• International Journal of Reliability and Applications
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• v.2 no.2
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• pp.117-130
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• 2001

Consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions. We first treat the orthogonal reparametrization and then, using this reparametrization, derive Jeffreys'prior, reference prior, and matching priors. We next provide the suffcient condition for propriety of posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of the parameter of interest in some special cases.

• Fire Science and Engineering
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• v.30 no.2
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• pp.62-67
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• 2016

In this study, the optical depth is analyzed with the effects of droplet size distribution of the water curtain nozzle to attenuate the radiative heat transfer. The HELOS/VARIO equipment is used for the measurement of the droplet size distributions. The spray characteristics are quantified by the investigation of Deirmenjian's modified gamma distribution function. The distribution constant of the nozzle can be obtained as ${\alpha}=1$ and ${\gamma}=5.2$. The generalized equation of the optical depth related with the droplet size distribution is introduced. These results will be applicable to the analysis of the design condition of the water curtain nozzle.

• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.435-442
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• 1993

For the generalized gamma distribution, exact inferences about quantiles need many computations involving complicated numerical integrations. This paper suggests approximate confidence intervals which are easily obtained by considering the alternative location-scale model. Also, these intervals are very accurate even for small sample size. Approximate confidence intervals about quantiles in the lognormal distribution are also considered. With type 2 censoring data, approximate confidence intervals can also be obtained directly by the suggested methods.

• Ocean Systems Engineering
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• v.4 no.4
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• pp.293-308
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• 2014

Unlike the traditional displacement type vessels, the high speed planing crafts are supported by the lift forces which are highly non-linear. This non-linear phenomenon causes their motions in an irregular seaway to be non-Gaussian. In general, it may not be possible to express the probability distribution of such processes by an analytical formula. Also the process might not be stationary or ergodic in which case the statistical behavior of the motion to be constantly changing with time. Therefore the extreme values of such a process can no longer be calculated using the analytical formulae applicable to Gaussian processes. Since closed form analytical solutions do not exist, recourse is taken to fitting a distribution to the data and estimating the statistical properties of the process from this fitted probability distribution. The peaks over threshold analysis and fitting of the Generalized Pareto Distribution are explored in this paper as an alternative to Weibull, Generalized Gamma and Rayleigh distributions in predicting the short term extreme value of a random process.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.239-259
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• 2019

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1037-1047
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• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.435-442
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• 2001

Bayes estimators and generalized ML estimators for reliability of a k-unit hot standby system with the perfect switch based upon a complete sample of failure times observed from an exponential distribution using noninformative, generalized uniform, and gamma priors for the failure rate are proposed, and MSE's of proposed several estimators for the standby system reliability are compared numerically each other through the Monte Carlo simulation.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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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.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.27 no.4
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• pp.274-279
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• 2015

Wave data acquired over eleven years near Sokcho Harbor located in the central area of the east coast were analyzed using spectral method and wave-by-wave analysis method and its major wave characteristics were examined. Significant wave heights were found to be high in winter and low in summer, and peak periods were also found to be long in winter and short in summer. The maximum significant wave height observed was 8.95 m caused by the East Sea twister. The distributional pattern of the significant wave heights and peak periods were both fitted better by Kernel distribution function than by Generalized Gamma distribution function and Generalized Extreme Value distribution function. The wave data were compiled to subdivide the wave height into intervals for each month, and the cumulative occurrence rates of wave heights were calculated to be utilized for the design and construction works in nearby construction works.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.27 no.2
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• pp.142-147
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• 2015

Wave data acquired over seven years near Daejin Harbor located in the north central area of the east coast was analyzed using spectral method and wave-by-wave analysis method and its major wave characteristics were examined. Significant wave heights were found to be high in winter and low in summer, and peak periods were also found to be long in winter and short in summer. The maximum significant wave height observed was 6.59 m and was caused by Typhoon No. 1216, SANBA. The distributional pattern of the significant wave heights and peak periods were both reproduced better by Kernel distribution function than by Generalized Gamma distribution function and Generalized Extreme Value distribution function. Meanwhile, the wave data was subdivided by month and wave height level and the cumulative appearance rate was proposed to aid designing and constructing works in nearby coastal areas.