• Korean Journal of Mathematics
• /
• 제29권1호
• /
• pp.75-80
• /
• 2021

For a locus with two alleles (IA and IB), the frequencies of the alleles are represented by $$p=f(I^A)={\frac{2N_{AA}+N_{AB}}{2N} },\;q=f(I^B)={\frac{2N_{BB}+N_{AB}}{2N}}$$ where NAA, NAB and NBB are the numbers of IA IA, IA IB and IB IB respectively and N is the total number of populations. The frequencies of the genotypes expected are calculated by using p2, 2pq and q2. So in this paper, we consider the method of whether some genotypes is in Hardy-Weinburg equilibrium. Also we calculate the probability generating function for the offspring number of genotype produced by a mating of the ith male and jth female under a diploid model of N population with N1 males and N2 females. Finally, we have conditional joint probability generating function of genotype frequencies.

• Journal of the Korean Statistical Society
• /
• 제36권3호
• /
• pp.349-355
• /
• 2007

In this paper we study some important properties of the bivariate generalized hypergeometric probability (BGHP) distribution by establishing the existence of all the moments of the distribution and by deriving recurrence relations for raw moments. It is shown that certain mixtures of BGHP distributions are again BGHP distributions and a limiting case of the distribution is considered.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.591-601
• /
• 2009

In the present paper, one new generalized 'useful' information generating function and two new relative 'useful' information generating functions have been defined with their particular and limiting cases. It is interesting to note that differentiations of these information generating functions at t=0 or t=1 give some known and unknown generalized measures of useful information and 'useful' relative information. The information generating functions facilitates to compute various measures and that has been illustrated by applying these information generating functions for Uniform, Geometric and Exponential probability distributions.

• 산업공학
• /
• 제24권4호
• /
• pp.323-329
• /
• 2011

We develop a stochastic model to predict the score of a soccer match. We describe the scoring process of the soccer match as a markovian arrival process (MAP). To do this, we define a two-state underlying Markov chain, in which the two states represent the offense and defense states of the two teams to play. Then, we derive the probability vector generating function of the final scores. Numerically inverting this generating function, we obtain the desired probability distribution of the scores. Sample numerical examples are given at the end to demonstrate how to utilize this result to predict the final score of the match.

• Journal of Communications and Networks
• /
• 제7권4호
• /
• pp.450-461
• /
• 2005

In this paper, we derive analytical expressions for the exact pairwise error probability (PEP) of a space-time coded system operating over spatially correlated fast (constant over the duration of a symbol) and slow (constant over the length of a code word) fad­ing channels using a moment-generating function-based approach. We discuss two analytical techniques that can be used to evaluate the exact-PEPs (and therefore, approximate the average bit error probability (BEP)) in closed form. These analytical expressions are more realistic than previously published PEP expressions as they fully account for antenna spacing, antenna geometries (uniform linear array, uniform grid array, uniform circular array, etc.) and scattering models (uniform, Gaussian, Laplacian, Von-mises, etc.). Inclusion of spatial information in these expressions provides valuable insights into the physical factors determining the performance of a space-time code. Using these new PEP expressions, we investigate the effect of antenna spacing, antenna geometries and azimuth power distribution parameters (angle of arrival/departure and angular spread) on the performance of a four-state QPSK space-time trellis code proposed by Tarokh et al. for two transmit antennas.

• Journal of applied mathematics & informatics
• /
• 제22권1_2호
• /
• pp.273-283
• /
• 2006

We obtain an asymptotic behavior of the loss probability for the GI/PH/1/K queue as K tends to infinity when the traffic intensity p is strictly less than one. It is shown that the loss probability tends to 0 at a geometric rate and that the decay rate is related to the matrix generating function describing the service completions during an interarrival time.

• Journal of applied mathematics & informatics
• /
• 제31권1_2호
• /
• pp.147-154
• /
• 2013

We analyze queueing model with priority scheduling by supplementary variable method. Customers are classified into two types (type-1 and type-2 ) according to their characteristics. Customers of each type arrive by independent Poisson processes, and all customers regardless of type have same general service time. The service order of each type is determined by the queue length of type-1 buffer. If the queue length of type-1 customer exceeds a threshold L, the service priority is given to the type-1 customer. Otherwise, the service priority is given to type-2 customer. Method of supplementary variable by remaining service time gives us information for queue length of two buffers. That is, we derive the differential difference equations for our queueing system. We obtain joint probability generating function for two queue lengths and the remaining service time. Also, the mean queue length of each buffer is derived.

• ETRI Journal
• /
• 제32권3호
• /
• pp.464-467
• /
• 2010

In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma-shadowed Rician fading channels for a binary differential phase-shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment-generating function (MGF) are derived. The average bit error probability can be calculated by averaging the conditional bit error probability over the PDF or using the MGF-based approach. Numerical results are graphically presented to show the effects of macrodiversity, correlation, number of diversity branches, and severity of both fading and shadowing.

• Journal of Communications and Networks
• /
• 제18권1호
• /
• pp.19-26
• /
• 2016

In this paper, the performance of dual-hop multi-relay maximum ratio transmission (MRT) over Rayleigh flat fading channels is studied with both conventional (all relays participate the transmission) and opportunistic (best relay is selected to maximize the received signal-to-noise ratio (SNR)) relaying. Performance analysis starts with the derivation of the probability density function, cumulative distribution function and moment generating function of the SNR. Then, both approximate and asymptotic expressions of symbol error rate (SER) and outage probability are derived for arbitrary numbers of antennas and relays. With the help of asymptotic SER and outage probability, diversity and array gains are obtained. In addition, impact of imperfect channel estimations is investigated and optimum power allocation factors for source and relay are calculated. Our analytical findings are validated by numerical examples which indicate that multi-relay MRT can be a low complexity and reliable option in cooperative networks.

• 대한전자공학회논문지
• /
• 제21권2호
• /
• pp.13-18
• /
• 1984

확산 스펙트럼 통신방식의 tracking 과정에서 hold-in time 및 false loch를 벗어나는 시간의 확률분포를 연구하였다. 이것은 correlator회로의 dwell time과 threshold level을 결정하는데 도움이 된다. 구하고자 하는 이산확률함수에 대한 발생함수를 급수전개하고 해당되는 항들의 계수를 합하여 동기 유지 시간의 확률분포를 유도하였다. 그리하여 일반적인 시스템 파라미터들로 표현된 결과식을 구하였다.