scholarly journals A Test for Normality in the Presence of Outliers

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Pooi Ah Hin ◽  
Soo Huei Ching
Keyword(s):  
Random Sample ◽  
Normal Population ◽  
Acceptance Region ◽  
Original Population ◽  
Normal Distributions ◽  
Normality Assumption ◽  
Standard Normal ◽  
The Given ◽  
Test For Normality

The Jarque-Bera test is a test based on the coefficients of skewness (S) and kurtosis (K) for testing whether the given random sample is from a normal population. When the random sample of size n contains m outliers, we use the remaining n-m observations to compute two statistics S* and K* which mimic the statistics S and K. The statistics S* and  K* are next  transformed to z1 and z2 which are uncorrelated and having standard normal distributions when the original population is normal. We show that the acceptance region given by a circle in the (z1, z2) plane is suitable for testing the normality assumption.

New multivariate process capability indices for measuring the performance of multivariate processes subject to non-normal distributions

2015 ◽  
Vol 33 (1) ◽  
pp. 42-61 ◽  
Author(s):  
Jeh-Nan Pan ◽  
Chung-I Li ◽  
Wei-Chen Shih
Keyword(s):  
Process Capability ◽  
Process Capability Indices ◽  
Process Data ◽  
Multivariate Process ◽  
Multivariate Processes ◽  
Content Type ◽  
Normal Distributions ◽  
Normality Assumption ◽  
Capability Indices ◽  
Multivariate Manufacturing

Purpose – In the past few years, several capability indices have been developed for evaluating the performance of multivariate manufacturing processes under the normality assumption. However, this assumption may not be true in most practical situations. Thus, the purpose of this paper is to develop new capability indices for evaluating the performance of multivariate processes subject to non-normal distributions. Design/methodology/approach – In this paper, the authors propose three non-normal multivariate process capability indices (MPCIs) RNMC p , RNMC pm and RNMC pu by relieving the normality assumption. Using the two normal MPCIs proposed by Pan and Lee, a weighted standard deviation method (WSD) is used to modify the NMC p and NMC pm indices for the-nominal-the-best case. Then the WSD method is applied to modify the multivariate ND index established by Niverthi and Dey for the-smaller-the-better case. Findings – A simulation study compares the performance of the various multivariate indices. Simulation results show that the actual non-conforming rates can be correctly reflected by the proposed capability indices. The numerical example further demonstrates that the actual quality performance of a non-normal multivariate process can properly reflected by the proposed capability indices. Practical implications – Process capability index is an important SPC tool for measuring the process performance. If the non-normal process data are mistreated as a normal one, it will result in an improper decision and thereby lead to an unnecessary quality loss. The new indices can provide practicing managers and engineers with a better decision-making tool for correctly measuring the performance for any multivariate process or environmental system. Originality/value – Once the existing multivariate quality/environmental problems and their Key Performance Indicators are identified, one may apply the new capability indices to evaluate the performance of various multivariate processes subject to non-normal distributions.

A nomogram to estimate the size for a random sample from a normal population for mean

1977 ◽  
Vol 114 (6) ◽  
pp. 475-478
Author(s):  
A. K. Awasthi ◽  
Surendar Kumar
Keyword(s):  
Random Sample ◽  
Normal Population

SummaryA method is presented using a nomogram to estimate the size of a random sample from a normal population.

scholarly journals Agglutinins found in the Serum of Subjects inoculated with Typhoid-Paratyphoid Vaccine

1933 ◽  
Vol 33 (3) ◽  
pp. 387-395 ◽  
Author(s):  
George Giglioli
Keyword(s):  
Random Sample ◽  
Normal Population ◽  
Preceding Paper ◽  
British Guiana ◽  
Cause Of Error

In the preceding paper (1933) I have recorded the results of an investigation on typhoid-paratyphoid agglutinins in a random sample of the normal population of British Guiana. It has been shown what a serious cause of error these “natural” agglutinins may represent in the carrying out of routine serological work in certain countries.

Traces of Matrix Products

2014 ◽  
Vol 27 ◽  
Author(s):  
John Greene
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Normal Distributions ◽  
Matrix Products ◽  
Standard Normal

Given two noncommuting matrices, A and B, it is well known that AB and BA have the same trace. This extends to cyclic permutations of products of A’s and B’s. It is shown here that for 2×2 matrices A and B, whose elements are independent random variables with standard normal distributions, the probability that Tr(ABAB) > Tr(AB) is exactly 1/\sqrt{2} .

IQ and Child Psychiatric Disorder

1982 ◽  
Vol 27 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Joseph H. Beitchman ◽  
Pat Patterson ◽  
Bob Gelfand ◽  
Gillian Minty
Keyword(s):  
Psychiatric Disorder ◽  
Clinical Sample ◽  
Normal Population ◽  
Verbal Iq ◽  
Child Psychiatric ◽  
Child Psychiatric Disorder ◽  
Care Facilities ◽  
Treatment Centre ◽  
Standard Normal ◽  
Iq Scores

The WISC-RIQ scores of 85 children between 7 and 12 years of age taken from the inpatient, outpatient and day care facilities of a Regional Treatment Centre were compared with the expected IQ scores of the standard normal population. In addition, analysis of variance techniques were used to test for an association between IQ variables and seven operationally defined symptom subtypes taken from the child's chart. Significant differences between the clinical sample and the standard normal population were found for the distribution and means for full scale IQ and verbal IQ but not performance IQ. In addition, significant associations were found between FSIQ and the level of aggressive symptoms, and between VIQ and the level of hyperkinetic and aggressive symptom subtypes. The importance of IQ variables and in particular VIQ in understanding the nature of childhood psychiatric disorder is emphasized. The implications of these findings for educational policy are discussed.

scholarly journals The property changes of ammunition elements due to the exploitation time

2015 ◽  
Vol 36 (1) ◽  
pp. 91-104
Author(s):  
Dariusz Ampuła
Keyword(s):  
Gamma Distribution ◽  
Research Methodology ◽  
Probability Distributions ◽  
Test Results ◽  
Normal Distributions ◽  
Standard Normal ◽  
Evaluation Module ◽  
Property Changes ◽  
Two Parameters ◽  
The Way

Abstract The way carry out of analysis concerning correctness working of evaluation module proposed in functioning research methodology, chosen features elements of artillery fuses was presented in the article. Probability distributions of the aptitude time of tested ammunition elements were applied for verification of undertaken post diagnostic decisions. The analysis of test results chosen fuses elements, based on the standard normal distributions were executed, further the graphic interpretations of these distributions were made. A measurement of the strength of resistance decline of the side-bolt spring was chosen for the analysis, as a way of checking MG-37 and MG-57 fuse types features. Furthermore, the author presents an illustrative comparison of normal distributions, which confirms that post diagnostic decisions had been undertaken correctly. The graphic interpretations of analyzed test results of MG-37 fuse elements type were executed by means of two-parameters gamma distribution in the comparison. Concise conclusions confirming the correctness of functioning of evaluation module in the research methodology were introduced at the end of the article.

scholarly journals Generation of pseudo-random numbers with the use of inverse chaotic transformation

2018 ◽  
Vol 16 (1) ◽  
pp. 16-22
Author(s):  
Marcin Lawnik
Keyword(s):  
Cumulative Distribution Function ◽  
Chaotic Maps ◽  
Continuous Distribution ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Standard Normal Distribution ◽  
Random Numbers ◽  
Simulation And Modeling ◽  
Standard Normal ◽  
The Given

AbstractIn (Lawnik M., Generation of numbers with the distribution close to uniform with the use of chaotic maps, In: Obaidat M.S., Kacprzyk J., Ören T. (Ed.), International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH) (28-30 August 2014, Vienna, Austria), SCITEPRESS, 2014) Lawnik discussed a method of generating pseudo-random numbers from uniform distribution with the use of adequate chaotic transformation. The method enables the “flattening” of continuous distributions to uniform one. In this paper a inverse process to the above-mentioned method is presented, and, in consequence, a new manner of generating pseudo-random numbers from a given continuous distribution. The method utilizes the frequency of the occurrence of successive branches of chaotic transformation in the process of “flattening”. To generate the values from the given distribution one discrete and one continuous value of a random variable are required. The presented method does not directly involve the knowledge of the density function or the cumulative distribution function, which is, undoubtedly, a great advantage in comparison with other well-known methods. The described method was analysed on the example of the standard normal distribution.

Estimating Precision in Heat Rate Testing

1974 ◽  
Vol 96 (3) ◽  
pp. 223-227
Author(s):  
W. H. Rousseau ◽  
E. L. Milgram
Keyword(s):  
Normal Population ◽  
Heat Rate ◽  
Normal Distributions ◽  
All Solutions ◽  
Rate Testing

Obtaining an estimate of the precision realized in heat rate testing is discussed in this paper. Heat rate precision depends largely on the scatter of the most important measurements, so we examine their scatter. All solutions proposed are based on the assumption that the data arise from a normal population, although answers are also useful for near-normal distributions. We propose a three-part procedure designed to ensure the gathering of data of a given precision with a given confidence. The procedure should fit easily into the test engineer’s routine.

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