• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권2호
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• pp.15-29
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• 2007

In this paper, we explore some interesting models of the quasi-negative-binomial distribution based on difference differential equations applicable to theory of microorganisms and the situations like that. Some characterizations based on conditional distributions and damage process have been obtained. Further, the distribution of number of accidents as the quasi-negative-binomial distribution in the light of Irwin's theory of ";proneness-liability"; model has been derived. Finally, the proposed model (QNBD) has been applied to study the Shunting accidents, home injuries, and strikes in industries.

• International Journal of Contents
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• 제3권1호
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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.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1493-1499
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• 2009

Let $A_1$ and $A_2$ be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = $c_1A_1$ + $c_2A_2$, where $c_1,\;c_2$ are nonzero complex scalars. In this paper, under an assumption of $A_1A_2$ = $A_2A_1$, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idem-potent by using the property of decomposition of a tripotent matrix, i.e. if $A_2$ is tripotent, then $A_2$ = $B_1-B_2$, where $B^2_i=B_i$, i = 1, 2 and $B_1B_2=B_2B_1=0$. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again.

• Journal of Communications and Networks
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• 제12권3호
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• pp.222-230
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• 2010

In this paper, we present a closed-form approximation of the average sum rate of zero-forcing (ZF) beamforming (BF) with semi-orthogonal user selection (SUS). We first derive the survival probability associated with the SUS that absolute square of the channel correlation between two users is less than the orthogonalization level threshold (OLT).With this result, each distribution for the number of surviving users at each iteration of the SUS and the number of streams for transmission is calculated. Secondly, the received signal power of ZF-BF is represented as a function of the elements of the upper triangular matrix from QR decomposition of the channel matrix. Thirdly, we approximate the received signal power of ZF-BF with the SUS as the maximum of scaled chisquare random variables where the scaling factor is approximated as a function of both OLT and the number of users in the system. Putting all the above derivations and order statistics together, the approximated ergodic sum rate of ZF-BF with the SUS is shown in a closed form. The simulation results verify that the approximation tightly matches with the sample average for any OLT and even for a small number of users.

• Advances in Energy Research
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• 제8권2호
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• pp.111-123
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• 2022

Solar Energy is the energy of solar radiation carried by them in the form of heat and light. It can be converted into electricity. Solar potential depends on the site's atmosphere; the solar energy distribution depends on many factors, e.g., turbidity, cloud types, pollution levels, solar altitude, etc. We estimated solar radiation with the help of the Ashrae clear-sky model for three locations in Pakistan, namely Pasni, Gwadar, and Jiwani. As these locations are close to each other as compared to the distance between the sun and earth, therefore a slight change of latitude and longitude does not make any difference in the calculation of direct beam solar radiation (BSR), diffuse solar radiation (DSR), and global solar radiation (GSR). A modified formula for declination angle is also developed and presented. We also created two different models for Ashrae constants. The values of these constants are compared with the standard Ashrae Model. A good agreement is observed when we used these constants to calculate BSR, DSR, GSR, the Root mean square error (RMSE), Mean Absolute error (MABE), Mean Absolute percent error (MAPE), and chisquare (χ²) values are in acceptance range, indicating the validity of the models.

• 응용통계연구
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• 제29권1호
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• pp.123-132
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• 2016

패널 시계열 자료를 소개하고 패널 1차 자기회귀 모형을 고려하였다. 패널 1차 자기회귀 모형의 동질성 검정을 위한 검정 통계량으로 Rao 통계량과 Wald 통계량을 제안하고, 그 극한분포를 제시하였다. 모의실험을 통해 패널의 수가 작을 때에도 패널의 수가 많을 때와 마찬가지로 두 검정 통계량의 분포가 카이제곱분포를 따르는 것을 확인하였으며, 패널의 수가 작을 때 Rao 통계량이 Wald 통계량 보다 더 우수한 검정력을 가짐을 모의실험을 통해 확인하였다. 시도별 월별 경제활동인구수 자료를 패널 1차 자기회귀 모형으로 적합하여 동질성 검정을 수행한 결과 동질성을 만족하였다. 동질성 검정을 만족한 자료를 시점별 평균을 이용하여 종합하고 이를 1차 자기회귀모형으로 적합하였다. 각각의 시도별로 적합한 모형과 시점별 평균을 이용하여 적합한 모형의 예측력을 비교한 결과 동질성 검정을 통과한 패널 1차 자기회귀모형의 경우 자료를 종합하여 적합한 모형의 예측력이 더 우수함을 확인하였다.

• 물과 미래
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• 제14권4호
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• pp.35-52
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• 1981

본 연구는 전국 주요 지점에 대한 월별, 계절별 및 연우량을 기본자료집단으로 하여 지점 및 지역 빈도 해석을 실시함으로써 면적 강우량을 산정한 내용이다. 기본자료집단은 전반기(1916년∼1944년; 29년간)와 후반기(1960년∼1979년; 20년간)로 양분하여 처리하고 비교 검토하였다. 지점 빈도해석에 있어서 적정 분포형은 변수변환법을 적용하고, $$-test 법을 이용하여 정규성 검정으로 설정하였으며, 지역 빈도 해석은 지형인자와 수문기상학적 인자를 고려하여 전국을 5개권역으로 구분하고 Thiessen 방법과 등우선법(Isohyetal Method)을 적용하여 비교 검토하였다. 본 연구를 통하여 얻어진 성과는 아래와 같다. 1) 전반기 자료집단에 의한 전국의 면적 강우량치는 후반기 자료집단에 의한 해석 결과치보다 70∼80mm 작은 값을 나타내고 있으므로 보아 현재까지의 1,150mm를 1,180mm 정도를 상향조정함이 바람직하다고 생각한다. 2) 전국을 5개 권역으로 구분하여 연평균 면적 강우량을 산정한 바, 춘계의 면적 강수량이 타계절에 비하여(약 5신) 크게 증가하고 있음은 수자원 적기 확보 방안 수립에 특기할 점이라 하겠다. 3) 면적 강수량 해석은 권역별로 구분하여 등우선도법으로 해석함이 합리적 방법이라고 생각된다.