scholarly journals Exact bounds on the closeness between the Student and standard normal distributions

2015 ◽  
Vol 19 ◽  
pp. 24-27 ◽  
Author(s):  
Iosif Pinelis
Keyword(s):  
Normal Distributions ◽  
Standard Normal ◽  
Exact Bounds

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} .

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 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.

Standard tables of truncated standard normal distribution using a new summarizing method

2018 ◽  
Vol 15 (2) ◽  
pp. 216-247
Author(s):  
Mohammad M. Hamasha ◽  
Mohammad Al-Rabayah ◽  
Faisal Aqlan
Keyword(s):  
Normal Distribution ◽  
Linear Interpolation ◽  
Standard Normal Distribution ◽  
Truncated Normal Distribution ◽  
Content Type ◽  
Normal Distributions ◽  
Population Distributions ◽  
Wide Range ◽  
Standard Normal ◽  
Truncated Normal

Purpose The single- and double-sided truncated normal distributions have been used in a wide range of engineering fields. However, most of the previous research works have focused primarily on the non-truncated population distributions. The authors present reference tables to estimate the values of density and cumulative density functions of truncated normal distribution for practitioners. Finally, the authors explain how to use the tables to estimate other properties, such as mean, median and variance. The purpose of this paper is to provide an efficient method to summarize tables, and furthermore, to provide readers with statistical tables on truncated standard normal distribution. Design/methodology/approach A new methodology is developed to summarize the tables with ordered values. The introduced method allows for the reduction of the number of pages required for such tables into a reasonable level by using linear interpolation. Moreover, it allows for the estimation of the required truncation values accurately with an error value less than 0.005. Findings The data in the tables can be summarized into a significantly reduced amount. The new summarized table can be designed for any number of pages and/or level of error wanted. However, with reducing the level of error, the number of pages increases and vice versa. Originality/value The value of this work is through two major points. First, all provided summarized tables in the literature are for single-sided and symmetry truncation cases. However, there is no attempt to summarize the tables of the asymmetry truncation normal distribution due to the requirement of huge number of pages. In this paper, the case of asymmetry truncation is included. Second, the methodology provided in this research can be used to summarize similar large tables.

Normal Distributions

1989 ◽  
Author(s):  
Teresa M. Amabile
Keyword(s):  
Normal Distributions

Distribution of in vivo insulin action in Pima Indians as mixture of three normal distributions

Diabetes ◽  
1989 ◽  
Vol 38 (11) ◽  
pp. 1423-1432 ◽  
Author(s):  
C. Bogardus ◽  
S. Lillioja ◽  
B. L. Nyomba ◽  
F. Zurlo ◽  
B. Swinburn ◽  
...  
Keyword(s):  
Insulin Action ◽  
Pima Indians ◽  
Normal Distributions

Sebaran Peluang Acak Kontinu, Distribusi Normal, Distribusi Normal Baku, Distribusi T, Distribusi Chi Square, dan Distribusi F

2020 ◽  
Author(s):  
Ahmad Sudi Pratikno
Keyword(s):  
Hypothesis Test ◽  
Standard Normal Distribution ◽  
Process Data ◽  
Nominal Data ◽  
Chi Square ◽  
Stable Curve ◽  
Standard Normal ◽  
Research Findings ◽  
F Distribution ◽  
T Distribution

In statistics, there are various terms that may feel unfamiliar to researcher who is not accustomed to discussing it. However, despite all of many functions and benefits that we can get as researchers to process data, it will later be interpreted into a conclusion. And then researcher can digest and understand the research findings. The distribution of continuous random opportunities illustrates obtaining opportunities with some detection of time, weather, and other data obtained from the field. The standard normal distribution represents a stable curve with zero mean and standard deviation 1, while the t distribution is used as a statistical test in the hypothesis test. Chi square deals with the comparative test on two variables with a nominal data scale, while the f distribution is often used in the ANOVA test and regression analysis.

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