• Title/Summary/Keyword: Chi-Square Goodness-of-Fit Test

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Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data

  • Sharma, Vikas Kumar;Singh, Sanjay Kumar;Singh, Umesh
    • Communications for Statistical Applications and Methods
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    • v.24 no.3
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    • pp.193-209
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    • 2017
  • The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley's approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions.

Applications on p-values of Chi-Square Distribution

  • Hong, Chong Sun;Hong, Sung Sick
    • Communications for Statistical Applications and Methods
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    • v.9 no.3
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    • pp.877-887
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    • 2002
  • In this paper, behaviors and properties of p-values for goodness-of-fit test are investigated. With some findings on the p-values, we consider some applications to determine sample size of a survey research using the regression equation based on a pilot study data. Regression equations are obtained by the well-known least squared method, and we find that regression lines could be formulated with only two data points, alternatively. For further studies, this works might be extended to t distributions for testing hypotheses about population mean in order to determine sample size of a prospective study. Also similar arguments could be explored for F test statistics.

On spectral and statistical characteristics of sea waves by the typhoons (태풍에 의한 파랑의 스펙트럼 및 통계적 특성)

  • Shim, Jae-Seol;Oh, Byung-Chul;Kim, Sang-Ik
    • Water for future
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    • v.22 no.4
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    • pp.441-451
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    • 1989
  • Using the wave data by typhoons LEE, VERA, THELMA which gave great damages in the Korean penisula, the significant waves based on zero-up & down crossing and Tucker-Draper method are compared with those from the wave energy spectrum. And the histograms of individual waves obtained from zero-up crossing method are presented and compared with the Rayleigh, Weibull, Gluhovski, Ibrageemov and Goda distributions, and also the Chi-square goodness of fit test is applied to each theoretical distributions. It is shown that the significant wave heights by zero-up crossing method are very well agreed to those by energy spectrum method. The wave heights are found to well follow the Rayleigh and Goda distributions by the Chi-square test.

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The Effects of Education on Breast Self-Examination Practices (유방자가검진 교육이 자가검진 행위에 미치는 영향)

  • 최경옥;서연옥
    • Journal of Korean Academy of Nursing
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    • v.28 no.3
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    • pp.718-728
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    • 1998
  • Breast self-examination is the most effective and easiest way for women to increase the responsible consciousness about their health. The purpose of this study was to test the variables impacted to promote breast self-examination practice. The research design used in this study was a nonequevalent control group of a non-synchronized design. The sample that was assembled consisted of 124 women. A purposive sample consisted of 124 women. Each subject was given to assessed on the following the demographic data related to the breast self-examination, knowledge of self-examination, accuracy, in performing self-examination, self-efficacy about breast cancer and breast self-examination, and the number of subjects who found a mass. The result of this study may be summarized as follows : 1. To examine the theretical model fit to the data, chi square test statistics and goodness of fit index were identified($\chi$$^2$=2.30, df=2, GFI=0.99, AGFI=0.94 RMSR=0.02, NFI=0.99, NNFI=0.99, Critical Number=439). 2. The direct effects of education of breast self-examination were knowledge, self-efficacy, accuracy, number finding a mass. But the Indirect effect of education on breast self-examination was frequency of breast self-examination. 3. Knowlege, as direct paths to the breast self-examination practices, was removed in the theoretical model. The parsimonious best fit model included self-efficacy, accuracy, the number finding mass, frequency of breast self-examination practices. 4. The final model produced a chi-square=5.58(p=0.35) with df=5, and GFI =0.99, AGFI =0.94, RMSR=0.03, NFI=0.99, NNFI=0.99, CN=339 indicating very a good fit. Based on the result of this study, education of breast self-examination is very effective for increasing the competency of the breast self-examination through the knowledge and self-efficacy. Resources to promote self-efficacy may be helpful to increase the frequency of self-examination because self-efficacy is a direct effect on it. These findings suggest the need to develop nursing strategy to promote the self-efficacy of breast self-examination.

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Effects of a Maternal Education Program Based on the Temperament Theory on the Temperamental Goodness-of-Fit between Mother and Child (기질이론에 근거한 어머니교육 프로그램이 모아기질조화에 미치는 효과)

  • Ahn, Min Soon
    • Journal of Korean Academy of Nursing
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    • v.35 no.6
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    • pp.1044-1053
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    • 2005
  • Purpose: This study was aimed to evaluate the effects of a maternal education program based on the temperament theory on the temperamental goodness-of-fit between mother and child. Method: The research method was a nonequivalent, control group, non-synchronized design and the experimental period was from May 10, 2004 to July 24, 2004. The subjects were mothers who had children 3-4 years old who registered in eight kindergartens or infant schools in M city. Among the total 94 subjects, 47 were allocated as an experimental group and 47 were a control group. Using the SPSS/WIN 10.0 program, the data was analyzed by a Chi-square test, and t-test. Result: 1. After treatment with a maternal education program based on the temperament theory, the experimental group significantly decreased in scores for perceived children's behavior problems in comparison to the control group(t=-4.01, p<.001). 2. After treatment with a maternal education program based on the temperament theory, the experimental group did not significantly decrease in scores for parenting stress in comparison to the control group(t=-.85, p=.40). 3. After treatment with a maternal education program based on the temperament theory, the experimental group did not significantly decrease in scores for rejective parenting behaviors in comparison to the control group(t=-1.32, p=.19). Conclusion: A maternal education program based on the temperament theory is a useful intervention to decrease perceived children's behavior problems.

A Structural Model for Maternal Adaptation and Family Stress in Families with Mentally Retarded Children (정신 박약 아동 어머니의 스트레스와 적응에 관한 구조 모형)

  • 이경희
    • Journal of Korean Academy of Nursing
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    • v.22 no.4
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    • pp.476-490
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    • 1992
  • This study was designed to develop and test a structural model for maternal adaptation and family stress in families with mentally handicapped children. A hypothetical model was constructed on the basis of the family stress theory developed by McCubbin etc. The model included 6 theoretical concepts and 11 paths. For the purpose of the model testing, empirical data were collected from May to August, 1992. The subjects of the study constituted 190 mothers of children in five special schools and one private institute in Seoul and Choong Nam. An SPSS PC+ and PC-LISREL 7.13 computer programs were used for descriptive and covariance structure analysis. The results of the study were as follows. (1) The hypothetical model showed itself a good fit to the empirical data [Chi - square=18.35(df=7, P=0.005), Goodness of Fit Index=0.991, Adjusted Goodness of Fit Index=0.959, Root Mean Square Residual=0.042), Non Normed Fit Index=0.90, Normed Fit Index=0.96]. (2) The results of Hypothesis testing indicated : 1) Social support(${\gamma}$$_{11}$=.238, T=2.352), Family functioning(${\gamma}$$_{12}$=.729, T=5.957) and Family life event stress(${\gamma}$$_{13}$=.125) had direct effects on situational definition. 2) Life event stress(${\gamma}$$_{23}$=.319, T=3.872) had direct effects on the effect of the handicapped child on the family. Family functioning(${\gamma}$$_{22}$=-.245) and situational definition($\beta$$_{21}$=-.335, T=3.227) had direct effects on the effect of the handicapped child on the family. 3) Situational definition($\beta$$_{31}$=-.273, T=3.493), family life event stress (${\gamma}$$_{33}$=.124, T=2.169) and the effect of the handicapped child on the family($\beta$$_{32}$=.264, T=-3.227) showed the direct effect on the maternal adaptation. The model was supported by the empirical data. Thus it was suggested that the model could be applied to family nursing care with the families with the mentally handicapped. The construction and testing of the comprehensive model seem to be the first trial in Korea.a.a.a.

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Numerical Approach with Kolmogorov-Smirnov Test for Detection of Impulsive Noise (임펄스성 잡음의 유무를 결정하는 Kolmogorov-Smirnov 검증의 수치적 접근의 효율성)

  • Oh, Hyungkook;Nam, Haewoon
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.39C no.9
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    • pp.852-860
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    • 2014
  • This paper proposes an efficient algorithm based on Kolmogorov-Smirnov test to determine the presence of impulsive noise in the given environment. Kolmogorov-Smirnov and Chi-Square tests are known in the literature to serve as a goodness-of-fit test especially for a testing for normality of the distribution. But these algorithms are difficult to implement in practice due to high complexity. The proposed algorithm gives a significant reduction of the computational complexity while decreasing the error probability of hypothesis test, which is shown in the simulation results. Also, it is worth noting that the proposed algorithm is not dependent on the noise environment.

Derivation and utilization of probability distribution of credit card usage behavior (신용카드 이용행태의 확률분포 도출과 활용)

  • Lee, Chan-Kyung;Roh, Hyung-Bong
    • Journal of Korean Society for Quality Management
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    • v.46 no.1
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    • pp.95-112
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    • 2018
  • Purpose: To find out the appropriate probability distribution of credit card usage behavior by considering the relationship among income, expenditure and credit card usage amount. Such relationship is enabled by Korea's especially high penetration of credit card. Method: Goodness-of-fit test and effect size statistic W were used to identify the distribution of income and credit card usage amount. A simulation model is introduced to generate the credit card transactions on individual user level. Result: The three data sets for testing had either passed the chi-square test or showed low W values, meaning they follow the exponential distribution. And the exponential distribution turned out to fit the data sets well. The r values were very high. Conclusion: The credit card usage behavior, denoted as the counts of users by usage amount band, follows the exponential distribution. This distribution is easy to manipulate, has a variety of applications and generates important business implications.

A Predictive Model of Behavioral Problems in Elementary School Children (초등학교 고학년 아동의 문제행동 예측 모형)

  • Song, Hee Seung;Shin, Hee Sun
    • Child Health Nursing Research
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    • v.20 no.1
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    • pp.1-10
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    • 2014
  • Purpose: The purposes of the study were to develop and test a model which explains the relationship among factors affecting behavioral problems in elementary school children. Methods: The participants for the study were 368 elementary school children and their mothers at 3 elementary schools in one city. Data analysis was done using the SPSS 17.0 program for t-test, -test, and ANOVA and the AMOS 17.0 program for theoretical model testing. Results: The theoretical model showed a significant goodness of fit to the empirical data (Goodness of Fit Index: .96, Adjusted Goodness of Fit Index: .93 Comparative Fit Index: .95, Root Mean Square Error of Approximation: .06, Standardized Root Mean Square Residual: .02). Six paths were found to be statistically significant including from child rearing attitude to self-esteem, stress, stress coping and behavioral problems, and from self-esteem to stress and behavioral problems. Child rearing attitude showed a significant effect to behavioral problems by total effect. Self-esteem affected behavioral problems by total and direct effects. Conclusion: Child rearing attitude and selfesteem of children are important factors affecting behavioral problems in elementary school children.

The Selection of Optimal Probability Distribution and Estimation for Design Hourly Factor in National Highway Roads (일반국도 설계시간계수의 적정 확률분포 선정 및 추정)

  • Jo, Jun-Han;Han, Jong-Hyeon;Kim, Seong-Ho;Lee, Byeong-Saeng
    • Journal of Korean Society of Transportation
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    • v.24 no.6 s.92
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    • pp.33-43
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    • 2006
  • This research is to the selection of optimal probability distribution as well as the estimation for design hourly factor in consideration of traffic characteristic, such as road function, lane number and AADT. To accomplish the objectives, we are applied to various probability distribution using traffic data that observed at permanent traffic count points in 2005. The parameters or the selected 14 probability distribution were estimated based on the method of maximum likelihood and the validity condition of the estimated parameter The goodness-of-fit test, such as chi-square test. was performed as well as the estimation of design hourly factor. As a result, An appropriate distributions of each case were selected : Pearson V for two lane of rural roads, LogLogistic for the four lane of rural roads, LogLogistic for the urban roads, Extreme value for recreation roads. And optimal K factor are as following : $0.1{\sim}0.2 $ for two lane of rural roads, $0.09{\sim}0.14$ for the four lane of rural roads. $0.07{\sim}0.13$ for the urban roads, $0.1{\sim}0.2$ for recreation roads.