• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

• Journal of Wetlands Research
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• v.17 no.4
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• pp.370-379
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• 2015

In recent, the natural disaster like localized heavy rainfall due to the climate change is increasing. Therefore, it is important issue that the precise observation of rainfall and accurate spatial distribution of the rainfall for fast recovery of damaged region. Thus, researches on the use of the radar rainfall data have been performed. But there is a limitation in the estimation of spatial distribution of rainfall using rain gauge. Accordingly, this study uses the Kriging method which is a spatial interpolation method, to measure the rainfall field in Namgang river dam basin. The purpose of this study is to apply KED(Kriging with External Drift) with OK(Ordinary Kriging) and CK(Co-Kriging), generally used in Korea, to estimate rainfall field and compare each method for evaluate the applicability of each method. As a result of the quantitative assessment, the OK method using the raingauge only has 0.978 of correlation coefficient, 0.915 of slope best-fit line, and 0.957 of $R^2$ and shows an excellent result that MAE, RMSE, MSSE, and MRE are the closest to zero. Then KED and CK are in order of their good results. But the quantitative assessment alone has limitations in the evaluation of the methods for the precise estimation of the spatial distribution of rainfall. Thus, it is considered that there is a need to application of more sophisticated methods which can quantify the spatial distribution and this can be used to compare the similarity of rainfall field.

• Journal of Dental Rehabilitation and Applied Science
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• v.19 no.2
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• pp.125-137
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• 2003

The use of screw-retaind prosthesis on an osseointegrated implant is a popular treatment modality offering relative ease in the removal of the restoration. One of the complications associated with this modality is the loosening of the abutment and coping screws. Loosening of the screws results in patient dissatisfaction, frustration to the dentist and, if left untreated, component fracture. There are several factors which contribute to the loosening of implant components which can be controlled by the restorative dentist and lab technician. This article offers pratical solutions to minimize this clinical problem and describes the factors involved in maintaining a stable screw joint assembly. To avoid joint failure, adherence to specific clinical, as well as mechanical, parameters is critical. With respect to hardware, optimal tolerance and fit, minimal rotational play, best physical properties, a predictable interface, and optimal torque application are mandatory. In the clinical arena, optimal implant distribution; load in line with implant axis; optimal number, diameter, and length of implants; elimination of cantilevers; optimal prosthesis fit; and occlusal load control are equally important.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.1039-1049
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• 1994

The intermitternt and transient fuel spray have been investigated from the simultaneous measurement of droplet sizes and velocities by using Phase/Doppler Particle Analyzer(PDPA). Measurement have been done on the spray axis and at the edge of the spray near nozzle at various gas-to-liquid density ratios(.rho./sub g//.rho./sub l/) that ranges from those found in free atmospheric jets to conditions typical of diesel engines. Probability density distributions of the droplet size and velocity were obtained from raw data and mathematical probability density functions which can fit the experimental distribations were extracted using the principle of maximum likelihood. In the near nozzle region on the spray axis, droplet sizes ranged from the lower limit of the measurement system to the order of nozzle diameter for all (.rho./sub g/ /.rho./sub l/) and droplet sizes tended to be small on the spray edge. At the edge of spray, average droplet velocity peaked during needle opening and needle closing. The rms intensity is greatly incresed as the radial distance from the nozzle is increased. The probability density function which can best fit the physical breakage process such as breakup of fuel drops is exponecially decreasing log-hypebolic function with 4 parameters.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• Asian Pacific Journal of Cancer Prevention
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• v.17 no.sup3
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• pp.311-316
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• 2016

Breast cancer is one of the most common causes of cancer mortality in Iran. Social determinants of health are among the key factors affecting the pathogenesis of diseases. This cross-sectional study aimed to determine the social determinants of breast cancer survival time with parametric and semi-parametric regression models. It was conducted on male and female patients diagnosed with breast cancer presenting to the Cancer Research Center of Shohada-E-Tajrish Hospital from 2006 to 2010. The Cox proportional hazard model and parametric models including the Weibull, log normal and log-logistic models were applied to determine the social determinants of survival time of breast cancer patients. The Akaike information criterion (AIC) was used to assess the best fit. Statistical analysis was performed with STATA (version 11) software. This study was performed on 797 breast cancer patients, aged 25-93 years with a mean age of 54.7 (${\pm}11.9$) years. In both semi-parametric and parametric models, the three-year survival was related to level of education and municipal district of residence (P<0.05). The AIC suggested that log normal distribution was the best fit for the three-year survival time of breast cancer patients. Social determinants of health such as level of education and municipal district of residence affect the survival of breast cancer cases. Future studies must focus on the effect of childhood social class on the survival times of cancers, which have hitherto only been paid limited attention.

• Ocean Systems Engineering
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• v.9 no.3
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• pp.287-328
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• 2019

Comprehensive understanding of the flood risk assessments via frequency analysis often demands multivariate designs under the different notations of return periods. Flood is a tri-variate random consequence, which often pointing the unreliability of univariate return period and demands for the joint dependency construction by accounting its multiple intercorrelated flood vectors i.e., flood peak, volume & durations. Selecting the most parsimonious probability functions for demonstrating univariate flood marginals distributions is often a mandatory pre-processing desire before the establishment of joint dependency. Especially under copulas methodology, which often allows the practitioner to model univariate marginals separately from their joint constructions. Parametric density approximations often hypothesized that the random samples must follow some specific or predefine probability density functions, which usually defines different estimates especially in the tail of distributions. Concentrations of the upper tail often seem interesting during flood modelling also, no evidence exhibited in favours of any fixed distributions, which often characterized through the trial and error procedure based on goodness-of-fit measures. On another side, model performance evaluations and selections of best-fitted distributions often demand precise investigations via comparing the relative sample reproducing capabilities otherwise, inconsistencies might reveal uncertainty. Also, the strength & weakness of different fitness statistics usually vary and having different extent during demonstrating gaps and dispensary among fitted distributions. In this literature, selections efforts of marginal distributions of flood variables are incorporated by employing an interactive set of parametric functions for event-based (or Block annual maxima) samples over the 50-years continuously-distributed streamflow characteristics for the Kelantan River basin at Gulliemard Bridge, Malaysia. Model fitness criteria are examined based on the degree of agreements between cumulative empirical and theoretical probabilities. Both the analytical as well as graphically visual inspections are undertaken to strengthen much decisive evidence in favour of best-fitted probability density.

• Journal of Korea Water Resources Association
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• v.42 no.10
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• pp.857-866
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• 2009

In this study, basic data is consisted annual maximum rainfall at 56 stations that has the rainfall records more than 30years in Korea. The 14 probability distributions which has been widely used in hydrologic frequency analysis are applied to the basic data. The method of moments, method of maximum likelihood and probability weighted moments method are used to estimate the parameters. And 4-tests (chi-square test, Kolmogorov-Smirnov test, Cramer von Mises test, probability plot correlation coefficient (PPCC) test) are used to determine the goodness of fit of probability distributions. This study emphasizes the necessity for considering the variability of the estimate of T-year event in hydrologic frequency analysis and proposes a framework for evaluating probability distribution models. The variability (or estimation error) of T-year event is used as a criterion for model evaluation as well as three goodness of fit criteria (SLSC, MLL, and AIC) in the framework. The Jackknife method plays a important role in estimating the variability. For the annual maxima of rainfall at 56 stations, the Gumble distribution is regarded as the best one among probability distribution models with two or three parameters.

• Journal of The Korean Astronomical Society
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• v.43 no.4
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• pp.105-113
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• 2010

We study the dynamical evolution of the M87 globular cluster (GC) system using the most advanced and realistic Fokker-Planck (FP) model.By comparing our FP models with both mass function (MF) and radial distribution (RD) of the observed GC system, we find the best-fit initial (at M87's age of 2-3 Gyr) MF and RD for three GC groups: all GCs, blue GCs, and red GCs. We estimate the initial total mass in GCs to be $1.8^{+0.3}_{-0.2}{\times}10^{10}M_{\bigodot}$, which is about 100 times larger than that of the Milky Way GC system. We also find that the fraction of the total mass currently in GCs is 34\%. When blue and red GCs are fitted separately, blue GCs initially have a larger total mass and a shallower radial distribution than red GCs. If one assumes that most of the significant major merger events of M87 have ended by the age of 2-3 Gyr, our finding that blue (metal-poor) GCs initially had a shallower radial distribution supports the major merger scenario for the origin of metallicity bimodality.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.3
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• pp.22-34
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• 1996

Regarding the plate bending process by line heating method, in this study a simplified numerical analysis is performed for a beam model to predict its residual deformation and stress distribution. Using the modified strip theory and beam finite element method, a PC-based simulation program is developed for a thermo-elastic-plastic beam. The plate bending problem can be approximately replaced by a beam model using distributed springs to account for the effect of adjacent strips. The spring constants are chosen as the best fit with experiments. In this paper, it is assumed that the temperature distribution is already given and the temperature-dependent material properties are considered. To verify the simulation program, the results using present numerical algorithm are compared with other published experimental results and similar numerical studies. The comparison shows good agreement. The present PC-based computer program also shows good efficiency in computing time.