• Journal of the Korean Data and Information Science Society
• /
• 제25권1호
• /
• pp.255-261
• /
• 2014

Many studies have estimated a mixture of binomial distributions. This paper considers an extension, a mixture of shifted binomial distributions, and the estimation of the distribution. The range of each component binomial distribution is rst evaluated and then for each possible value of shifted parameters, the EM algorithm is employed to estimate those parameters. From a set of possible value of shifted parameters and corresponding estimated parameters of the distribution, the likelihood of given data is determined. The simulation results verify the performance of the proposed method.

• 대한수학회논문집
• /
• 제29권2호
• /
• pp.239-255
• /
• 2014

We develop a set of identities for Euler type sums. In particular we investigate products of shifted harmonic numbers of order two and reciprocal binomial coefficients.

• 호남수학학술지
• /
• 제34권3호
• /
• pp.327-340
• /
• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. Very recently, Choi defined a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}^2_n({\cdot})$ and presented their several generating functions. Also, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in m variables to give two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, in the sequel of the above results for their possible general $q$-extensions in several variables, again, we aim at trying to define a $q$-extension of the generalized three variable Gottlieb polynomials ${\varphi}^3_n({\cdot})$ and present their several generating functions.

• 충청수학회지
• /
• 제25권2호
• /
• pp.253-265
• /
• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subse- quently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. Also, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in $m$ variables to give two generating functions of the generalized Gottlieb polynomials ${\varphi}_{n}^{m}(\cdot)$. Here, we aim at defining a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}_{n}^{2}(\cdot)$ and presenting their several generating functions.

• 한국통신학회논문지
• /
• 제17권12호
• /
• pp.1343-1352
• /
• 1992

본 논문에서는 일정한 구간 내에 한정되고 최대치가 균일하도록 설정된 임의 차수 여현펄스의 푸리에 변환을 유도하기 위한 새롭고 용이한 방법을 제안하였다. 제안된 방법은 수치적 해법에 원활하게 적용될 수 있도록 함수의 각 차수에 따라 순환적으로 유도되는 공식에 초점을 두고 있다. 반면에, 유도된 관계식은 용이하게 계산될 수 있는 두함수의 합에 의하여 나타나므로 해석적 해법의 관점에서도 기존의 방법보다 간결한 과정을 제공한다. 특히, 저자 등에 의하여 발견된 계수 분리법에 의하여 공식은 완전 순환적 알고리듬으로 표현되며, 그 결과로 나타나는 자동방정식은 초기 'Sinc'함수가 차수에 따라 지연되어 상수가 곱해진 형태의 합으로 주어진다. 이 때 곱해지는 각 상수는 이항계수로부터 용이하게 결정되며, 'Sinc'함수의 지연요소도 이항식 $(a+b)^n$의 전개식에서 해당되는 항의 지수차에 의하여 쉽게 얻어진다.