• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.325-337
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• 2017

In this paper, we proposed a new long-term lifetime distribution with four parameters inserted in a risk competitive scenario with decreasing, increasing and unimodal hazard rate functions, namely the Weibull-Poisson long-term distribution. This new distribution arises from a scenario of competitive latent risk, in which the lifetime associated to the particular risk is not observable, and where only the minimum lifetime value among all risks is noticed in a long-term context. However, it can also be used in any other situation as long as it fits the data well. The Weibull-Poisson long-term distribution is presented as a particular case for the new exponential-Poisson long-term distribution and Weibull long-term distribution. The properties of the proposed distribution were discussed, including its probability density, survival and hazard functions and explicit algebraic formulas for its order statistics. Assuming censored data, we considered the maximum likelihood approach for parameter estimation. For different parameter settings, sample sizes, and censoring percentages various simulation studies were performed to study the mean square error of the maximum likelihood estimative, and compare the performance of the model proposed with the particular cases. The selection criteria Akaike information criterion, Bayesian information criterion, and likelihood ratio test were used for the model selection. The relevance of the approach was illustrated on two real datasets of where the new model was compared with its particular cases observing its potential and competitiveness.

• Journal of the Korean Society of Hazard Mitigation
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• v.11 no.2
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• pp.31-37
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• 2011

Understanding of the phase distribution in a multi-phase polycrystalline material is important because it can affect material properties and mechanical behaviors significantly. In this research, probability functions (two-point correlation and lineal-path functions) are used to represent the phase distributions of microstructures. The two-phase microstructures with random phase distribution are reconstructed using probability functions and compared with original samples. Mechanical behaviors of the virtual samples for different directions are evaluated using a finite element method. It is confirmed that microstructures with the same statistical characteristics can be generated using the reconstruction method. It is also demonstrated that the characteristics of the probability functions and mechanical reponses between the original and reconstructed microsturctures are statistically identical.

• Journal of Mechanical Science and Technology
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• v.14 no.10
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• pp.1041-1050
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• 2000

In this paper the effect of specimen thickness on fatigue crack growth with the spatial distribution of material properties is presented. Basically, the material resistance to fatigue crack growth is treated as a spatial stochastic process, which varies randomly on the crack surface. The theoretical autocorrelation functions of fatigue crack growth resistance with specimen thickness are discussed for several correlation lengths. Constant ${\Delta}K$ fatigue crack growth tests were also performed on CT type specimens with three different thicknesses of BS 4360 steel. Applying the proposed stochastic model and statistical analysis procedure, the experimental data were analyzed for different specimen thicknesses for determining the autocorrelation functions and probability distributions of the fatigue crack growth resistance.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.125-134
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• 2014

Kullback-Leibler (KL) information is a measure of discrepancy between two probability density functions. However, several nonparametric density function estimators have been considered in estimating KL information because KL information is not well-defined on the empirical distribution function. In this paper, we consider the KL information of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF), and propose an EDF-based goodness of fit test statistic. We evaluate the performance of the proposed test statistic for an exponential distribution with Monte Carlo simulation. We also extend the discussion to the censored case.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.199-210
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• 1997

Using regression methods based on quasi-likelihood equation, one only needs to specify the conditional mean and variance functions for the response variable in the analysis. In this paper, an omnibus lack-of-fit test is proposed to test the validity of these two functions. Our test is consistent against the alternative under which either the mean or the variance is not the one specified in the null hypothesis. The large-sample null distribution of our test statistics can be approximated through simulations. Extensive numerical studies are performed to demonstrate that the new test preserves the prescribed type I error probability. Power comparisons are conducted to show the advantage of the new proposal.

• Wind and Structures
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• v.31 no.5
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• pp.419-430
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• 2020

Weibull distribution is a conspicuous distribution known for its accuracy and its usage for wind energy analysis. The two and three parameter Weibull distributions are adopted in this study to fit wind speed data. The daily mean wind speed data of Ennore, Tamil Nadu, India has been used to validate the procedure. The parameters are estimated using maximum likelihood method, least square method and moment method. Four statistical tests namely Root mean square error, R2 test, Kolmogorov-Smirnov test and Anderson-Darling test are employed to inspect the fitness of Weibull probability density functions. The value of shape factor, scale factor, wind speed and wind power are determined at a height of 100m using extrapolation of numerical equations. Also, the value of capacity factor is calculated mathematically. This study provides a way to evaluate feasible locations for wind energy assessment, which can be used at any windy site throughout the world.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1161-1168
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• 2011

The approximation for the distribution functions of nonparametric test statistics is a significant step in statistical inference. A rank sum test for dispersions proposed by Ansari and Bradley (1960), which is widely used to distinguish the variation between two populations, has been considered as one of the most popular nonparametric statistics. In this paper, the statistical tables for the distribution of the nonparametric Ansari-Bradley statistic is produced by use of polynomially adjusted normal approximation as a semi parametric density approximation technique. Polynomial adjustment can significantly improve approximation precision from normal approximation. The normal-polynomial density approximation for Ansari-Bradley statistic under finite sample sizes is utilized to provide the statistical table for various combination of its sample sizes. In order to find the optimal degree of polynomial adjustment of the proposed technique, the sum of squared probability mass function(PMF) difference between the exact distribution and its approximant is measured. It was observed that the approximation utilizing only two more moments of Ansari-Bradley statistic (in addition to the first two moments for normal approximation provide) more accurate approximations for various combinations of parameters. For instance, four degree polynomially adjusted normal approximant is about 117 times more accurate than normal approximation with respect to the sum of the squared PMF difference.

• Journal of Mechanical Science and Technology
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• v.16 no.1
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• pp.60-74
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• 2002

In this study, normal, log-normal, triangular, uniform. Weibull, Erlang and unit beta probability density functions are tried to represent the behaviour of frequency distributions of workpiece dimensions collected from various manufacturing firms. Among the distribution functions, the unit beta distribution function is found to be the best fit using the chi-square test of fit. An attempt is made for the adoption of the unit beta model to x-bar charts of quality control in manufacturing. In this direction, upper and lower control limits (UCL and LCL) of x-bar control charts of dimension measurements are estimated for the beta model, and the observed differences between the beta and normal model control limits are discussed for the measurement sets.

• Earthquakes and Structures
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• v.10 no.6
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• pp.1291-1314
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• 2016

The paper presents the development of experimental fragility functions for exterior RC beam-column connections based on results obtained from extensive testing carried out in the present study. Three typical types of seismically deficient beam-column connections, which are commonly prevalent in Indian sub-continent, were considered. These specimens were tested under cyclic displacement histories with different characteristics to induce different damage states. Rehabilitation specific fragility functions for damaged specimens were developed considering drift angle as a demand parameter. Four probability distributions were fit to the data and suitability of each distribution was evaluated using standard statistical method. Specimens with different damage states were rehabilitated appropriately and rehabilitated specimens were tested under similar displacement histories. Fragility functions for rehabilitated specimens have also been developed following similar procedure. Comparison of fragility functions for both original and rehabilitated specimens for each rehabilitation method showed close agreement, which establishes the effectiveness of the adopted rehabilitation strategies and hence would provide confidence in field application.

• Journal of The Korean Astronomical Society
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• v.27 no.2
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• pp.103-117
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• 1994

To extend the work of Gott, Park, and Lee (1989), statistical properties of gravitational lensing in a wide variety of cosmological models involving non-zero cosmological constant is investigated, using the redshifts of both lens and source and observed angular separation of images for gravitational lens systems. We assume singular isothermal sphere as lensing galaxy in homogenous and isotropic Friedmann­Lemaitre-Robertson- Walker universe, Schechter luminosity function, standard angular diameter distance formula and other galaxy parameters used in Fukugita and Turner (1991). To find the most adequate flat cosmological model and put a limit on the value of dimensionless cosmological constant $\lambda_0$, the mean value of the angular separation of images, probability distribution of angular separation and cumulative probability are calculated for given source and lens redshifts and compared with the observed values through several statistical methods. When there is no angular selection effect, models with highest value of $\lambda_0$ is preferred generally. When the angular selection effects are considered, the preferred model depends on the shape of the selection functions and statistical methods; yet, models with large $\lambda_0$ are preferred in general. However, the present data can not rule out any of the flat universe models with enough confidence. This approach can potentially select out best model. But at the moment, we need more data.