• 충청수학회지
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• 제25권3호
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• pp.501-505
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• 2012

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

• Communications for Statistical Applications and Methods
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• 제16권5호
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• pp.859-870
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• 2009

We obtain a skewed double Weibull distribution by a double Weibull distribution, and evaluate its coefficient of skewness. And we obtain the approximate maximum likelihood estimator(AML) and moment estimator of skew parameter in the skewed double Weibull distribution, and hence compare simulated mean squared errors(MSE) of those estimators. We compare simulated MSE of two proposed reliability estimators in two independent skewed double Weibull distributions each with different skew parameters. Finally we introduce a skewed double Weibull distribution generated by a uniform kernel.

• Communications for Statistical Applications and Methods
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• 제24권5호
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2016년도 학술발표회
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집A
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• pp.272-277
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• 2001

In order to evaluate variation of fatigue data of the LP steam turbine blade steel, it is important to estimate P - S - N curves to accurately define the probability distributions. In this study, new procedure is introduced to determine the expression of P - S - N curves. For this purpose, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue life were examined by the proposed analysis. Furthermore, parameter estimation for P - S - N curves was performed using various optimization to maximize the correlation coefficient. As a result of this, sequential linear programing method is used for estimation of P - S - N curves.

• 충청수학회지
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• 제26권3호
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• pp.441-451
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• 2013

In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.

• 대한전기학회논문지:전력기술부문A
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• 제51권1호
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• pp.7-14
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• 2002

In power system study, relibility assessment has been an important topic during past several decards because sudden power interruption can bring about enormous economic loss. although the size of a substation is smaller than that of generation system or transmission system, switching actions after fault(s) make reliability assessment of substation rather complex situations such as switching actions easily and permit various probability distributions in describing substation elements. Despite this ability of Monte Carlo simulation, one-parameter exponential distribution is still popular in this reliability assessment. This paper examines the characteristics of several two-parameter probability distributions, and offers new parameter decision rule based on average and variance of the target to be modelled. In case study, this paper shows the profits by using Weibull distribution which is one of two-parameter probabilistic distributions instead of exponential one.

• Communications for Statistical Applications and Methods
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• 제23권5호
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• pp.363-383
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• 2016

The Weibull family of lifetime distributions play a fundamental role in reliability engineering and life testing problems. This paper investigates the potential usefulness of transmuted new generalized Weibull (TNGW) distribution for modeling lifetime data. This distribution is an important competitive model that contains twenty-three lifetime distributions as special cases. We can obtain the TNGW distribution using the quadratic rank transmutation map (QRTM) technique. We derive the analytical shapes of the density and hazard functions for graphical illustrations. In addition, we explore some mathematical properties of the TNGW model including expressions for the quantile function, moments, entropies, mean deviation, Bonferroni and Lorenz curves and the moments of order statistics. The method of maximum likelihood is used to estimate the model parameters. Finally the applicability of the TNGW model is presented using nicotine in cigarettes data for illustration.

• Communications for Statistical Applications and Methods
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• 제24권3호
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• pp.271-290
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• 2017

We study a bivariate response regression model with arbitrary marginal distributions and joint distributions using Frank and Clayton's families of copulas. The proposed model is used for fitting dependent bivariate data with explanatory variables using the log-odd log-logistic Weibull distribution. We consider likelihood inferential procedures based on constrained parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the bivariate odd-log-logistic-Weibull regression model. Sensitivity analysis methods (such as local and total influence) are investigated under three perturbation schemes. The methodology is illustrated in a study to assess changes on schoolchildren's oral health-related quality of life (OHRQoL) in a follow-up exam after three years and to evaluate the impact of caries incidence on the OHRQoL of adolescents.

• Communications for Statistical Applications and Methods
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• 제25권5호
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• pp.523-544
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• 2018

Bivariate distributions play a fundamental role in survival and reliability studies. We consider a regression model for bivariate survival times under right-censored based on the bivariate Kumaraswamy Weibull (Cordeiro et al., Journal of the Franklin Institute, 347, 1399-1429, 2010) distribution to model the dependence of bivariate survival data. We describe some structural properties of the marginal distributions. The method of maximum likelihood and a Bayesian procedure are adopted to estimate the model parameters. We use diagnostic measures based on the local influence and Bayesian case influence diagnostics to detect influential observations in the new model. We also show that the estimates in the bivariate Kumaraswamy Weibull regression model are robust to deal with the presence of outliers in the data. In addition, we use some measures of goodness-of-fit to evaluate the bivariate Kumaraswamy Weibull regression model. The methodology is illustrated by means of a real lifetime data set for kidney patients.