Search results for "Normal Distribution"
showing 10 items of 135 documents
Probabilities in Risk Management
2014
A project is generally a complex undertaking in which most things are uncertain (durations, costs, project and suppliers performance, weather, soil geology, public reaction, etc.), and thus, risk permeates everything. Risk is closely related to uncertainty, and the latter with probabilities and distributions the conceptual aspects of which are explained in Chap. 9. It is inconceivable to address risk without considering probabilities of occurrence, and the measures that must be taken to prevent or mitigate risk; in that sense, the ‘buffer’ concept is introduced. In Chap. 2, a comparison was mentioned between CPM, PERT and MC; now, Chap. 3 proposes a case for numerically demonstrating the ad…
Project During Execution – Strategy – Updating
2014
This chapter fundamentally examines project performance during its execution period, however, risk must always be considered, especially at the very beginning of the project when the risk is normally maximum, and at each update. In the Project Monitoring stage, this chapter explores what happens with foreseen risks, that is, if they really happened or not and their consequences. In the Project Control stage, the chapter uses Earned Value Analysis and examines Performance Factors, which are used to predict completion regarding time and cost. However, because these calculations are based on past performance, there is always the risk that this performance will not be replicated in the future, …
A Synthetic Approach to Multivariate Normal Clustering
1982
Two methods have been suggested for grouping together observations originated from the same multivariate normal distributions, both based on a maximum-likelihood (ML) estimation, but leading to different conclusions. In this paper we compare the use of Day’s approach and that of Scott and Symons in clustering procedures from the theoretical and computational point of view. Based on this comparison, we suggest an approach unifying those approaches. The workability of the approach will be verified by numerical experiments.
Error calculation for the PSA quotient.
2008
Abstract Objective Prostate specific antigen (PSA) assays have significant measurement errors, but the error associated with the PSA quotient (free to total PSA) often remains unknown. Methods We used both Gaussian error calculation and measurement of imprecision to investigate the level of error associated with the PSA quotient. Results Surprisingly, we found that the error of the PSA quotient at low levels is markedly smaller than that of the total PSA value. Conclusions The PSA quotient should be calculated and considered as a clinically relevant value.
Scene-based spectral calibration assessment of high spectral resolution imaging spectrometers
2009
An accurate knowledge of the spectral calibration of imaging spectrometers is required for optimum data processing and interpretation. The scene-based spectral characterization of imaging spectrometers is frequently necessary to update or replace the pre-flight laboratory-based spectral characterization supplied by the data provider. An automatic method for the estimation of spectral calibration parameters (channel position and bandwidth) at atmospheric absorption regions from high spectral resolution imaging spectrometers (spectral sampling interval below 5 nm) is presented in this contribution. The method has been tested on two commercial instruments with spectral sampling intervals below…
NRTK, PPP or Static, That Is the Question. Testing Different Positioning Solutions for GNSS Survey
2021
Worldwide, the determination of the coordinates from a Global Navigation Satellite System (GNSS) survey (in Network Real Time Kinematic, Precise Point Positioning, or static mode) has been analysed in several scientific and technical applications. Many of those have been carried out to compare Precise Point Positioning (PPP), Network Real Time Kinematic (NRTK), and static modes’ solutions, usually, using the latter as the true or the most plausible solution. This approach is not always possible as the static mode solution depends on several parameters (baseline length, acquisition time, ionospheric, and tropospheric models, etc.) that must be considered to evaluate the accuracy of the metho…
Non-Gaussian Distribution for Var Calculation
2003
Publisher Summary This chapter compares different approaches to computing Value-at-Risk (VaR) for heavy tailed return series. Each model has been submitted to a backtest analysis. The most representative asset returns of the Italian stock market and the exchange rates for the major currencies are used. The results obtained confirm that when the percentiles are below 5%, the hypothesis of normality of the conditional return distribution determines intervals of confidence whose forecast ability is low. In fact, it is observed that the return distributions are asymmetric and leptokurtic and the hypothesis of normality is usually rejected when subject to statistical test. Among the alternative …
Two-stage adaptive designs with correlated test statistics.
2005
When performing a trial using an adaptive sequential design, it is usually assumed that the data for each stage come from different units; for example, patients. However, sometimes it is not possible to satisfy this condition or to check whether it is satisfied. In these cases, the test statistics and p-values of each stage may be dependent. In this paper we investigate the type I error of two-stage adaptive designs when the test statistics from the stages are assumed to be bivariate normal. Analytical considerations are performed under the restriction that the conditional error function is constant in the continuation region. We show that the decisions can become conservative as well as an…
Multivariate equivalence tests for use in pharmaceutical development.
2014
Statistical equivalence analyses are well-established parts of many studies in the biomedical sciences. Also in pharmaceutical development and manufacturing equivalence testing methods are required in order to statistically establish similarities between machines, process components, or complete processes. This article presents a choice of multivariate equivalence testing procedures for normally distributed data as generalizations of existing univariate methods. In all derived methods, variability is interpreted as nuisance parameter. The use of the proposed methods in pharmaceutical development is demonstrated with a comparative analysis of dissolution profiles.
Kullback-Leibler distance as a measure of the information filtered from multivariate data
2007
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown. We propose to make use of the Kullback-Leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures. We also show how to use this distance to measure the stability of filtering procedures with respect to s…