• Bulletin of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.979-991
• /
• 2022

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

• Journal of the military operations research society of Korea
• /
• v.25 no.1
• /
• pp.55-74
• /
• 1999

In this study, a nonsymmetric model of directional probability variation (dpv), which is fundamental and conforms well to various moving situations of attacking tanks, is obtained based on the Whittaker's theory. It is shown that it produces the same expression of the probability density function as the Whittaker's under the special moving condition of an attacking tank. Using the derived dpvs, the probability densities for the various cases of some examples are calculated numerically to verify the derived formulas, and compared with other existing symmetrical distributions widely used to grasp characteristics of them. As a result, it is noted that the plots of the probability density function for various cases selected exhibit very different and useful behavioral features. Applying the results with respect to the every tank in the computer simulation of engagement between two tank forces, it is expected that more reasonable shot distributions can be given comparing with other existing symmetrical ones. The derived dpvs may be utilized to decide shot distribution of other weapon systems through small modification.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.8 no.2
• /
• pp.116-120
• /
• 2008

Clustering is a method for unsupervised learning. General clustering tools have been depended on statistical methods and machine learning algorithms. One of the popular clustering algorithms based on machine learning is the self organizing map(SOM). SOM is a neural networks model for clustering. SOM and extended SOM have been used in diverse classification and clustering fields such as data mining. But, SOM has had a problem determining optimal number of clusters. In this paper, we propose an improvement of SOM using gap statistic and probability distribution. The gap statistic was introduced to estimate the number of clusters in a dataset. We use gap statistic for settling the problem of SOM. Also, in our research, weights of feature nodes are updated by probability distribution. After complete updating according to prior and posterior distributions, the weights of SOM have probability distributions for optima clustering. To verify improved performance of our work, we make experiments compared with other learning algorithms using simulation data sets.

• Journal of the Korean Data and Information Science Society
• /
• v.17 no.4
• /
• pp.1405-1412
• /
• 2006

We shall derive the UMVUE of the tail probability in Poisson, Binomial, and negative Binomial distributions, and compare means squared errors of the UMVUE and the MLE of the tail probability in each case.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.10 no.1
• /
• pp.110-120
• /
• 1986

45.deg. corss jet flow, at the mixing of two jet flows, was experimentally studied. For this study, only the statistical turbulent characteristics and high order moments will be analysed by on-line computer system (hot-wire anemometer system, dynamic analyser and computer system, plotting and printing system). Since mean velocity distributions, intensities of turbulence, Reynolds stresses, correlation coefficients, and other general results were already studied and presented. One dimensional probability density distributions of u', v', and w' were analysed comparing with Gaussian curve, which showed skew and flat tendency according to the Y and Z directions. For the analysis of the joint flow of turublent components, the joint probability density distributions were examined. The fagures were drawn so as to be read joint probabilities, joint probability densities, fluctuating velocities u', v', and w'. For further detailed examination of the variations of skewness and flatness phenomena, iso-joint probability density contours obtained from the profiles of the joint probability density distributions were studied. According to the displacement of positions from the center of the mixing flow and the directions, the flatness and skewness factors were increased.

• Smart Structures and Systems
• /
• v.25 no.5
• /
• pp.593-604
• /
• 2020

Temperature may have more significant influences on structural responses than operational loads or structural damage. Therefore, a comprehensive understanding of temperature distributions has great significance for proper design and maintenance of bridges. In this study, the temperature distribution of the steel box girder is systematically investigated based on the structural health monitoring system (SHMS) of the Sutong Cable-stayed Bridge. Specifically, the characteristics of the temperature and temperature difference between different measurement points are studied based on field temperature measurements. Accordingly, the probability density distributions of the temperature and temperature difference are calculated statistically, which are further described by the general formulas. The results indicate that: (1) the temperature and temperature difference exhibit distinct seasonal characteristics and strong periodicity, and the temperature and temperature difference among different measurement points are strongly correlated, respectively; (2) the probability density of the temperature difference distribution presents strong non-Gaussian characteristics; (3) the probability density function of temperature can be described by the weighted sum of four Normal distributions. Meanwhile, the temperature difference can be described by the weighted sum of Weibull distribution and Normal distribution.

• Wind and Structures
• /
• v.33 no.6
• /
• pp.423-435
• /
• 2021

Although existing algorithms can predict wind speed using historical observation data, for engineering feasibility, most use moment methods and probability density functions to estimate fitted parameters. However, extreme wind speed prediction accuracy for long-term return periods is not always dependent on how the optimized frequency distribution curves are obtained; long-term return periods emphasize general distribution effects rather than marginal distributions, which are closely related to potential extreme values. Moreover, there are different wind speed parent sample types; how to theoretically select the proper extreme value distribution is uncertain. The influence of different sampling time intervals has not been evaluated in the fitting process. To overcome these shortcomings, updated steps are introduced, involving parameter sensitivity analysis for different sampling time intervals. The extreme value prediction accuracy of unknown parent samples is also discussed. Probability analysis of mean wind is combined with estimation of the probability plot correlation coefficient and the maximum likelihood method; an iterative estimation algorithm is proposed. With the updated steps and comparison using a Monte Carlo simulation, a fitting policy suitable for different parent distributions is proposed; its feasibility is demonstrated in extreme wind speed evaluations at Longhua and Chuansha meteorological stations in Shanghai, China.

• International Journal of Reliability and Applications
• /
• v.4 no.3
• /
• pp.97-111
• /
• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 2009.01a
• /
• pp.246-249
• /
• 2009

Due to the additive white Gaussian noise (AWGN), images are often corrupted. In recent days, Bayesian estimation techniques to recover noisy images in the wavelet domain have been studied. The probability density function (PDF) of an image in wavelet domain can be described using highly-sharp head and long-tailed shapes. If a priori probability density function having the above properties would be applied well adaptively, better results could be obtained. There were some frequently proposed PDFs such as Gaussian, Laplace distributions, and so on. These functions model the wavelet coefficients satisfactorily and have its own of characteristics. In this paper, mixture distributions of Gaussian and Laplace distribution are proposed, which attempt to corporate these distributions' merits. Such mixture model will be used to remove the noise in images by adopting Maximum a Posteriori (MAP) estimation method. With respect to visual quality, numerical performance and computational complexity, the proposed technique gained better results.

• Wind and Structures
• /
• v.36 no.4
• /
• pp.249-261
• /
• 2023

Aerodynamic force coefficients are generally prescribed by an ensemble average of ten and/or twenty 10-minute samples. However, this makes it difficult to identify the exact probability distribution and exceedance probability of the prescribed values. In this study, 12,600 10-minute samples on three tall buildings were measured, and the probability distributions were first identified and the aerodynamic force coefficients corresponding to the specific non-exceedance probabilities (cumulative probabilities) of wind load were then evaluated. It was found that the probability distributions of the mean and fluctuating aerodynamic force coefficients followed a normal distribution. The ratios of aerodynamic force coefficients corresponding to the specific non-exceedance probabilities (C_f,Non) to the ensemble average of 12,600 samples (C_f,Ens), which was defined as an adjusting factor (C_f,Non/C_f,Ens), were less than 2%. The effect of coefficient of variation of wind speed on the adjusting factor is larger than that of the annual non-exceedance probability of wind load. The non-exceedance probabilities of the aerodynamic force coefficient is between P_C,nonex = 50% and 60% regardless of force components and aspect ratios. The adjusting factors from the Gumbel distribution were larger than those from the normal distribution.