregate index and selected sub-sectors. It is clear that normality is rejected in most cases. It is often argued that observed differences in real estate returns are a measurement issue resulting from appraiser behaviour. However, unsmoothing the series does not assist in modelling returns. A large proportion of returns are close to zero. This would be characteristic of a thinly-traded market where new information arrives infrequently. Analysis of quarterly data suggests that, over longer trading periods, return distributions may conform more closely to those found in other asset markets. These results have implications for the formulation and implementation of a multi-asset portfolio allocation strategy

Rainfall-Runoff Relationships and flow forecasting, Ogun river Nigeria

An excess or a lack of rainfall are the major causes of most hydrological hazards, and the need for a systematic approach to river flow forecasting based on rainfall is imperative, especially in Nigeria. A study was carried out on three major gauging stations of the Ogun river basin to determine the rainfall-discharge relationship and model equations for use in the basin and similar basins. Stream flow and rainfall data for at least seven consecutive years for each station were collected and analyzed. The rainfall-runoff data were subjected to linear, exponential and higher order analysis. Stream flow data were also fitted to normal, log-normal and log-Pearson Type III distributions. The selection of the appropriate probability distribution model for each gauging station was based on graphical comparisons between observed and predicted flows and goodness-of-fit tests using chi-square and probability correlation coefficients. Results show that model equations with logarithmic and exponential relationships between rainfall and discharge gave better and more realistic prediction estimates and can be used for the basin. It was determined that the peak discharges occurred when the rainfall values were at their maximum, and a distinct relationship between the discharge and rainfall exists at each of the gauging stations

Intrinsic data depth for Hermitian positive definite matrices

Nondegenerate covariance, correlation and spectral density matrices are necessarily symmetric or Hermitian and positive definite. The main contribution of this paper is the development of statistical data depths for collections of Hermitian positive definite matrices by exploiting the geometric structure of the space as a Riemannian manifold. The depth functions allow one to naturally characterize most central or outlying matrices, but also provide a practical framework for inference in the context of samples of positive definite matrices. First, the desired properties of an intrinsic data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally fast pointwise and integrated data depth functions that satisfy each of these requirements and investigate several robustness and efficiency aspects. As an application, we construct depth-based confidence regions for the intrinsic mean of a sample of positive definite matrices, which is applied to the exploratory analysis of a collection of covariance matrices associated to a multicenter research trial