• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.363-376
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• 2017

The insurance market is saturated and its growth engine is exhausted; consequently, the insurance industry is now in a low growth period with insurance companies that face a fierce competitive environment. In such a situation, it will be an important issue to find the probability distributions that can explain the flow of insurance claims, which are the basis of the actuarial calculation of the insurance product. Insurance claims are generally known to be well fitted by lognormal distributions or Pareto distributions biased to the left with a thick tail. In recent years, skew normal distributions or skew t distributions have been considered reasonable distributions for describing insurance claims. Cooray and Ananda (2005) proposed a composite lognormal-Pareto distribution that has the advantages of both lognormal and Pareto distributions and they also showed the composite distribution has a higher fitness than single distributions. In this paper, we introduce new composite distributions based on skew normal distributions or skew t distributions and apply them to Danish fire insurance claim data and US indemnity loss data to compare their performance with the other composite distributions and single distributions.

• International Journal of Contents
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• v.2 no.2
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• pp.17-24
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• 2006

The work presented in this paper is divided into two parts. The first part presents finite urn problems which generate truncated negative binomial random variables. Some combinatorial identities that arose from the negative binomial sampling and truncated negative binomial sampling are established. These identities are constructed and serve important roles when we deal with these distributions and their characteristics. Other important results including cumulants and moments of the distributions are given in somewhat simple forms. Second, the distributions of the maximum of two chi-square variables and the distributions of the maximum correlated F-variables are then derived within the negative binomial sampling scheme. Although multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information and deeper insight regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of these distributions. We supplement our findings with exact simple computational methods where no interpolations are involved.

• Journal of Forest and Environmental Science
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• v.36 no.1
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• pp.7-16
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• 2020

Tree size distribution modelling is an integral part of forest management. Most distribution yield systems rely on some flexible probability models. In this study, a simple finite mixture of two components two-parameter Weibull distribution was compared with complex four-parameter distributions in terms of their fitness to predict tree size distribution of teak (Tectona grandis Linn f) plantations. Also, a system of equation was developed using Seemingly Unrelated Regression wherein the size distributions of the stand were predicted. Generalized beta, Johnson's SB, Logit-Logistic and generalized Weibull distributions were the four-parameter distributions considered. The Kolmogorov-Smirnov test and negative log-likelihood value were used to assess the distributions. The results show that the simple finite mixture outperformed the four-parameter distributions especially in stands that are bimodal and heavily skewed. Twelve models were developed in the system of equation-one for predicting mean diameter, seven for predicting percentiles and four for predicting the parameters of the finite mixture distribution. Predictions from the system of equation are reasonable and compare well with observed distributions of the stand. This simplified mixture would allow for wider application in distribution modelling and can also be integrated as component model in stand density management diagram.

• Journal of The Korean Society of Agricultural Engineers
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• v.50 no.6
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• pp.37-47
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• 2008

Photovoltaic power generation is currently being recognized as one of the most popular sources for renewable resources over the country. Although it is also being adapted to rural area for may reasons, it is important to estimate the magnitudes of power outputs with reliable statistical methodologies, while applying historical daily solar energy data, for correct feasibility analysis. In this study, one of the well-known statistical methodologies is employed to define the appropriate probability distributions for monthly power outputs for the selected rural area, county of Seo-san, province of Chungnam. The results imply that the assumption of normal distributions for several months may lead to incorrect decision-making and therefore lead to the unreliable feasibility analysis. Generalized beta and triangular distributions were found to be superior to normal distribution, when describing monthly probability distributions for daily photovoltaic power. Based on the appropriate distributions resulted from this study, Monte Carlo simulation technique was also applied to provide additional flexible information for the relevant decision makers. This study found out new finding that the probability distributions should be considered to make planning of the photovoltaic power system in rural village unit, in order to give reasonable economic analysis to the decision makers.

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.47-56
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• 1998

Zero-Inflated Poisson models are mixed models of the Poisson and Bernoulli models. Recently Zero-Inflated Poisson distributions have been used frequently rather than previous Poisson distributions because the developement of industrial technology make few defects in manufacturing process. It is important that univariate Zero-Inflated Poisson distributions are extended to bivariate distributions to generalize the multivariate distributions. In this paper we proposed three types of the bivariate Zero-Inflated Poisson distributions and obtained these moments. We compared the three types of distributions by using the moments.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.702-707
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• 2001

The characteristics of flow in dividing regions are precise, therefore their classification is very important not only in industry but also in hydrodynamics. By now, many studies of flow in dividing regions have been performed, but flow characteristics that use visualization in dividing regions have not been studied. The present study of the PIV and the CFD exhibit average velocity distributions, kinetic energy distributions and total pressure distributions etc of the total flow field due to the development of the accurate visualization optical laser and of optical equipment. Also, PIV is accurate with the flows characteristics of the dividing region as continuous analysis is done using input equipment. The study analyzes average velocity vector field, average kinetic energy, x-axis stress distributions, average and total pressure distributions of dividing regions with flow for visualization of the PIV and the CFD measurement in a dividing rectangular duct.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.97-100
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• 2000

A FEA(finite element analysis) model was proposed to study stress and strain distributions in thick composites with various types of fiber waviness under tensile and compressive loadings. Three types of model were considered in this study: uniform fiber waviness, graded fiber waviness and localized fiber waviness models. In the analysis, both material and geometrical nonlinearities due to fiber waviness were incorporated into the model utilizing energy density and incremental method. The strain distributions of uniform fiber waviness model were strongly influenced whereas the stress distributions were little influenced by fiber waviness. The stress and strain distributions of graded and localized fiber waviness models showed more complex distributions than those of uniform fiber waviness model due to the variation of fiber waviness along the thickness and length directions. It was concluded that the stress and strain distributions of composites with fiber waviness were significantly affected by types of fiber waviness.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1125-1145
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• 2010

For modeling(skewed) semicircular data, we derive a new exponential family of distributions. We extend it to the l-axial exponential family of distributions by a projection for modeling any arc of arbitrary length. It is straightforward to generate samples from the l-axial exponential family of distributions. Asymptotic result reveals that the linear exponential family of distributions can be used to approximate the l-axial exponential family of distributions. Some trigonometric moments are also derived in closed forms. The maximum likelihood estimation is adopted to estimate model parameters. Some hypotheses tests and confidence intervals are also developed. The Kolmogorov-Smirnov test is adopted for a goodness of t test of the l-axial exponential family of distributions. Samples of orientations are used to demonstrate the proposed model.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.233-239
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• 2015

This study compares two generalized Lindley distributions and assesses consistency between theoretical and analytical results. Data (complete and censored) assumed to follow the Lindley distribution are generated and analyzed using two generalized Lindley distributions, and maximum likelihood estimates of parameters from the generalized distributions are obtained. Size and power of tests of hypotheses on the parameters are assessed drawing on asymptotic properties of the maximum likelihood estimates. Results suggest that whereas size of some of the tests of hypotheses based on the considered generalized distributions are essentially ${\alpha}$-level, some are possibly not; power of tests of hypotheses on the Lindley distribution parameter from the two distributions differs.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2002.10a
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• pp.225-228
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• 2002

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall in 38 Korean rainfall stations. To select the fit appropriate distribution of annual maximum daily rainfall data according to rainfall stations, applied were Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) probability distributions were applied. and their aptness was judged Dusing an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test, the aptitude was judged of applied distributions such as GEV, GLO and GPA. The GEV and GLO distributions were selected as the appropriate distributions. Their parameters were estimated Targetingfrom the observed and simulated annual maximum daily rainfalls and using Monte Carlo techniques, the parameters of GEV and GLO selected as suitable distributions were estimated and. dDesign rainfallss were then derived, using the L-moment. Appropriate design rainfalls were suggested by doing a comparative analysis of design rainfall from the GEV and GLO distributions according to rainfall stations.