• Title/Summary/Keyword: Derivation

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Derivation of the likelihood function for the counting process (계수과정의 우도함수 유도)

  • Oh, Changhyuck
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.1
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    • pp.169-176
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    • 2014

  • Counting processes are widely used in many fields, whose properties are determined by the intensity function. For estimation of the parameters of the intensity functions when the process is observed continuously over a fixed interval, the likelihood function is of interest. However in the literature there are only heuristic derivations and some results are not coincident. We thus in this note derive the likelihood function of the counting process in a rigorous way. So this note fill up a hole in derivation of the likelihood function.

  • https://doi.org/10.7465/jkdi.2014.25.1.169 인용 PDF KSCI

A GROWING ALGEBRA CONTAINING THE POLYNOMIAL RING

  • Choi, Seul-Hee
    • Honam Mathematical Journal
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    • v.32 no.3
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    • pp.467-480
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    • 2010

  • There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra (see [2], [3], [4], [5], [6], [10], [13], [15], [16]). We and all the derivations of the growing algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)[1] with the set of all right annihilators $T_3$ = $\{id,\;\partial_1,\;\partial_2,\;\partial_3\}$ in the paper. The dimension of $Der_{non}$(WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$) of the algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$ is one and every derivation of the algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$ is outer. We show that there is a class P of purely outer algebras in this work.

  • https://doi.org/10.5831/HMJ.2010.32.3.467 인용 PDF KSCI