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본 연구에서는 우리나라 관할 및 주변 해역의 산업화와 인구 집중, 그리고 주변 국가들과의 영토 갈등 상황 속에서 해양경찰의 효율적인 해양경비 체계 구축의 필요 성을 다루고 있다. 이러한 배경하에, 본 연구는 해양 사고의 선제적 예방과 대비, 그 리고 해상 경비 임무 수행 여건 변화에 대한 해양경찰의 능동적 대응을 위한 해양경 비 체계의 고도화 방안을 모색한다. 2021년 해양경찰법의 제정 이후, 해양 영유권 갈 등, 불법조업, 주변국의 팽창 정책, 남북 대치 상황 등 해양환경의 변화에 따른 해양 경비 수요에 효과적으로 대응하기 위해 한정된 경비 세력으로 해양 경비를 효율적이 고 체계적으로 운영하는 방안이 요구되고 있다. 본 논문은 표본해양경찰서를 대상으 로 탄력적인 한국형 해양 경비 체계를 분석하였으며, 주요 분석 결과를 바탕으로 해 상 경비 소요와 해양경찰의 경비 세력 운용에 관한 개선 방안을 제안한다. 푸아송 분포를 활용한 사고 발생률 예측을 통해 해양 경찰의 탄력적인 경비체계 구축 방안 을 제시하며, 현재의 경비 순찰 방식이 전국의 해역별 특성에 맞지 않게 이루어지고 있음을 지적하고, 각 함정 요원의 경험과 사전지식에 따라서 순찰 경비가 이루어지 고 있음을 밝힌다. 또한, 본 연구는 구조 도착 세력들의 평균 선속과 목표 도달 시간 을 기준으로 구역별 최적의 경비 세력 배치를 제안하며, 각 해양 경찰서마다 특성에 따른 각기 다른 경비구조 운영시스템 구축의 필요성을 강조한다. 마지막으로, 실용적이고 체계적이며 과학적인 경비세력 배치계획 수립과 경비 방 식 마련을 위해 현재의 조직체계 개편과 경비구역의 효율적인 운영, 그리고 장기적 으로는 경비구역의 재조정을 통한 효과적인 해양 통제력 확보를 위한 대책이 제시된 다. 과거 발생한 해양조난사고에 따른 소요를 기반으로 현 함정 경비체계에 대하여 분석하고, 해양경찰이 보유한 각 경비세력의 관할 영역과 운용방법에 대한 개선방안 을 제안하여 합리적이고 효율적인 경비세력 운용할 필요성이 있기에 사고 발생률 예 측에 대한 푸아송 분포의 적용을 통한 해양 경찰의 탄력적인 경비체계 구축 방안을 제시하고자 한다.

In this study, we address the need to establish an efficient maritime patrol system for the Korea Coast Guard amidst the industrialization and population concentration in our territorial and surrounding waters, as well as territorial disputes with neighboring countries. Against this backdrop, the study seeks to enhance the maritime patrol system for proactive prevention and preparedness against maritime accidents, as well as for the Coast Guard's agile response to changes in maritime patrol conditions. Following the enactment of the coast guard Act in 2021, there is a demand for an effective and systematic operation of maritime patrols with limited forces to respond to the changing maritime environment, including maritime territorial disputes, illegal fishing, expansion policies of neighboring countries, and North-South standoff situations. This paper analyzes a resilient Korean-style maritime patrol system based on a sample of coast guard stations and proposes improvements to the demand for maritime patrols and the operation of the Coast Guard's forces based on key findings. By predicting the accident rate using the Poisson distribution, the study presents a plan to build a flexible patrol system for the Coast Guard, pointing out that the current patrol method does not suit the characteristics of the maritime areas nationwide and is being conducted based on the experience and prior knowledge of each ship's crew. Additionally, the study suggests the optimal deployment of patrol forces in each area based on the average speed and target arrival time of the rescue forces, emphasizing the need to build different patrol structures and operating systems for each coast guard station according to their characteristics. Lastly, the study presents measures for establishing a practical, systematic, and scientific plan for deploying patrol forces, reorganizing the current organizational structure, operating patrol zones efficiently, and securing effective maritime control through the long-term readjustment of patrol zones. Analyzing the current patrol system based on the requirements stemming from past maritime distress accidents, the study proposes improvements in the jurisdiction and operation methods of each patrol force held by the Coast Guard, highlighting the need for a rational and efficient operation of patrol forces. Therefore, the study aims to present a plan for building a flexible patrol system for the Coast Guard through the application of the Poisson distribution for predicting the accident rate.

대설재난은 풍수해에 이어 두 번째로 피해가 큰 자연재난으로 연도별, 지역별로 발생빈도와 피해규모의 차이가 크다. 대설재난은 이산적으로 발생하기 때문에 포아송 분포의 특성을 가진다. 선진국에서는 다양한 재난과 사고를 대상으로 평균 발생 횟수 및 발생 확률을 기반으로 하는 포아송 분포모형을 통해 발생확률을 산정해왔다. 본 연구의 목적은 이산적 변수의 확률분포를 산정하는 포아송 분포모형을 적용하여 대설재난에 일선 행정기관으로 대응하는 252개 시⋅군⋅구의 강설단계별 발생확률을 산정하고, 대설재난의 발생확률 지도를 작성하는 것이다. 대설재난 단계별 발생확률을 산정하기 위해 지난 36년(1979년-2014년) 동안의 국민안전처 재해연보 자료를 통해 84개 대설재난 사례와 기상청 일일 신적설 자료를 DB로 구축하였다. 구축된 일일 최대 신적설자료를 기반으로 5단계로 구분하여 252개 시⋅군⋅구의 대설재난 발생빈도를 산정하였다. 본 연구의 결과는 지역별 대설재난특성을 고려한 대응정책 수립과 대설재난 위험지역을 대상으로 한 예방사업 추진, 보험요율 산정 등에 기초자료로 활용할 수 있다.

Heavy snowfall is the second-ranked natural disaster after the typhoon and flood disasters in South Korea, but its frequency and severity vary by regions. Heavy snowfall disasters tend to follow a Poisson distribution due to their discrete occurrence, and thus the distribution has been widely used in the literature for estimating a probability of disaster or accident. The objective of this research is to compute probabilities of heavy snowfall disasters in 252 Si-Gun-Gu’s (primary jurisdictions) by five levels using the Poisson distribution model and to draw maps of the heavy snowfall probabilities. This research identifies eighty-four heavy snowfall disaster cases in South Korea during the period of 1979-2014 based on the annual natural disaster yearbooks and the KMA’s daily new snowfall data. The results from this research could be used to guide regionally-specific policies for disaster mitigation and response.

본 연구에서는 휴대전화 통화연결음악 선호도와 친숙도의 분포를 비교하고 음악적 커뮤니케이션 차원에서 일정 기간 뒤에 형성될 미래의 음악적 패러다임 유형을 유추하고자 했다. 이에 통화연결음악 선택 성향이 음악적 특성 변화에 의한 특정 분포를 따른다고 가정하여 향후 나타날 수 있는 선택 요인에 대한 확률변수를 파악했다. 연구의 결과 음악에 대한 친숙도가 통화연결음악 선택의 과정에 커다란 영향요인으로 작용되지 않는다는 것을 알 수 있었다. 즉, 통화연결음악 소비자는 다른 영역의 제품이나 서비스를 선택할 때보다 통화연결음악을 선택할 때 상대적으로 관여도나 가치기준을 고려하지 않는다는 의미로 해석된다.음악의 특성별 표본의 선호도를 포아송분포에 적용시켜 확인한 결과 각 영역별 선호도의 증감이 미래의 선호 성향을 예측할 수 있는 근거가 될 수 있음을 알 수 있었다. 이와 같은 방법에 의한 해석은 향후 소비자 관련 경쟁 제품 및 브랜드 전략의 커뮤니케이션 방향을 파악하는데 유의미한 가치가 있으리라 생각한다.

The purpose of this study is to give technical base for how to use mobile-phone call linking music by examining the preference beside familarity distribution characteristics and communication factors. Add to analysis of musical characteristics and probability forecast by Poisson's distribution. Thus the first independent of variable is mobile-phone call linking music preference and familarity. The second is musical characteristics distinction. The dependent variable is communication factors in brand image in mobile-phone call linking music preference and familarity. This study was conducted through a survey, contents analysis and distribution calculate. The subjects of this survey are 230 university student. They were given some mobile-phone call linking music and questionnaire for preference and familarity. mobile-phone call linking music for the test were chosen from popularity ranking in a web-site. Distribution calculate methode were used by Poisson's distribution table. The results of this study are the following. First, there is no strong relationship between population and preference. Familarity were also. Second, musical characteristic of mobile-phone call linking musics are significantly related. Third, most characteristics of mobile-phone call linking music trends maybe continuous. And the result show the mo-bile-phone call linking music trends were conclude about musical characteristics. Moreover the result show musical characteristics are exist in communication factor.

한반도는 지형학적 요건으로 인하여 태풍과 관련된 재난이 매년 발생하여 막대한 피해를 유발하고 있다. 태풍 내습시 폭풍해일과 집중호우가 동시에 발생한다면 해안지역의 침수피해는 더욱 증가할 것으로 사료된다. 이러한 관점에서 태풍과 폭풍해일의 상호의존성을 정량적으로 규명하는 것은 해안지역의 재해분석에 필수적이다. 본 연구에서는 Bayesian 기법을 기반으로 절점기준을 초과하는 임계값의 초과확률을 산정하기 위하여 Poisson 분포와 Generalized-Pareto 분포를 이용한 Poisson-GP 폭풍해일 빈도해석 기법을 개발하였다. 본 연구를 통하여 개발된 Poisson-GP 폭풍해일 빈도해석 기법은 설계해수면의 불확실성을 정량적으로 제시하였으며 해안지역의 폭풍해일 관련 방재기술 향상에 기여할 것으로 판단된다.

The Korean Peninsula is considered as one of the most typhoon related disaster prone areas. In particular, the potential risk of flooding in coastal areas would be greater when storm surge and heavy rainfall occurred at the same time. In this context, understanding the mechanism of the interactions between them and estimating the risk associated with the concurrent occurrence are of particular interests especially in low-lying coastal areas. In this study, we developed a Poisson-Generalized Pareto (Poisson-GP) distribution based storm surge frequency analysis model to combine the occurrence of the exceedance of a threshold, that is the peaks over threshold (POT), within a Bayesian framework. The storm surge frequency analysis technique developed through this study might contribute to the improvement of disaster prevention technology related to storm surge in the coastal area.

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d<t), the optimal decision rule is; reject H$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

Let's say that we are given a k number of random variables following Poisson distribution that are individually dependent and which forms multivariate Poisson distribution. We particularly dealt with a method of creating random numbers that satisfies the covariance matrix, where the elements of covariance matrix are parameters forming a multivariate Poisson distribution. To create such random numbers, we propose a new algorithm based on the method reducing the number of parameter set and deal with its relationship to the Park et al.(1996) algorithm used in creating multivariate Bernoulli random numbers.

A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.

In this paper, we consider the random number generation method for multivariate Poisson distribution with specific covariance matrix. Random number generating method for the multivariate Poisson distribution is considered into two part, by first solving the linear equation to determine the univariate Poisson parameter, then convoluting independent univariate Poisson variates with appropriate expectations. We propose a numerical algorithm to solve the linear equation given the specific covariance matrix.

This paper introduces three different simulation algorithms of the shifted Poisson distribution. The first algorithm is the inverse transform method, the second is the rejection sampling, and the third is gamma-Poisson hierarchy sampling. Three algorithms have different regions of parameters at which they are efficient. We numerically compare those algorithms with different sets of parameters. As an application, we give a simulation method of the constant elasticity of variance model.

In this paper, we develop a new time series model for predicting IPO (initial public offering) data with non-negative integer value. The proposed model is based on integer-valued autoregressive (INAR) model with a Poisson thinning operator. Just as the heterogeneous autoregressive (HAR) model with daily, weekly and monthly averages in a form of cascade, the integer-valued heterogeneous autoregressive (INHAR) model is considered to reflect efficiently the long memory. The parameters of the INHAR model are estimated using the conditional least squares estimate and Yule-Walker estimate. Through simulations, bias and standard error are calculated to compare the performance of the estimates. Effects of model fitting to the Korea's IPO are evaluated using performance measures such as mean square error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) etc. The results show that INHAR model provides better performance than traditional INAR model. The empirical analysis of the Korea's IPO indicates that our proposed model is efficient in forecasting monthly IPO volumes.

The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Poisson distribution series. To be more precise,we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk.

This paper introduces a new subclass of uniformly convex functions with negative coefficients defined by the Miller Ross-type Poisson distribution series. We obtain the coefficient bounds, extreme points closure theorems, and radii of starlikeness and convexity for functions belonging to the class. Furthermore, we discussed partial sums and neighborhood results for this class.

Zero-Inflated Poisson distribution is Poisson distribution with excess zeros. Recently defects of product hardley happen in the manufacturing process. In this case it is desirable to apply to the Zero-Inflated Poisson distribution rather than Poisson. Our target of this paper is to study the tests for changes of rate of defects after the unknown change-point. We are going to compare the powers of the two proposed tests with likelihood tests by the simulations.

Spatial dependency is important to recognize because of the mapping of pedestrian injury counts analysis. Road safety has been a major issue in contemporary societies, with road crashes incurring major human and materials costs annually worldwide. South Korea’s pedestrian traffic accident rate is the highest among the Organization for Economic Cooperation and Development (OECD) countries. In this paper, we use spatially lagged covariate model with zero inflated Conway-Maxwell-Poisson distribution model to account for spatial autocorrelation of no. of pedestrian crashes with cars. Alternatively, the Conway-Maxwell-Poisson (CMP) distribution, first proposed by Conway and Maxwell (1962) has the flexibility to handle all levels of dispersion, including underdispersion. We test spatial autocorrelation of pedestrian injury counts at 2474 sites, with several weights matrices using Moran's I statistics, under permutation scheme. Then we fit different 20 models, and finally choose the best model by the AIC and SBC values.

The purpose of the present paper is to obtain some sufficient conditions for analytic functions, whose coefficients are probabilities of the Miller-Ross type-Poisson distribution series, to belong to classes 𝓖(λ, 𝛿) and 𝓚(λ, 𝛿).

We investigate the averaging value of a random sampling of a Dirichlet series with some condition using Poisson distribution. Our result is the following: Let $L(s)={\sum}^{\infty}_{n=1}{\frac{a_n}{n^s}}$ be a Dirichlet series that converges absolutely for Re(s) > 1. If $X_t$ is an increasing random sampling with Poisson distribution and there exists a number $0<{\alpha}<{\frac{1}{2}}$ such that ${\sum}_{n{\leq}u}a_n{\ll}u^{\alpha}$, then we have $${\mathbb{E}}L(1/2+iX_t)=O(t^{\alpha}{\sqrt{{\log}t}})$$, for all sufficiently large t in ${\mathbb{R}}$. As a result, we get the behaviour of $L({\frac{1}{2}}+it)$ such that L is a Dirichlet L-function or a modular L-function, when t is sampled by the Poisson distribution.

The present work is concerned with the study of a new subclass of analytic functions, 𝓣𝓜^m_{𝛼,𝜌,𝜑}(𝛄), defined in terms of negatively normalized Mittag-Leffler type functions. It establishes conditions under which these functions exhibit significant geometric properties such as starlikeness, convexity, close-to-convexity and boundedness of coefficients within the open unit disc 𝔻. The work further explores various function theoretic aspects, including extremal functions, sharp coefficient bounds, integral means inequalities and growth and distortion theorems. In addition, it examines the impact of certain integral operators on the structure of this function class. These results offer a unified framework that encompasses several known subclasses and lays the groundwork for further research in geometric function theory, fractional calculus and operator theory.

In this paper Bayes estimator of the parameter and reliability function of the zero-truncated Poisson distribution are obtained. Furthermore, recurrence relations for the estimator of the parameter are also derived. Monte Carlo simulation technique has been made for comparing the Bayes estimator and reliability function with the corresponding maximum likelihood estimator (MLE) of zero-truncated Poisson distribution.

It is derived that conditions of counting process ($\{N(t){\mid}t\;{\geq}\;0\}$) in which the number of events in time interval [0, t] has a (n, n+1)-generalized Poisson distribution with parameters (${\theta}t,\;{\lambda}$) and a generalized inflated Poisson distribution with parameters (${\{\lambda}t,\;{\omega}\}$.