• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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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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• v.3 no.1
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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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• v.27 no.5_6
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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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• v.12 no.3
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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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• v.8 no.2
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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.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.123-132
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• 2016

We can achieve the principle of parsimony and efficiency if homogeneity for panel time series model is satisfied. We suggest a Rao test statistic and a Wald test statistic for the test of homogeneity for panel AR(1) and derived the limit distribution. We performed a simulation to examine statistics with the same chisquare distribution when number of the individual is small and in common with large. We also simulated to compare the empirical power of the statistics in a small panel. In application, we fit panel AR(1) model using regional monthly economical active population data and test homogeneity for panel AR(1). It is satisfied homogeneity, so it could be fitted AR(1) using the sample mean at the time point. We also compare the power of prediction between each individual and pooled model.

• Water for future
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• v.14 no.4
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• pp.35-52
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• 1981

This study is to evaluate the areal precipitation from the basic data groups of monthly, seasonal, and annual rainfalls over all ma in stations in Korea. The evaluating pocesses are performed through the point and regional frequency analysis from the basic data. The basic data groups are divided into two periods-the first(1916-1944) and the second (1960-1979)-which are compared with each other. In the point frequecny analysis, the variable transformation method is applied to the best fitting distribution, and the normal fittings are established by using the Chisquare test method. In the regional frequency analysis, the geomorphologic factors and hydrometeorological factors are taken into consideration when dividing into five zones and Thiessen method and the Isohyetal method are applied. The results of this study are as follows: 1)The areal precipitation values of the first period are about 70-80mm less than that of the second period for the whole of Korea. Therefore, a new precipitation value of 1180mm is considered more suitable than the value of 1159mm, which has been up till now. 2)As the annual areal precipitiation values areevaluated over the five divide zones, it tis noticed that the difference between the values of the first period and the second is the largest in spring (to the extent of 5 times that in the other seasonas). Thereform it is considered that this result is necessary for the establishment of a timely insurance plan for the water resources. 3)The application of the Isohyetal method through the division of Korea into five zones is considered to be a reasonable procedure in the analysis of areal precipitation.