• Title, Summary, Keyword: normal distribution

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Some counterexamples of a skew-normal distribution

  • Zhao, Jun;Lee, Sang Kyu;Kim, Hyoung-Moon
    • Communications for Statistical Applications and Methods
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    • v.26 no.6
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    • pp.583-589
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    • 2019
  • Counterexamples of a skew-normal distribution are developed to improve our understanding of this distribution. Two examples on bivariate non-skew-normal distribution owning marginal skew-normal distributions are first provided. Sum of dependent skew-normal and normal variables does not follow a skew-normal distribution. Continuous bivariate density with discontinuous marginal density also exists in skew-normal distribution. An example presents that the range of possible correlations for bivariate skew-normal distribution is constrained in a relatively small set. For unified skew-normal variables, an example about converging in law are discussed. Convergence in distribution is involved in two separate examples for skew-normal variables. The point estimation problem, which is not a counterexample, is provided because of its importance in understanding the skew-normal distribution. These materials are useful for undergraduate and/or graduate teaching courses.

A Family of Truncated Skew-Normal Distributions

  • Kim, Hea-Jung
    • Communications for Statistical Applications and Methods
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    • v.11 no.2
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    • pp.265-274
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    • 2004
  • The paper extends earlier work on the skew-normal distribution, a family of distributions including normal, but with extra parameter to regulate skewness. The present work introduces a singly truncated parametric family that strictly includes a truncated normal distribution, and studies its properties, with special emphasis on the relation with bivariate normal distribution.

On the STSP Normal Distribution

  • Choi, Jeen-Kap
    • Journal of the Korean Data and Information Science Society
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    • v.16 no.2
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    • pp.451-456
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    • 2005
  • We introduce the standard two-sided power normal distribution and consider the relation between the probability in standard two-sided power distribution and the probability in standard two-sided power normal distribution and obtain the even moment of the special two-sided power normal distribution including the cases considered by Gupta and Nadarajah(2004)

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Further Applications of Johnson's SU-normal Distribution to Various Regression Models

  • Choi, Pilsun;Min, In-Sik
    • Communications for Statistical Applications and Methods
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    • v.15 no.2
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    • pp.161-171
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    • 2008
  • This study discusses Johnson's $S_U$-normal distribution capturing a wide range of non-normality in various regression models. We provide the likelihood inference using Johnson's $S_U$-normal distribution, and propose a likelihood ratio (LR) test for normality. We also apply the $S_U$-normal distribution to the binary and censored regression models. Monte Carlo simulations are used to show that the LR test using the $S_U$-normal distribution can be served as a model specification test for normal error distribution, and that the $S_U$-normal maximum likelihood (ML) estimators tend to yield more reliable marginal effect estimates in the binary and censored model when the error distributions are non-normal.

Estimating Suitable Probability Distribution Function for Multimodal Traffic Distribution Function

  • Yoo, Sang-Lok;Jeong, Jae-Yong;Yim, Jeong-Bin
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.21 no.3
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    • pp.253-258
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    • 2015
  • The purpose of this study is to find suitable probability distribution function of complex distribution data like multimodal. Normal distribution is broadly used to assume probability distribution function. However, complex distribution data like multimodal are very hard to be estimated by using normal distribution function only, and there might be errors when other distribution functions including normal distribution function are used. In this study, we experimented to find fit probability distribution function in multimodal area, by using AIS(Automatic Identification System) observation data gathered in Mokpo port for a year of 2013. By using chi-squared statistic, gaussian mixture model(GMM) is the fittest model rather than other distribution functions, such as extreme value, generalized extreme value, logistic, and normal distribution. GMM was found to the fit model regard to multimodal data of maritime traffic flow distribution. Probability density function for collision probability and traffic flow distribution will be calculated much precisely in the future.

Pedagogical Implications for Teaching and Learning Normal Distribution Curves with CAS Calculator in High School Mathematics (CAS 계산기를 활용한 고등학교 정규분포곡선의 교수-학습을 위한 시사점 탐구)

  • Cho, Cheong-Soo
    • Communications of Mathematical Education
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    • v.24 no.1
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    • pp.177-193
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    • 2010
  • The purpose of this study is to explore normal distribution in probability distributions of the area of statistics in high school mathematics. To do this these contents such as approximation of normal distribution from binomial distribution, investigation of normal distribution curve and the area under its curve through the method of Monte Carlo, linear transformations of normal distribution curve, and various types of normal distribution curves are explored with CAS calculator. It will not be ablt to be attained for the objectives suggested the area of probability distribution in a paper-and-pencil classroom environment from the perspectives of tools of CAS calculator such as trivialization, experimentation, visualization, and concentration. Thus, this study is to explore various properties of normal distribution curve with CAS calculator and derive from pedagogical implications of teaching and learning normal distribution curve.

Selecting probability distribution of event mean concentrations from paddy fields (논으로부터 배출되는 유량가중평균 수질농도의 적정 확률분포 선정)

  • Jung, Jaewoon;Choi, Dongho;Yoon, Kwangsik
    • Journal of Environmental Impact Assessment
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    • v.23 no.4
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    • pp.285-295
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    • 2014
  • In this study, we analyzed probability distribution of EMCs (Event Mean Concentration) of COD, TOC, T-N, T-P and SS from rice paddy fields and compared the mean values of observed EMCs and the median values of estimated EMCs ($EMC_{50}$) through probability distribution. The field monitoring was conducted during a period of four crop-years (from May 1, 2008, to September 30. 2011) in a rice cultivation area located in Emda-myun, Hampyeong gun, Jeollanam-do, Korea. Four probability distributions such as Normal, Log-normal, Gamma, and Weibull distribution were used to fit values of EMCs from rice paddy fields. Our results showed that the applicable probability distributions were Normal, Log-normal, and Gamma distribution for COD, and Normal, Log- Normal, Gamma and Weibull distribution for T-N, and Log-normal, Gamma and Weibull distribution for T-P and TOC, and Log-normal and Gamma distribution for SS. Log-normal and Gamma distributions were acceptable for EMCs of all water quality constituents(COD, TOC, T-N, T-P and SS). Meanwhile, mean value of observed COD was similar to median value estimated by the gamma distribution, and TOC, T-N, T-P, and SS were similar to median value estimated by log-normal distribution, respectively.

A Study on a Didactic Transposition Method and Students' Understanding for the Normal Distribution (정규분포에 대한 교수학적 변환 방식과 학생들의 이해 분석)

  • Shin, Bo-Mi
    • Journal of Educational Research in Mathematics
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    • v.22 no.2
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    • pp.117-136
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    • 2012
  • The goal of this study is to investigate a didactic transposition method of text books and high school students' understanding for the Normal Distribution. To accomplish this goal, framework descriptors were developed to analyse the didactic transposition method and interpret the students' understanding based on the Historico-Genetic process of the Normal Distribution, the meaning of the Normal Distribution as a scholarly knowledge and the results of previous studies on students' understanding for the Normal Distribution. This study presented several recommendations for instruction of the Normal Distribution according to the results of analysing the didactic transposition method and interpreting the students' understanding in terms of the developed framework.

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Characteristics of Probability Distribution of BOD Concentration in Anseong Stream Watershed (안성천 유역의 BOD농도 확률분포 특성)

  • Kim, Kyung Sub;Ahn, Taejin
    • Journal of Korean Society on Water Environment
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    • v.25 no.3
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    • pp.425-431
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    • 2009
  • It is very important to know the probability distribution of water-quality constituents for water-quality control and management of rivers and reservoirs effectively. The probability distribution of BOD in Anseong Stream was analyzed in this paper using Kolmogorov-Smirnov test which is widely used goodness-of-fit method. It was known that the distribution of BOD in Anseong Stream is closer to Log-normal, Gamma and Weibull distributions than Normal distribution. Normal distribution can be partially applied depending on significance level, but Log-normal, Gamma and Weibull distributions can be used in any significance level. Also the estimated Log-normal distribution of BOD at Jinwi3 station was to be compared with the measured in 2001, 2002 and 2003 years. It was revealed that the estimated probability distribution of BOD at Jinwi3 follows a theoretical distribution very well. The applicable probability distribution of BOD can be used to explain more rigorously and scientifically the achievement or violation of target concentration in TMDL(Total Maximum Daily Load).

Saddlepoint Approximation to the Linear Combination Based on Multivariate Skew-normal Distribution (다변량 왜정규분포 기반 선형결합통계량에 대한 안장점근사)

  • Na, Jonghwa
    • The Korean Journal of Applied Statistics
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    • v.27 no.5
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    • pp.809-818
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    • 2014
  • Multivariate skew-normal distribution(distribution that includes multivariate normal distribution) has been recently applied to many application areas. We consider saddlepoint approximation for a statistic of linear combination based on a multivariate skew-normal distribution. This approach can be regarded as an extension of Na and Yu (2013) that dealt saddlepoint approximation for the distribution of a skew-normal sample mean for a linear statistic and multivariate version. Simulations results and examples with real data verify the accuracy and applicability of suggested approximations.