• East Asian mathematical journal
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• v.34 no.1
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• pp.59-67
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• 2018

We present new recurrence formulas for the raw and central moments of a compound binomial random variable. Our approach involves relating two compound binomial random variables that have parameters with a difference of 1 for the number of trials, but which have the same parameters for the success probability for each trial. As a consequence of our recursions, the raw and central moments of a binomial random variable are obtained in a recursive manner without the use of Stirling numbers.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.385-391
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• 2003

A sequence of n Bernoulli trials which violates the constant success probability assumption is termed as "Poisson trials". In this paper, the recurrence formula for the r-th central moment of number of successes with n Poisson trials is derived. Romanovsky's method, based on the differentiation of characteristic function, is used in the derivation of recurrence formula for the central moments of conventional binomial distribution. Romanovsky's method is applied to that of Poisson trials in this paper. Some central moment calculation results are given to compare the central moments of Poisson trials with those of conventional binomial distribution.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.279-288
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• 1999

In many cases where the conventional binomial distribution fails to apply to real world data, it is mainly due to the lack of independence among Bernoulli trials. Several authors have proposed models that are useful when independence assumption is not satisfied. In this paper, one proposed model is adapted, and estimators of dependence related parameter that is crucial in defining that model are considered. Simulation is performed to compare two estimators(method of moment estimator and maximum likelihood estimator) of dependence related parameter, and conclusions are made.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.725-736
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• 2003

Let $A_1,{\;}A_2,...,A_n$ be a sequence of events on a given probability space. Let $m_n$ be the number of those $A'_{j}s$ which occur. Upper bounds of P($m_n{\;}\geq{\;}1) are obtained by means of probability of consecutive terms which reduce the number of terms in binomial moments $S_2,n,S_3,n$ and $S_4,n$.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.187-200
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• 1992

Samples are often found to be too heterogeneous to be explained by a one-parameter family of models in the sense that the implicit mean-variance relationship in such a family is violated by the data. This phenomenon is often called over-dispersion. The most frequently used method in dealing with over-dispersion is to mix a one-parameter family creating a two parameter marginal mixture family for the data. In this paper, we investigate performance of estimators such as maximum likelihood estimator, method of moment estimator, and maximum quasi-likelihood estimator in negative binomial and beta-binomial distribution. Simulations are done for various mean parameter and dispersion parameter in both distributions, and we conclude that the moment estimators are very superior in the sense of bias and asymptotic relative efficiency.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.305-313
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• 2007

Let $A_1,\;A_2,\;\ldots,\;A_m$ and $B_1,\;B_2,\;\ldots,\;B_n$ be two sequences of events on the same probability space. Let $X=X_m(A)\;and\;Y=Y_n(B)$, respectively, denote the numbers of those $A_i's\;and\;B_j's$ which occur. We establish new bivariate Bonferroni-type inequalities using consecutive events and deduce a known result.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.789-795
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• 1999

Let $A_1$,A$_2$…, A\ulcorner and B$_1$,B$_2$…, B\ulcorner be two sequences of events on the same probability space. Let X= X\ulcorner(A) and Y-Y\ulcorner)(B), repectively, by the number of those A\ulcorner and B\ulcorner which oc-cur. We establish bivariate lower bounds on the distribution P(X$\geq$1, Y, $\geq$1)and P(X$\geq$i , $Y\geq$j)by linear combinations of the bino-mial moments S\ulcorner, \ulcorner, 1$\leq$i$\leq$j

• Korean Journal of Construction Engineering and Management
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• v.18 no.3
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• pp.74-83
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• 2017

The recently introduced public rental housing REITs was just different the business structure from the existing public rental housing system and the basic supply system is the same. So the ownership conversion for public house over 10 years rental duration is possible after half of the obligated rental duration according to the agreement between lessor and lessee. However rental business operators are likely to have a negative attitude to the early ownership conversion because of less expected profit. Thus, there is a need for an analysis of proper early ownership conversion moment that can achieve public purposes while ensuring the profitability of public rental housing REITs. In this study, the characteristics of the ownership conversion rights that can lessee to exercise considered to be options. Also the nature of 'REITs', 'public rental housing REITs' is considered to be affected by the macroeconomic variables. Thus, this study analyzed the value for ownership conversion in the public rental housing REITs according to real option scenarios reflecting macroeconomic variables. As a result, according to the change of the variation rate of the macroeconomic variables, it was found that with adjustable early ownership conversion time using the DCF(Discounted Cash Flow) model. Therefore, it is possible to ensure profitability of early ownership conversion by predicting the variation of variables.

• Journal of the Korean Magnetics Society
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• v.9 no.3
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• pp.136-142
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• 1999

$Ni_{0.65}Zn_{0.35}Cu_{0.3}Fe_{1.7}O_4$ has been studied with x-ray diffraction, Mossbauer spectroscopy, and vibrating sample magnetometer. The crystal structure is found to be a cubic spinel with the lattice constant $a_0=8.403{\AA}$. Mossbauer spectra of have been taken at various temperatures ranging from 12 K to 665 K. as the temperature increases toward $T_N$ a systematic line broadening effect in the Mossbauer spectrum is observed and interpreted to originate from different temperature dependencies of the magenetic hyperfine fields at various iron sites. Also, by using binomial distribution equation we obtained the hyperfine fields of tetrahedral[A] and octahedral sites[B], $H_{hf}(A)=470\;kOe,\; H_{hf}(B0)=495 \;kOe,\; H_{hf}(B1)=485\;kOe, \;H_{hf}(B2)=453\;kOe,\; H_{hf}(B3)=424\;kOe,\; H_{hf}(B4)=390\;kOe,\; H_{hf}(Bavr)=451\;kOe$ respectively at room temperature. The isomer shift indicates that the iron ions are ferric at tetrahedral[A] and octahedral sites[B], respectively. The Neel temperature is determined to be $T_N=665\;K$. The results of the VSM data gave the magnetic moment and coercivity values of $M_S=66\; emu/g\;and\;H_C=36\;Oe$.