• Title, Summary, Keyword: distributions

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New composite distributions for insurance claim sizes (보험 청구액에 대한 새로운 복합분포)

  • Jung, Daehyeon;Lee, Jiyeon
    • 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.

Exponential family of circular distributions

  • Kim, Sung-Su
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.6
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    • pp.1217-1222
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    • 2011
  • In this paper, we show that any circular density can be closely approximated by an exponential family of distributions. Therefore we propose an exponential family of distributions as a new family of circular distributions, which is absolutely suitable to model any shape of circular distributions. In this family of circular distributions, the trigonometric moments are found to be the uniformly minimum variance unbiased estimators (UMVUEs) of the parameters of distribution. Simulation result and goodness of fit test using an asymmetric real data set show usefulness of the novel circular distribution.

A Class of Bivariate Linear Failure Rate Distributions and Their Mixtures

  • Sarhan, Ammar M.;El-Gohary, A.;El-Bassiouny, A.H.;Balakrishnan, N.
    • International Journal of Reliability and Applications
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    • v.10 no.2
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    • pp.63-79
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    • 2009
  • A new bivariate linear failure rate distribution is introduced through a shock model. It is proved that the marginal distributions of this new bivariate distribution are linear failure rate distributions. The joint moment generating function of the bivariate distribution is derived. Mixtures of bivariate linear failure rate distributions are also discussed. Application to a real data is given.

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On Perturbed Symmetric Distributions Associated with the Truncated Bivariate Elliptical Models

  • Kim, Hea-Jung
    • Communications for Statistical Applications and Methods
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    • v.15 no.4
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    • pp.483-496
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    • 2008
  • This paper proposes a class of perturbed symmetric distributions associated with the bivariate elliptically symmetric(or simply bivariate elliptical) distributions. The class is obtained from the nontruncated marginals of the truncated bivariate elliptical distributions. This family of distributions strictly includes some univariate symmetric distributions, but with extra parameters to regulate the perturbation of the symmetry. The moment generating function of a random variable with the distribution is obtained and some properties of the distribution are also studied. These developments are followed by practical examples.

COMPARISON STUDY OF BIVARIATE LAPLACE DISTRIBUTIONS WITH THE SAME MARGINAL DISTRIBUTION

  • Hong, Chong-Sun;Hong, Sung-Sick
    • Journal of the Korean Statistical Society
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    • v.33 no.1
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    • pp.107-128
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    • 2004
  • Bivariate Laplace distributions for which both marginal distributions and Laplace are discussed. Three kinds of bivariate Laplace distributions which are extended bivariate exponential distributions of Gumbel (1960) are introduced in this paper. These symmetrical distributions are compared with asymmetrical distributions of Kotz et al. (2000). Their probability density functions, cumulative distribution functions are derived. Conditional skewnesses and kurtoses are also defined. Their correlation coefficients are calculated and compared with others. We proposed bivariate random vector generating methods whose distributions are bivariate Laplace. With sample means and medians obtained from generated random vectors, variance and covariance matrices of means and medians are calculated and discussed with those of bivariate normal distribution.

The Role of Negative Binomial Sampling In Determining the Distribution of Minimum Chi-Square

  • Hamdy H.I.;Bentil Daniel E.;Son M.S.
    • International Journal of Contents
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    • v.3 no.1
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    • pp.1-8
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    • 2007
  • The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. 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 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 the distributions. The computation methods we adopted are exact and no interpolations are involved.

Distributions on F0 and Amplitude of Persons with Cerebral Palsy in the Reading Task (읽기과제에서 나타난 뇌성마비인의 기본주파수 및 진폭의 분포 특성)

  • Nam, Hyun-Wook;Choi, Yang-Gyu
    • MALSORI
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    • no.66
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    • pp.1-20
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    • 2008
  • The purpose of this study was to investigate the characteristics of fundamental frequency(F0) and amplitude distributions in persons with cerebral palsy(CP) in the reading task. Participants were divided into three groups: 6 persons with spastic CP, 6 persons with athetoid CP and 6 normal persons who are around 15-20 years old. On the results of this study, firstly, in F0 distributions, most of the spastic CPs tended to appear narrow distributions on the basis of mode, but most of the athetoid CPs were opposite, and both of the CP groups tended to distribute highly on lower and higher frequencies than mean and mode. On the other hand, normal persons had a tendency to appear narrow distributions on the basis of mode. Finally, in amplitude distributions, the spastic CPs showed a tendency that there are little differences between the distribution of mode and the others, and most of the athetoid CPs showed a tendency that the distributions of mode were higher than the others. In addition to, the normal persons had a tendency that the distributions of mode were remarkably higher than both of the CP groups.

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Closeness of Lindley distribution to Weibull and gamma distributions

  • Raqab, Mohammad Z.;Al-Jarallah, Reem A.;Al-Mutairi, Dhaifallah K.
    • Communications for Statistical Applications and Methods
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    • v.24 no.2
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    • pp.129-142
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    • 2017
  • In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.

ON THE MINIMAX ROBUST APPROACH TO THE TRUNCATION OF DISTRIBUTIONS

  • Lee, Jae-Won;Shevlyakov, Georgiy-L.;Park, Sung-Wook
    • The Pure and Applied Mathematics
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    • v.8 no.2
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    • pp.79-85
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    • 2001
  • As most Of distributions in applications have a finite support, we introduce the class of finite distributions with the known shape of their central part and the unknown tails. Furthermore, we use the Huber minimax approach to determine the unknown characteristics of this class. We obtain the least informative distributions minimizing Fisher information for location in the classes of the truncated Gaussian and uniform distributions, and these results give the reasonable values of the thresholds of truncation. The properties of the obtained solutions are discussed.

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Nonparametric analysis of income distributions among different regions based on energy distance with applications to China Health and Nutrition Survey data

  • Ma, Zhihua;Xue, Yishu;Hu, Guanyu
    • Communications for Statistical Applications and Methods
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    • v.26 no.1
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    • pp.57-67
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    • 2019
  • Income distribution is a major concern in economic theory. In regional economics, it is often of interest to compare income distributions in different regions. Traditional methods often compare the income inequality of different regions by assuming parametric forms of the income distributions, or using summary statistics like the Gini coefficient. In this paper, we propose a nonparametric procedure to test for heterogeneity in income distributions among different regions, and a K-means clustering procedure for clustering income distributions based on energy distance. In simulation studies, it is shown that the energy distance based method has competitive results with other common methods in hypothesis testing, and the energy distance based clustering method performs well in the clustering problem. The proposed approaches are applied in analyzing data from China Health and Nutrition Survey 2011. The results indicate that there are significant differences among income distributions of the 12 provinces in the dataset. After applying a 4-means clustering algorithm, we obtained the clustering results of the income distributions in the 12 provinces.