• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.385-396
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• 2016

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.237-244
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• 2014

It is known that the dierence in the length between two location parameters of two random variables is equivalent to the difference in the area between two cumulative distribution functions. In this paper, we suggest two applications by using the difference of distribution functions. The first is that the difference of expectations of a certain function of two continuous random variables such as the differences of two kth moments and two moment generating functions could be defined by using the difference between two univariate distribution functions. The other is that the difference in the volume between two empirical bivariate distribution functions is derived. If their covariance is estimated to be zero, the difference in the volume between two empirical bivariate distribution functions could be defined as the difference in two certain areas.

• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.19-30
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• 2003

In this paper we present a new family of distributions that allows a continuous variation not only from normality to non-normality but also from unimodality to bimodality. Its properties are especially useful in studying and making inferences about models involving the univariate truncated normal distribution. The properties of the family and its applications are given.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.475-477
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• 2014

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations and show that the particular solutions satisfying the initial conditions are uniquely determined to be Lomax, exponential and power function distributions respectively.

• Korean Journal of Plant Taxonomy
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• v.35 no.4
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• pp.247-272
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• 2005

The Philadelphus schrenkii complex including P. schrenkii var. schrenkii, P. schrenkii var. jackii, P. schrenkii var. mandshuricus, P. tenuifolius, P. pekinensis, P. seoulensis, P. lasiogynus, and P. scaber, is distributed in China, Korea, japan, and far eastern Russia. Their taxonomic delimitations are obscure because quantitative characters, such as presence/absence and density of hair on leaf, petiole, style, disc, calyx-tube, and pedicel, are highly variable with no apparent characteristics that consistently distinguish from each other within the group. Thus, these morphological characters are reexamined using univariate analyses. P. pekinenesis is distinct from other taxa in having glabrous disk, calyx, pedicel, and leaf blade. In addition, the number of flowers in an inflorescence [(5)7-9(11) vs 5-7 in other taxa], smaller calyx tube [2.5-3 mm vs. (2.5)3-4(5.9) in other taxa], and slightly divided styles help distinguish P. pekinenesis from other related taxa in Korea. However, P. schrenkii var. schrenkii, P. schrenkii var. jackii, P. schrenkii var. mandshuricus, and P. lasiogynus show continuous variation in the pubescence of disk, calyx, pedicel, and leaf blade, and this may reflect a lack of divergence among them. Particular emphases are placed on P. tenuifolius and P. seoulensis, because of the high degree of morphological intergradation with respect to the degree of pubescence in disk, calyx, pedicel, and leaf blade and their inconsistent circumscription across various systematic treatments. P. scaber, distributed in the southern Korea, has often been treated as an independent species having exfoliated branchlets, distinct serrated leaf margin, and recurved styles. However, this current study suggests that P. scaber should be recognized as a form of P. tenuifolius because these distinguishing characters are continuous between P. tenuifolius and P. scaber. In geographical distribution, P. pekinensis is mainly distributed in the southern part of Korea, while P. tenuifoilus and P. schrenkii are commonly found all over the country.