• 제목/요약/키워드: R-functions

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SOME EXTENSION RESULTS CONCERNING ANALYTIC AND MEROMORPHIC MULTIVALENT FUNCTIONS

  • Ebadian, Ali;Masih, Vali Soltani;Najafzadeh, Shahram
    • 대한수학회보
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    • 제56권4호
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    • pp.911-927
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    • 2019

  • Let $\mathscr{B}^{{\eta},{\mu}}_{p,n}\;({\alpha});\;({\eta},{\mu}{\in}{\mathbb{R}},\;n,\;p{\in}{\mathbb{N}})$ denote all functions f class in the unit disk ${\mathbb{U}}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: $$\|\[{\frac{f^{\prime}(z)}{pz^{p-1}}}\]^{\eta}\;\[\frac{z^p}{f(z)}\]^{\mu}-1\| <1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. And $\mathscr{M}^{{\eta},{\mu}}_{p,n}\;({\alpha})$ indicates all meromorphic functions h in the punctured unit disk $\mathbb{U}^*$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy: $$\|\[{\frac{h^{\prime}(z)}{-pz^{-p-1}}}\]^{\eta}\;\[\frac{1}{z^ph(z)}\]^{\mu}-1\|<1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex p-valent functions of order ${\gamma}$ and type ${\beta}$, are also considered.

  • https://doi.org/10.4134/BKMS.b180679 인용 PDF KSCI

Analyze the parameter uncertainty of SURR model using Bayesian Markov Chain Monte Carlo method with informal likelihood functions

  • Duyen, Nguyen Thi;Nguyen, Duc Hai;Bae, Deg-Hyo
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 2021년도 학술발표회
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    • pp.127-127
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    • 2021

  • In order to estimate parameter uncertainty of hydrological models, the consideration of the likelihood functions which provide reliable parameters of model is necessary. In this study, the Bayesian Markov Chain Monte Carlo (MCMC) method with informal likelihood functions is used to analyze the uncertainty of parameters of the SURR model for estimating the hourly streamflow of Gunnam station of Imjin basin, Korea. Three events were used to calibrate and one event was used to validate the posterior distributions of parameters. Moreover, the performance of four informal likelihood functions (Nash-Sutcliffe efficiency, Normalized absolute error, Index of agreement, and Chiew-McMahon efficiency) on uncertainty of parameter is assessed. The indicators used to assess the uncertainty of the streamflow simulation were P-factor (percentage of observed streamflow included in the uncertainty interval) and R-factor (the average width of the uncertainty interval). The results showed that the sensitivities of parameters strongly depend on the likelihood functions and vary for different likelihood functions. The uncertainty bounds illustrated the slight differences from various likelihood functions. This study confirms the importance of the likelihood function selection in the application of Bayesian MCMC to the uncertainty assessment of the SURR model.

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통계공학을 위한 R 패키지 응용 (Applications of R package for statistical engineering)

  • 장대흥
    • 응용통계연구
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    • 제33권1호
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    • pp.87-105
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    • 2020

  • 통계공학은 실험계획법, 품질관리/품질경영, 신뢰성공학으로 구성된다. R은 무료로 개방되어 있는 통계패키지로서 통계모형, 통계 계산 및 통계 그래픽 관련 패키지가 방대하다. 우리는 이러한 R 패키지를 통계공학을 위한 기본 통계패키지로 유용하게 사용할 수 있다. 본 논문에서는 통계공학을 위한 R 패키지 응용을 살펴보고 통계공학 관련 CRAN Task Views가 필요함을 제안하였다.

  • https://doi.org/10.5351/KJAS.2020.33.1.087 인용 PDF KSCI