• 충청수학회지
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• 제23권2호
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• pp.245-250
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• 2010

We present characterizations of the Weibull distribution by the independent property of record values that F(x) has a Weibull distribution if and only if $\frac{X_{U(m)}}{X_{U(n)}}$ and $X_{U(n)}$ or $\frac{X_{U(n)}}{X_{U(n)}{\pm}X_{U(m)}}$ and $X_{U(n)}$ are independent for $1{\leq}m.

• International Journal of Reliability and Applications
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• 제16권2호
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• pp.81-98
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• 2015

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.

• 산업경영시스템학회지
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• 제26권1호
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• pp.85-94
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• 2003

In this paper, a mathematical model is developed for economic design of multi-stage distribution system that consists of factory, central distribution centers, local distribution centers and retailers. The retailers are supplied products from different stage suppliers according to order size. The retailers are supplied products from factory if demand amount is large, central distribution center if medium, local distribution center if small. The economic design is to determine the economic size of facility factors that consist of distribution system. The cost factors are transportation cost from supply places to demand places, handling cost at distribution centers and inventory holding cost at retailers. It is to determine the transportation route of each retailer, the size and number of the vehicle at factory and distribution centers, the handling amount at distribution centers in order to minimize the total costs. The mathematical model is represented, the solution procedure is developed, and a numerical example is shown.

• Archives of Pharmacal Research
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• 제3권1호
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• pp.13-16
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• 1980

The model of an isolated organ system has been constructed to simulated the behavior of drug in the circulatory system of an acting organ or site. The model is developed on the following assumptions : The drug in the microcirculatory system cannot permeate the capilary walls. The capilary bed is modeled as a simple ideal plug flow system with and without radial concentration gradient. The mathematical model is developed from basic considerations of drug distribution with hemodynamical and pharmacokinetical meanings. It is considered that a nonmetabolic drug substance is injected into the arterial inflow site of an isolated organ at a constant rate. The concentration of the drug in the outflow site is mathematically expressed as a function of time.

• 호남수학학술지
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• 제46권2호
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• 대한수학회논문집
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• 제28권2호
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• pp.383-396
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• 2013

We consider an M/PH/1 queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 하계종합학술대회 논문집(1)
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• pp.197-200
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• 2000

This paper presents a mathematical model of the output of Rake receiver of W-CDMA signals for various outdoor channel environment and different bandwidths. This mathematical model is represented as Rayleigh and noncentral chi distribution with 3 degrees of freedom. Those are obtained from the statistics of numerically generated signals. We employ Chi-square test to show how the mathematical model fits signal statistics, and confirmed that this model is appropriate for representing W-CDMA signals.

• 대한수학회지
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• 제33권4호
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• pp.993-1008
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• 1996

The white noise analysis, initiated by Hida [3] in 1975, has been developed to an infinite dimensional distribution theory on Gaussian space $(E^*, \mu)$ as an infinite dimensional analogue of Schwartz distribution theory on Euclidean space with Legesgue measure. The mathematical framework of white noise analysis is the Gel'fand triple $(E) \subset (L^2) \subset (E)^*$ over $(E^*, \mu)$ where $\mu$ is the standard Gaussian measure associated with a Gel'fand triple $E \subset H \subset E^*$.

• 대한수학회보
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• 제50권4호
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• pp.1157-1171
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• 2013

In this paper, by using the $q$-difference analogue of lemma on the logarithmic derivative lemma to re-establish some estimates of Nevanlinna characteristics of $f(qz)$, we deal with the value distribution and uniqueness of certain types of $q$-difference polynomials.

• 대한수학회지
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• 제44권2호
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• pp.455-466
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• 2007

The zero-distribution of the Fourier integral $${\int}^{\infty}_{-{\infty}}\;Q(u)e^{p(u)+^{izu}du$$, where P is a polynomial with leading term $-u^{2m}(m\;{\geq}\;1)$ and Q an arbitrary polynomial, is described. To this end, an asymptotic formula for the integral is established by applying the saddle point method.