• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.10 no.5
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• pp.372-379
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• 2017

Software reliability factor during the software development process is elementary. Case of the infinite failure NHPP for identifying software failure, the occurrence rates per fault (hazard function) have the characteristic point that is constant, increases and decreases. In this paper, we propose a reliability model using the chi - square distribution which depends on the degree of freedom that represents the application efficiency of software reliability. Algorithm to estimate the parameters used to the maximum likelihood estimator and bisection method, a model selection based on the mean square error (MSE) and coefficient of determination($R^2$), for the sake of the efficient model, were employed. For the reliability model using the proposed degree of freedom of the chi - square distribution, the failure analysis using the actual failure interval data was applied. Fault data analysis is compared with the intensity function using the degree of freedom of the chi - square distribution. For the insurance about the reliability of a data, the Laplace trend test was employed. In this study, the chi-square distribution model depends on the degree of freedom, is also efficient about reliability because have the coefficient of determination is 90% or more, in the ground of the basic model, can used as a applied model. From this paper, the software development designer must be applied life distribution by the applied basic knowledge of the software to confirm failure modes which may be applied.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.5-9
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• 2001

In this paper, we propose the new audio watermarking method and can be used on line processing. Instead of the wavelet transform, we use the integer wavelet transform for the reduction of the computational load. The watermark associated with the chi-square distribution is inserted into the signal on the integer wavelet domain. When extracting the watermark, the spread spectrum methods are used with the coefficients associated with the covariance sequence. We show that the chi-square distribution is a good tool for the spread spectrum method on the wavelet domain. This watermarking technique may be used for the control of the electrical product which can be controlled with the hidden signals and can be moved according to the audible signals simultaneously.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.1-7
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• 1994

Using a Monte-Carlo simulation technique we evaluate the empiricla distribution of a pseudo-chi-square statistic based on symmetrically Winsorized sum of squares when the population is normally distributed, and search for a chi-square distribution with appropriate degrees of freedom which can be referred to an approximate distribution for Winsorized chi-square.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1465-1475
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• 2013

The chi-square type test statistic is the most commonly used test in terms of measuring testing goodness-of-fit for multinomial logistic regression model, which has its grouped data (binomial data) and ungrouped (binary) data classified by a covariate pattern. Chi-square type statistic is not a satisfactory gauge, however, because the ungrouped Pearson chi-square statistic does not adhere well to the chi-square statistic and the ungrouped Pearson chi-square statistic is also not a satisfactory form of measurement in itself. Currently, goodness-of-fit in the ordinal setting is often assessed using the Pearson chi-square statistic and deviance tests. These tests involve creating a contingency table in which rows consist of all possible cross-classifications of the model covariates, and columns consist of the levels of the ordinal response. I examined goodness-of-fit tests for a proportional odds logistic regression model-the most commonly used regression model for an ordinal response variable. Using a simulation study, I investigated the distribution and power properties of this test and compared these with those of three other goodness-of-fit tests. The new test had lower power than the existing tests; however, it was able to detect a greater number of the different types of lack of fit considered in this study. I illustrated the ability of the tests to detect lack of fit using a study of aftercare decisions for psychiatrically hospitalized adolescents.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.479-488
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• 1999

Moore and Stubblebine(1981) suggested a chi-square test for multivariate normality based on cell counts calculated from the sample Mahalanobis distances. They derived the limiting distribution of the test statistic only when equiprobable cells are employed. Using conditional limit theorems, we derive the limiting distribution of the statistic as well as the asymptotic normality of the cell counts. These distributions are valid even when equiprobable cells are not employed. We finally apply this method to a real data set.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.109-119
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• 1995

A two sample chi-square test is introduced for testing the equality of the distributions of two populations when observations are subject to random censorship. The statistic is appropriate in testing problems where a two-sided alternative is of interest. Under the null hypothesis, the asymptotic distribution of the statistic is a chi-square distribution. We obtain two types of chi-square statistics ; one as a nonnegative definite quadratic form in difference of observed cell probabilities based on the product-limit estimators, the other one as a summation form. Data pertaining to a cancer chemotheray experiment are examined with these statistics.

• International Journal of Contents
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• v.2 no.2
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• pp.17-24
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• 2006

The work presented in this paper is divided into two parts. The first part presents finite urn problems which generate truncated negative binomial random variables. Some combinatorial identities that arose from the negative binomial sampling and truncated negative binomial sampling are established. These identities are constructed and serve important roles when we deal with these distributions and their characteristics. Other important results including cumulants and moments of the distributions are given in somewhat simple forms. Second, the distributions of the maximum of two chi-square variables and the distributions of the maximum correlated F-variables are then derived within the negative binomial sampling scheme. Although multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information and deeper insight regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of these distributions. We supplement our findings with exact simple computational methods where no interpolations are involved.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.745-758
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• 2005

This paper presents a statistical analysis on the position-specific distributions of amino acid residues in transmembrane proteins. A hidden Markov model segments membrane proteins to produce segmented regions of homogeneous statistical property from variable-length amino acids sequences. These segmented residues are analyzed by using chi-square statistic and relative-entropy in order to find position-specific amino acids. This analysis showed that isoleucine and valine concentrated on the center of membrane-spanning regions, tryptophan, tyrosine and positive residues were found frequently near both ends of membrane.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.349-365
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• 1994

We develop in this paper the likelihood ratio test (LRT) for testing $H_1 : F_1 \preceq F_2$ against $H_2 - H_1$ where $H_2$ imposes no restriction on $F_1$ and $F_2$ and '$\preceq$' means failure rate ordering. Both one and two-sample problems will be considered. In the one-sample case, one of the two distributions is known, while we assume in the other case both are unknown. We derive the asymptotic null distribution of the LRT statistic which will be of chi-bar-square type. The main issue here is to determine the least favorable distribution which is stochastically largest within the class of null distributions.

• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.17-26
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• 1978

For testing $\beta_i=\beta, i=1,...,k$, in the regression model $Y_{ij} = \alpha_i + \beta_ix_{ij} + e_{ij}, j=1,...,n_i$, a simple and robust test based on Kendall's tau is proposed. Its asymptotic distribution is proved to be chi-square under the null hypthesis and noncentral chi-square under an appropriate sequence of alternatives. For the optimal designs, the asymptotic relative efficiency of the proposed procedure with respect to the least squares procedure is the same as that of the Wilcoxon test with respect to the t-test.