• Journal of Communications and Networks
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• 제18권2호
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• pp.182-189
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• 2016

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

• 한국전자통신학회논문지
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• 제18권5호
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• pp.867-876
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• 2023

본 연구에서는 감마족 분포(Erlang, Log-Logistic, Rayleigh)을 적용한 NHPP 소프트웨어 개발 비용 모형의 속성을 새롭게 분석하였고, 모형의 속성을 검증하기 위해 Goel-Okumoto 기본 모형과 비교한 후, 이를 근거로 최적의 모형도 제시하였다. 소프트웨어 신뢰도를 분석하기 위하여 시스템 운영 중 랜덤하게 발생한 고장 시간 데이터를 활용하였고, 모수의 계산은 최우추정법을 사용하여 해결하였다. 다양한 속성 분석(평균값 함수, 개발 비용, 최적의 방출시간)을 통하여 종합적으로 평가한 결과, Rayleigh 모형이 가장 우수한 성능을 가진 모형임을 확인하였다. 본 연구를 통하여, 기존 연구 사례가 없는 감마족 분포를 적용한 소프트웨어 개발비용 모형의 속성을 새롭게 규명하였다. 또한, 개발자들이 초기 단계에서 본 연구 데이터를 효율적으로 활용할 수 있도록 기초적인 설계 데이터도 제시할 수 있었다.

• 대한수학회보
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• 제55권6호
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• pp.1755-1771
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• 2018

In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.

• Journal of the Korean Statistical Society
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• 제13권1호
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• pp.25-31
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• 1984

A technique which has been used for the evaluation of certain kinds of multiple integrals, viz., the technique of imcomplete gamma function operators, is employed and extended to the case where the parameters and arguments are non-equal and non-integer for the probability integral of the inverted Dirichlet distribution. Several types of recurrence formulas have been developed for the tail probabilities and a subset selection procedure in ranking variances is discussed as an application.

• Communications for Statistical Applications and Methods
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• 제4권2호
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• pp.491-496
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• 1997

For the survival data analysis of no covariate the discount survival model is proposed to estimate the time-varying hazard rate and the survival function recursively. In comparison with the covariate case it provide the distributionally explicit evolution of hazard rate between time intervals under the assumption of a conjugate gamma distribution. Also forecasting of the hazard rate in the next time interval is suggested, which leads to the forcecasted survival function.

• Communications for Statistical Applications and Methods
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• 제26권5호
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• pp.473-495
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• 2019

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.

• Journal of the Korean Data and Information Science Society
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• 제1권
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• pp.67-76
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• 1990

For a two-parameter Pareto distribution, the uniformly minimum variance unbiased estimateors(UMVUE) for the function of the two parameters are expressed in terms of confluent hypergeometric function. The variance of the UMVUE is also expressed in terms of hypergeometric function of several variables. UMVUE's for the ${\gamma}th$ moment about zero and several useful parametric functions, and their variances are obtained as special cases. The estimators of Baxter(1980) and Saksena and Johnson(1984) are special cases of our estimator.

• Journal of Astronomy and Space Sciences
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• 제19권1호
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• pp.1-6
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• 2002

Recently, one interesting possibility is proposed that a magnetar can be a progenitor of short and hard gamma-ray bursts (GRBs). If this is true, one may expect that the short and hard GRBs, at least some of GRBs in this class, are distributed in the Euclidean space and that the angular position of these GRBs is correlated with galaxy clusters. Even though it is reported that the correlation is statistically marginal, the observed value of < $V/V_{max}$ > deviates from the Euclidean value. The latter fact is often used as evidence against a local extragalactic origin for short GRB class. We demonstrate that GRB sample of which the value of < $V/V_{max}$ > deviates from the Euclidean value can be spatially confined within the low value of z. We select very short bursts (TgO < 0.3 sec) from the BATSE 4B catalog. The value of < $V/V_{max}$ > of the short bursts is 0.4459. Considering a conic-beam and a cylindrical beam for the luminosity function, we deduce the corresponding spatial distribution of the GRB sources. We also calculate the fraction of bursts whose redshifts are larger than a certain redshift z', i.e. f>z'. We find that GRBs may be distributed near to us, despite the non-Euclidean value of < $V/V_{max}$ >. A broad and uniform beam pattern seems compatible with the magnetar model in that the magnetar model requires a small $z_{max}$.

• 물과 미래
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• 제28권4호
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• pp.185-194
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• 1995

강우-유출모형의 유도와 적용에 고려되야할 규모문제를 검토하여 모형의 지형매개변수와 해상도간의 관계를 분석하고자 한다. 일반적으로 지형인자들의 측정과 계산은 주어진 정보의 해상도에 의존하며 또한 민감하다. 따라서 지형인자를 적용하는 강우-유출 모형은 분석에 이용한 해상도의 영향을 반영할 수 있어야 한다. 본 연구에서 유도된 강우-유출모형은 규모문제가 고려될 수 있는 GIUH 모형으로 이 모형은 유역의 수문응답을 하도망응답과 사면응답으로 분리하여 모의한다. 하도망응답의 계산은 선형화된 St. Venant 식으로부터 유도한 확산근사법을 이용하였고 사면응답은 2모수 gamma 분포식을 사용하였다. 하도망의 지형적 특성과 응답의 초기분포는 폭함수에 의하여 나타내어진다. 본 연구에서는 규모문제를 고려하여 Fractal 이론 및 Melton의 지형법식을 이용하여 폭함수를 유도한국였고 이를 유원위치함수를 이용하여 가중치를 부가하였다.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.643-652
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• 2005

It has been known that the exponentiated exponential distribution can be used as a possible alternative to the gamma distribution or the Weibull distribution in many situations. But the maximum likelihood method does not admit explicit solutions when the sample is multiply censored. So we derive the approximate maximum likelihood estimators for the location and scale parameters in the exponentiated exponential distribution that are explicit function of order statistics. We also compare the proposed estimators in the sense of the mean squared error for various censored samples.