The Research on Two Test Methods of the Normal Distribution

2013 ◽  
Vol 710 ◽  
pp. 772-774
Author(s):  
Jin Huang Wu ◽  
Jun Sheng Wang ◽  
Yi Dong Wang ◽  
Jun Wei Lei
Keyword(s):  
Standard Deviation ◽  
Normal Distribution ◽  
Coefficient Of Variation ◽  
Test Methods ◽  
Parent Population ◽  
Normal Parent ◽  
Characteristic Value ◽  
The Mean

The characteristic value of the normal parent population, such as the mean, the percentile, the percentage, the standard deviation and the coefficient of variation, are often tested in engineering. The Shapiro-Wilk test and Epps-Pulley test are established in this paper to get the characteristic value of the normal parent population, which can satisfy different practical requirements.

A Proof for Rhiel's Range Estimator of the Coefficient of Variation for Skewed Distributions

2007 ◽  
Vol 100 (1) ◽  
pp. 208-210 ◽  
Author(s):  
G. Steven Rhiel
Keyword(s):  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Research Study ◽  
Skewed Distributions ◽  
The Mean ◽  
Standard Deviations

In this research study is proof that the coefficient of variation ( CVhigh-low) calculated from the highest and lowest values in a set of data is applicable to specific skewed distributions with varying means and standard deviations. Earlier Rhiel provided values for dn, the standardized mean range, and an, an adjustment for bias in the range estimator of μ. These values are used in estimating the coefficient of variation from the range for skewed distributions. The dn and an values were specified for specific skewed distributions with a fixed mean and standard deviation. In this proof it is shown that the dn and an values are applicable for the specific skewed distributions when the mean and standard deviation can take on differing values. This will give the researcher confidence in using this statistic for skewed distributions regardless of the mean and standard deviation.

scholarly journals Statistical Analysis of Basketball Teams Through Normal Distribution and R Programming

2020 ◽  
Vol 4 (9) ◽  
Author(s):  
Megan Wang
Keyword(s):  
Statistical Analysis ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Normal Distribution ◽  
Sports Analytics ◽  
R Programming Language ◽  
General Improvement ◽  
The Mean ◽  
R Programming ◽  
Two Parameters

Basketball has existed for almost 130 years, becoming one of the most famous sports worldwide by affecting millions of lives and having national and global tournaments. With the general improvement of people's concern and love for sports competition, sports analytics’ role will become more prominent. Hence, this paper combines the relevant knowledge of statistics and typical basketball competition cases from NBA, expounding the application of statistics in sports competition. The paper first examines the importance of normal distribution (also called Gaussian distribution) in statistics through its probability density function and the function's graph. The function has two parameters: the mean for the maximum and standard deviation for the distance away from the mean[1]. By compiling datasets of past teams and individuals for their basketball performances and making simple calculations of their standard deviation and mean, the paper constructs normal distribution graphs using the R programming language. Finally, the paper examines the Real Plus-Minus value and its importance in basketball.

scholarly journals Properties of the Standard Deviation that are Rarely Mentioned in Classrooms

2016 ◽  
Vol 38 (3) ◽  
Author(s):  
Mohammad Fraiwan Al-Saleh ◽  
Adil Eltayeb Yousif
Keyword(s):  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Sample Variance ◽  
Mean Absolute Deviation ◽  
Hidden Information ◽  
Absolute Deviation ◽  
Sample Mean ◽  
The Mean ◽  
Vague Concept ◽  
Chebyshev's Inequality

Unlike the mean, the standard deviation ¾ is a vague concept. In this paper, several properties of ¾ are highlighted. These properties include the minimum and the maximum of ¾, its relationship to the mean absolute deviation and the range of the data, its role in Chebyshev’s inequality and the coefficient of variation. The hidden information in the formula itself is extracted. The confusion about the denominator of the sample variance being n ¡ 1 is also addressed. Some properties of the sample mean and varianceof normal data are carefully explained. Pointing out these and other properties in classrooms may have significant effects on the understanding and the retention of the concept.

SEA‐GRAVIMETER TRIALS ON THE HALIFAX TEST RANGE ABOARD CSS HUDSON, 1972

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 700-711 ◽  
Author(s):  
H. D. Valliant ◽  
J. Halpenny ◽  
R. Beach ◽  
R. V. Cooper
Keyword(s):  
Standard Deviation ◽  
Normal Distribution ◽  
Test Range ◽  
Simultaneous Test ◽  
The Mean ◽  
The Difference ◽  
Test Profiles ◽  
Gravity Test ◽  
Three Components

A simultaneous test of a LaCoste and Romberg and a Graf‐Askania sea gravimeter was made over the Halifax Gravity Test Range aboard CSS Hudson in 1972. The test consisted of a total of 33 traverses over precisely located and calibrated test profiles established for this purpose. If errors are defined as the difference between surface and underwater values compared on a common datum, the mean LaCoste gravimeter error observed during a traverse varied from run‐to‐run to form a near normal distribution with mean of 1.8 mgal and standard deviation of 1.0 mgal. The corresponding statistics for the Askania are 2.1 mgal and 3.4 mgal, respectively, with the distribution markedly skew. The data were correlated with three components of accelerations as measured by the LaCoste and Romberg inertial platform. No significant correlation was evident for the LaCoste meter. Some correlation for the Graf‐Askania data, to which crosscoupling corrections are not normally applied, was observed.

Correction for Rhiel's Theory for the Range Estimator of the Coefficient of Variation for Skewed Distributions

2010 ◽  
Vol 106 (1) ◽  
pp. 93-94
Author(s):  
G. Steven Rhiel
Keyword(s):  
Standard Deviation ◽  
Correction Factor ◽  
Coefficient Of Variation ◽  
Unbiased Estimate ◽  
Correction Factors ◽  
Skewed Distributions ◽  
The Mean

In 2007, Rhiel presented a technique to estimate the coefficient of variation from the range when sampling from skewed distributions. To provide an unbiased estimate, a correction factor ( an) for the mean was included. Numerical correction factors for a number of skewed distributions were provided. In a follow-up paper, he provided a proof he claimed showed the correction factor was independent of the mean and standard deviation, making the factors useful as these parameters vary; however, that proof did not establish independence. Herein is a proof which establishes the independence.

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