• Title/Summary/Keyword: normal distribution fit

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Goodness-of-fit test for normal distribution based on parametric and nonparametric entropy estimators (모수적 엔트로피 추정량과 비모수적 엔트로피 추정량에 기초한 정규분포에 대한 적합도 검정)

  • Choi, Byungjin
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.4
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    • pp.847-856
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    • 2013
  • In this paper, we deal with testing goodness-of-fit for normal distribution based on parametric and nonparametric entropy estimators. The minimum variance unbiased estimator for the entropy of the normal distribution is derived as a parametric entropy estimator to be used for the construction of a test statistic. For a nonparametric entropy estimator of a data-generating distribution under the alternative hypothesis sample entropy and its modifications are used. The critical values of the proposed tests are estimated by Monte Carlo simulations and presented in a tabular form. The performance of the proposed tests under some selected alternatives are investigated by means of simulations. The results report that the proposed tests have better power than the previous entropy-based test by Vasicek (1976). In applications, the new tests are expected to be used as a competitive tool for testing normality.

A Goodness of Fit Tests Based on the Partial Kullback-Leibler Information with the Type II Censored Data

  • Park, Sang-Un;Lim, Jong-Gun
    • Proceedings of the Korean Statistical Society Conference
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    • 2003.10a
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    • pp.233-238
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    • 2003
  • Goodness of fit test statistics based on the information discrepancy have been shown to perform very well (Vasicek 1976, Dudewicz and van der Meulen 1981, Chandra et al 1982, Gohkale 1983, Arizona and Ohta 1989, Ebrahimi et al 1992, etc). Although the test is well defined for the non-censored case, censored case has not been discussed in the literature. Therefore we consider a goodness of fit test based on the partial Kullback-Leibler(KL) information with the type II censored data. We derive the partial KL information of the null distribution function and a nonparametric distribution function, and establish a goodness of fit test statistic. We consider the exponential and normal distributions and made Monte Calro simulations to compare the test statistics with some existing tests.

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Effects of Calibration Rounds on the Statistical Distribution of Muzzle Velocity in Acceptance Test of Propelling Charge (추진장약 수락시험시 포구속도 확률분포에 기준탄이 미치는 영향)

  • Park, Sung-Ho;Kim, Jae-Hoon
    • Journal of the Korea Institute of Military Science and Technology
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    • v.17 no.2
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    • pp.204-212
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    • 2014
  • The purpose of this paper is to investigate the effects of calibration rounds on the statistical distribution of the muzzle velocity in acceptance test of propelling charge. It is shown that the normal distribution fits best among statistical distributions from goodness-of fit test. The 3p-Weibull distribution is also acceptable because the shape of the probability density function curve is similar to that of normal distribution and it also has near zero skewness value. Muzzle velocities of test rounds uncompensated by calibration rounds showed high variation and had comparatively higher skewness. Because the skewness of normal distribution is defined to be zero, calibration rounds make the normality of data higher.

Quantiles for Shapiro-Francia W' Statistic

  • Rahman, Mezbahur;Ali, Mir Masoom
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.1
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    • pp.1-10
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    • 1999
  • Table of the empirical quantiles for the well known Shapiro-Francia W' goodness of fit statistic is produced which is more accurate than the existing ones. Prediction equation for the quantiles of W' statistic for sample sizes 30 or more we developed. The process of computing the expected values for the standard normal variate is discussed. This work is intended to make the Shapiro-Francia W' statistic more accessible to the practitioner.

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Goodness of Fit and Independence Tests for Major 8 Companies of Korean Stock Market (한국 주식시장 상위 8개사에 대한 적합도 검정 및 독립성 검정)

  • Min, Seungsik
    • The Korean Journal of Applied Statistics
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    • v.28 no.6
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    • pp.1245-1255
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    • 2015
  • In this paper, we investigated the major 8 companies of Korean stock market, and carried out the goodness of fit and independence tests. We found out the distributions of absolute returns are closed to compressed exponential distribution. The parameters are dominant that 1 < ${\beta}$ < 2, followed by ${\beta}=1$(exponential distribution) and ${\beta}=2$(normal distribution). Meanwhile, we assured that most of the absolute returns for major 8 companies have relevance to each other by chi-square independence test.

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).

Reference Intervals from Hospital-Based Data for Hematologic and Serum Chemistry Values in Dogs (병원자료에 근거한 혈액 및 혈액화학 검사항목의 참고구간 설정)

  • Kwon, Young-Wook;Pak, Son-Il
    • Journal of Veterinary Clinics
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    • v.27 no.1
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    • pp.66-70
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    • 2010
  • Reference interval is critical for interpreting laboratory results, monitoring response to therapy and predicting the prognosis of the patients in clinical settings. The aim of the present study was to update established reference intervals for routine hematologic and serum chemistry values for a population of clinically healthy dogs (range, 1-8 years) seen in an animal hospital. Blood was obtained by venipuncture while animals were physically restrained, and samples were analyzed for 9 chemistries on MS9-5H (Melot Schloesing Lab, France) and 6 hematology on Vet Test 8008 (IDEXX, USA). Data from 105 dogs (52 males and 53 females) for hematology and 113 dogs (37 males and 76 females) for chemistry were used to determine reference intervals using the parametric, nonparametric and bootstrap methods. Prior to analysis, all parameters were tested for normal distribution using Anderson-Darling criterion. Of the 9 biochemical analytes, alkaline phosphatase, alanine aminotransferase, aspartate aminotransferase, creatinine, total protein, and glucose concentrations did not fit normal distribution for both original and transformed data. All but eosinophil count satisfied normal distribution for either original or transformed data. Parametric method can be used for original cholesterol concentrations, RBC, WBC, and neutrophil counts. This technique can also be used for power-transformed values of blood urea nitrogen concentrations and for logarithm of lymphocyte and monocyte counts. Non-parametric or bootstrap method was the preferred choice for the remaining 7 biochemical parameters and eosinophil count as they did not follow normal distributions. All three statistical techniques performed in similar reference intervals. When establishing reference intervals for clinical laboratory data, it is essential to assess the distribution of the original data to increase the accuracy of the interval, and non-parametric or bootstrap methods are of alternative for the data that do not fit normal distribution.

A Study on the Normal Values of Lead Exposure Indices (연폭로 지표들의 정상치에 관한 연구)

  • Shin, Hai-Rim;Kim, Joon-Youn
    • Journal of Preventive Medicine and Public Health
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    • v.19 no.2 s.20
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    • pp.167-176
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    • 1986
  • For the purpose of determinating the normal values of some parameters relevant to lead exposure, a study was carried out from April 1 to June 30, 1986 on 258 healthy Korean adults who have had no apparant lead exposure. The lead indices subjected to this study were as follows; blood lead (PbB), hemoglobin (Hb), zinc protoporphyrin in blood (ZPP), delta-aminolevulinic acid dehydratase (ALAD) activity in blood, coproporphyrin in urine (CPU), delta-aminolevulinic acid in urine (ALAU). 1) The mean value of PbB was $17.17{\pm}7.87{\mu}g/100ml$, and there was no statistically significant difference by age & sex. The distribution of PbB fitted to the log-normal distribution ($x^2=7.38$, p>0.1). 2) The mean value of Hb in male ($15.17{\pm}1.56g/100ml$) was higher than in female ($13.22{\pm}1.51g/100ml$)(p<0.01). The distribution of Hb fitted to the normal distribution ($x^2=9.40$, p>0.1). 3) The mean value of ZPP was $32.61{\pm}8.78{\mu}g/100ml$, and there was no statistically significant difference by age & sex. The distribution of ZPP fitted to the normal distribution ($x^2=13.93$, p>0.05). The correlation of ZPP & ALAD (r=-0.229), CPU (r=0.183) was statistically significant respectively. 4) The mean value of ALAD was $30.20{\pm}10.96{\mu}mol$ ALA/min/L of R.B.C., and there was no statistically significant difference by age & sex. The distribution of ALAD activity did not fit to the normal distribution. The correlation between ALAD & PbB (r=-0.219) was statistically significant 5) The mean value of CPU was $36.10{\pm}24.54{\mu}g/L$, and there was no statistically significant difference by age & sex. The distribution of CPU did not fit to the normal distribution. The correlation between CPU & PbB (r=0.185), ZPP (r=0.183) was statistically signinificant respectively. 6) The mean value of ALAU was $1.94{\pm}0.96mg/L$, and there was no statistically significant difference by age & sex. The distribution of ALAU fitted to the normal distribution ($x^2=9.76$, p>0.1).

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Modeling Circular Data with Uniformly Dispersed Noise

  • Yu, Hye-Kyung;Jun, Kyoung-Ho;Na, Jong-Hwa
    • The Korean Journal of Applied Statistics
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    • v.25 no.4
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    • pp.651-659
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    • 2012
  • In this paper we developed a statistical model for circular data with noises. In this case, model fitting by single circular model has a lack-of-fit problem. To overcome this problem, we consider some mixture models that include circular uniform distribution and apply an EM algorithm to estimate the parameters. Both von Mises and Wrapped skew normal distributions are considered in this paper. Simulation studies are executed to assess the suggested EM algorithms. Finally, we applied the suggested method to fit 2008 EHFRS(Epidemic Hemorrhagic Fever with Renal Syndrome) data provided by the KCDC(Korea Centers for Disease Control and Prevention).

A Note on Parametric Bootstrap Model Selection

  • Lee, Kee-Won;Songyong Sim
    • Journal of the Korean Statistical Society
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    • v.27 no.4
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    • pp.397-405
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    • 1998
  • We develop parametric bootstrap model selection criteria in an example to fit a random sample to either a general normal distribution or a normal distribution with prespecified mean. We apply the bootstrap methods in two ways; one considers the direct substitution of estimated parameter for the unknown parameter, and the other focuses on the bias correction. These bootstrap model selection criteria are compared with AIC. We illustrate that all the selection rules reduce to the one sample t-test, where the cutoff points converge to some certain points as the sample size increases.

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