DS Normal Distribution: Properties and Applications

2021 ◽  
Vol 42 (12) ◽  
pp. 2980-2999
Author(s):  
P. Sulewski
Keyword(s):  
Normal Distribution

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

Interrelations of Thrombo-Embolic Diseases and Blood-Group Distribution

1963 ◽  
Vol 09 (02) ◽  
pp. 472-474 ◽  
Author(s):  
W Dick ◽  
W Schneider ◽  
K Brockmüller ◽  
W Mayer
Keyword(s):  
Normal Distribution ◽  
Blood Group ◽  
Blood Groups ◽  
The Other ◽  
Other Hand ◽  
Group Distribution

SummaryA comparison between the repartition of the blood groups in 461 patients suffering from thromboembolic disorders and the normal distribution has shown a statistically ascertained predominance of the group A1. On the other hand the blood groups 0 and A2 are distinctly less frequent than in the normal distribution.

Bankruptcy Model Construction and its Limitation in Input Data Quality

2019 ◽  
Vol 10 (2) ◽  
pp. 117-125
Author(s):  
Dana Kubíčková ◽  
◽  
Vladimír Nulíček ◽  
Keyword(s):  
Data Quality ◽  
Normal Distribution ◽  
Input Data ◽  
Model Construction ◽  
The Third ◽  
Third Stage ◽  
Discriminant Analyses ◽  
One Year ◽  
The University ◽  
Multivariate Discriminant

The aim of the research project solved at the University of Finance and administration is to construct a new bankruptcy model. The intention is to use data of the firms that have to cease their activities due to bankruptcy. The most common method for bankruptcy model construction is multivariate discriminant analyses (MDA). It allows to derive the indicators most sensitive to the future companies’ failure as a parts of the bankruptcy model. One of the assumptions for using the MDA method and reassuring the reliable results is the normal distribution and independence of the input data. The results of verification of this assumption as the third stage of the project are presented in this article. We have revealed that this assumption is met only in a few selected indicators. Better results were achieved in the indicators in the set of prosperous companies and one year prior the failure. The selected indicators intended for the bankruptcy model construction thus cannot be considered as suitable for using the MDA method.

Analytical Representation of the Density Function of Normal Distribution of Noise

2015 ◽  
Vol 47 (8) ◽  
pp. 24-40 ◽  
Author(s):  
Telman Abbas ogly Aliev ◽  
Naila F. Musaeva ◽  
Matanat Tair kyzy Suleymanova ◽  
Bahruz Ismail ogly Gazizade
Keyword(s):  
Normal Distribution ◽  
Density Function ◽  
Analytical Representation

Technology for Calculating the Parameters of the Density Function of the Normal Distribution of the Useful Component in a Noisy Process

2016 ◽  
Vol 48 (4) ◽  
pp. 39-55 ◽  
Author(s):  
Telman Abbas ogly Aliev ◽  
Naila Fuad kyzy Musaeva ◽  
Matanat Tair kyzy Suleymanova ◽  
Bahruz Ismail ogly Gazizade
Keyword(s):  
Normal Distribution ◽  
Density Function

Variable Precision Depth Encoding for 3D Range Geometry Compression

2020 ◽  
Vol 2020 (17) ◽  
pp. 34-1-34-7
Author(s):  
Matthew G. Finley ◽  
Tyler Bell
Keyword(s):  
Normal Distribution ◽  
Arbitrary Distribution ◽  
File Size ◽  
Geometry Compression ◽  
Variable Precision ◽  
Wide Range ◽  
Novel Method ◽  
Encoding Method ◽  
Rgb Image ◽  
Color Channels

This paper presents a novel method for accurately encoding 3D range geometry within the color channels of a 2D RGB image that allows the encoding frequency—and therefore the encoding precision—to be uniquely determined for each coordinate. The proposed method can thus be used to balance between encoding precision and file size by encoding geometry along a normal distribution; encoding more precisely where the density of data is high and less precisely where the density is low. Alternative distributions may be followed to produce encodings optimized for specific applications. In general, the nature of the proposed encoding method is such that the precision of each point can be freely controlled or derived from an arbitrary distribution, ideally enabling this method for use within a wide range of applications.

Verification of the Calculation Assumptions Applied to Solutions of the Acoustic Measurements Uncertainty

2015 ◽  
Vol 39 (2) ◽  
pp. 199-202
Author(s):  
Wojciech Batko ◽  
Renata Bal
Keyword(s):  
Normal Distribution ◽  
Confidence Intervals ◽  
Uncertainty Of Measurement ◽  
Acoustic Measurements ◽  
Uncertainty In Measurement ◽  
Sound Levels ◽  
Measurement Results ◽  
Analysis Of Results ◽  
Essential Problem ◽  
Expression Of Uncertainty

Abstract The assessment of the uncertainty of measurement results, an essential problem in environmental acoustic investigations, is undertaken in the paper. An attention is drawn to the - usually omitted - problem of the verification of assumptions related to using the classic methods of the confidence intervals estimation, for the controlled measuring quantity. Especially the paper directs attention to the need of the verification of the assumption of the normal distribution of the measuring quantity set, being the base for the existing and binding procedures of the acoustic measurements assessment uncertainty. The essence of the undertaken problem concerns the binding legal and standard acts related to acoustic measurements and recommended in: 'Guide to the expression of uncertainty in measurement' (GUM) (OIML 1993), developed under the aegis of the International Bureau of Measures (BIPM). The model legitimacy of the hypothesis of the normal distribution of the measuring quantity set in acoustic measurements is discussed and supplemented by testing its likelihood on the environment acoustic results. The Jarque-Bery test based on skewness and flattening (curtosis) distribution measures was used for the analysis of results verifying the assumption. This test allows for the simultaneous analysis of the deviation from the normal distribution caused both by its skewness and flattening. The performed experiments concerned analyses of the distribution of sound levels: LD, LE, LN, LDWN, being the basic noise indicators in assessments of the environment acoustic hazards.

Sign in / Sign up

Export Citation Format

Share Document