Search results for: Poisson point process

Authors: H. J. Wattimanela, U. S. Passaribu, N. T. Puspito, S. W. Indratno

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Banda Sea collision zone (BSCZ) of is the result of the interaction and convergence of Indo-Australian plate, Eurasian plate and Pacific plate. This location in the eastern part of Indonesia. This zone has a very high seismic activity. In this research, we will be calculated rate (λ) and Mean Square Eror (MSE). By this result, we will identification of Poisson distribution of earthquakes in the BSCZ with the point process approach. Chi-square test approach and test Anscombe made in the process of identifying a Poisson distribution in the partition area. The data used are earthquakes with Magnitude ≥ 6 SR and its period 1964-2013 and sourced from BMKG Jakarta. This research is expected to contribute to the Moluccas Province and surrounding local governments in performing spatial plan document related to disaster management.

Keywords: molluca banda sea collision zone, earthquakes, mean square error, poisson distribution, chi-square test, anscombe test

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Authors: Jihad Daba, Jean-Pierre Dubois

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Multi path fading noise degrades the performance of cellular communication, most notably in femto- and pico-cells in 3G and 4G systems. When the wireless channel consists of a small number of scattering paths, the statistics of fading noise is not analytically tractable and poses a serious challenge to developing closed canonical forms that can be analysed and used in the design of efficient and optimal receivers. In this context, noise is multiplicative and is referred to as stochastically local fading. In many analytical investigation of multiplicative noise, the exponential or Gamma statistics are invoked. More recent advances by the author of this paper have utilized a Poisson modulated and weighted generalized Laguerre polynomials with controlling parameters and uncorrelated noise assumptions. In this paper, we investigate the statistics of multi-diversity stochastically local area fading channel when the channel consists of randomly distributed Rayleigh and Rician scattering centers with a coherent specular Nakagami-distributed line of sight component and an underlying doubly stochastic Poisson process driven by a lognormal intensity. These combined statistics form a unifying triply stochastic filtered marked Poisson point process model.

Keywords: cellular communication, femto and pico-cells, stochastically local area fading channel, triply stochastic filtered marked Poisson point process

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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Authors: Pitsanu Tongkhow, Pichet Jiraprasertwong

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This research investigates risk factors for defective products in autoparts factories. Under a Bayesian framework, a generalized linear mixed model (GLMM) in which the dependent variable, the number of defective products, has a Poisson distribution is adopted. Its performance is compared with the Poisson GLM under a Bayesian framework. The factors considered are production process, machines, and workers. The products coded RT50 are observed. The study found that the Poisson GLMM is more appropriate than the Poisson GLM. For the production Process factor, the highest risk of producing defective products is Process 1, for the Machine factor, the highest risk is Machine 5, and for the Worker factor, the highest risk is Worker 6.

Keywords: defective autoparts products, Bayesian framework, generalized linear mixed model (GLMM), risk factors

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Authors: Rong-Tsorng Wang

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In this paper, we derive a pricing formula for catastrophe equity put options (or CatEPut) with non-homogeneous loss and approximated compound distributions. We assume that the loss claims arrival process is a nonhomogeneous Poisson process (NHPP) representing the clustering occurrences of loss claims, the size of loss claims is a sequence of independent and identically distributed random variables, and the accumulated loss distribution forms a compound distribution and is approximated by a heavy-tailed distribution. A numerical example is given to calibrate parameters, and we discuss how the value of CatEPut is affected by the changes of parameters in the pricing model we provided.

Keywords: catastrophe equity put options, compound distributions, nonhomogeneous Poisson process, pricing model

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Authors: Nadarajah I. Ramesh

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Much of the research on stochastic point process models for rainfall has focused on Poisson cluster models constructed from either the Neyman-Scott or Bartlett-Lewis processes. The doubly stochastic Poisson process provides a rich class of point process models, especially for fine-scale rainfall modelling. This paper provides an account of recent development on this topic and presents the results based on some of the fine-scale rainfall models constructed from this class of stochastic point processes. Amongst the literature on stochastic models for rainfall, greater emphasis has been placed on modelling rainfall data recorded at hourly or daily aggregation levels. Stochastic models for sub-hourly rainfall are equally important, as there is a need to reproduce rainfall time series at fine temporal resolutions in some hydrological applications. For example, the study of climate change impacts on hydrology and water management initiatives requires the availability of data at fine temporal resolutions. One approach to generating such rainfall data relies on the combination of an hourly stochastic rainfall simulator, together with a disaggregator making use of downscaling techniques. Recent work on this topic adopted a different approach by developing specialist stochastic point process models for fine-scale rainfall aimed at generating synthetic precipitation time series directly from the proposed stochastic model. One strand of this approach focused on developing a class of doubly stochastic Poisson process (DSPP) models for fine-scale rainfall to analyse data collected in the form of rainfall bucket tip time series. In this context, the arrival pattern of rain gauge bucket tip times N(t) is viewed as a DSPP whose rate of occurrence varies according to an unobserved finite state irreducible Markov process X(t). Since the likelihood function of this process can be obtained, by conditioning on the underlying Markov process X(t), the models were fitted with maximum likelihood methods. The proposed models were applied directly to the raw data collected by tipping-bucket rain gauges, thus avoiding the need to convert tip-times to rainfall depths prior to fitting the models. One advantage of this approach was that the use of maximum likelihood methods enables a more straightforward estimation of parameter uncertainty and comparison of sub-models of interest. Another strand of this approach employed the DSPP model for the arrivals of rain cells and attached a pulse or a cluster of pulses to each rain cell. Different mechanisms for the pattern of the pulse process were used to construct variants of this model. We present the results of these models when they were fitted to hourly and sub-hourly rainfall data. The results of our analysis suggest that the proposed class of stochastic models is capable of reproducing the fine-scale structure of the rainfall process, and hence provides a useful tool in hydrological modelling.

Keywords: fine-scale rainfall, maximum likelihood, point process, stochastic model

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Authors: Yosra Benchaabene, Noureddine Boujnah, Faouzi Zarai

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To meet the growing demand of users, the fifth generation (5G) will continue to provide services to higher data rates with higher carrier frequencies and wider bandwidths. As part of the 5G communication paradigm, Ultra Reliable Communication (URC) is envisaged as an important technology pillar for providing anywhere and anytime services to end users. Ultra Reliable Communication (URC) is considered an important technology that why it has become an active research topic. In this work, we analyze the availability of a service in the space domain. We characterize spatially available areas consisting of all locations that meet a performance requirement with confidence, and we define cell availability and system availability, individual user availability, and user-oriented system availability. Poisson point process (PPP) and Voronoi tessellation are adopted to model the spatial characteristics of a cell deployment in heterogeneous networks. Numerical results are presented, also highlighting the effect of different system parameters on the achievable link availability.

Keywords: URC, dependability and availability, space domain analysis, Poisson point process, Voronoi Tessellation

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Authors: Arthur Thirion

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Auxetic geometries allow the generation of a negative Poisson ratio (NPR) in conventional materials. This behaviour allows materials to have certain improved mechanical properties, including impact resistance and altered synclastic behaviour. This means these structures have significant potential when it comes to applications as chronic wound dressings. To this end, 6 different "perforated sheet" structure types were 3D printed. These structures all had variations of key geometrical features included cell length and angle. These were tested in compression and tension to assess their Poisson ratio. Both a positive and negative Poisson ratio was generated by the structures depending on the loading. The a/b ratio followed by θ has been shown to impact the Poisson ratio significantly. There is still a significant discrepancy between modelled and observed behaviour.

Keywords: auxetic materials, 3D printing, negative Poisson's ratio, tunable Poisson's ratio

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Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

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Authors: Mohammad Tahmasebipour, Hosein Salarpour

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Researchers suggest that variations in Poisson’s ratio affect the behavior of Timoshenko micro beam. Therefore, in this study, two epoxy Timoshenko micro beams with different dimensions were modeled using the finite element method considering all boundary conditions and initial conditions that govern the problem. The effect of Poisson’s ratio on the resonant frequency, maximum deflection, and maximum rotation of the micro beams was examined. The analyses suggest that an increased Poisson’s ratio reduces the maximum rotation and the maximum rotation and increases the resonant frequency. Results were consistent with those obtained using the couple stress, classical, and strain gradient elasticity theories.

Keywords: microbeam, microsensor, epoxy, poisson’s ratio, dynamic behavior, static behavior, finite element method

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Authors: O. Anan, D. Böhning, A. Maruotti

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The purpose of the study is to estimate the elusive target population size under a truncated count model that accounts for heterogeneity. The purposed estimator is based on the generalized Poisson distribution (GPD), which extends the Poisson distribution by adding a dispersion parameter. Thus, it becomes an useful model for capture-recapture data where concurrent events are not homogeneous. In addition, it can account for over-dispersion and under-dispersion. The ratios of neighboring frequency counts are used as a tool for investigating the validity of whether generalized Poisson or Poisson distribution. Since capture-recapture approaches do not provide the zero counts, the estimated parameters can be achieved by modifying the EM-algorithm technique for the zero-truncated generalized Poisson distribution. The properties and the comparative performance of proposed estimator were investigated through simulation studies. Furthermore, some empirical examples are represented insights on the behavior of the estimators.

Keywords: capture, recapture methods, ratio plot, heterogeneous population, zero-truncated count

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Authors: Sajidullah Khan, Najeeb Ullah, Wang Yin Chai, Chai Soo See

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In this paper, we propose an approach to remove impulse and Poisson noise from X-ray images. Many filters have been used for impulse noise removal from color and gray scale images with their own strengths and weaknesses but X-ray images contain Poisson noise and unfortunately there is no intelligent filter which can detect impulse and Poisson noise from X-ray images. Our proposed filter uses the upgraded layer discrimination approach to detect both Impulse and Poisson noise corrupted pixels in X-ray images and then restores only those detected pixels with a simple efficient and reliable one line equation. Our Proposed algorithms are very effective and much more efficient than all existing filters used only for Impulse noise removal. The proposed method uses a new powerful and efficient noise detection method to determine whether the pixel under observation is corrupted or noise free. Results from computer simulations are used to demonstrate pleasing performance of our proposed method.

Keywords: X-ray image de-noising, impulse noise, poisson noise, PRWF

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Authors: M. Z. Raqab, Debasis Kundu, M. A. Meraou

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In this paper, we have analyzed maximum precipitation data during a particular period of time obtained from different stations in the Global Historical Climatological Network of the USA. One important point to mention is that some stations are shut down on certain days for some reason or the other. Hence, the maximum values are recorded by excluding those readings. It is assumed that the number of stations that operate follows zero-truncated Poisson random variables, and the daily precipitation follows a lognormal random variable. We call this model a compound truncated Poisson lognormal model. The proposed model has three unknown parameters, and it can take a variety of shapes. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals also can be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model, it is observed that the proposed model provides a better fit than some of the existing models.

Keywords: compound Poisson lognormal distribution, EM algorithm, maximum likelihood estimation, approximate maximum likelihood estimation, Fisher information, skew distribution

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Authors: Dongxu Chen, Yipeng Li

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This paper presents an information geometry NonlocalMeans(NLM) algorithm for Poisson denoising. NLM estimates a noise-free pixel as a weighted average of image pixels, where each pixel is weighted according to the similarity between image patches in Euclidean space. In this work, every pixel is a Poisson distribution locally estimated by Maximum Likelihood (ML), all distributions consist of a statistical manifold. A NLM denoising algorithm is conducted on the statistical manifold where Fisher information matrix can be used for computing distribution geodesics referenced as the similarity between patches. This approach was demonstrated to be competitive with related state-of-the-art methods.

Keywords: image denoising, Poisson noise, information geometry, nonlocal-means

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Authors: Dina Kon Mushid, Kabutakapua Kakanda, Dibu Dave Mbako

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The failure of material usually involves elastoplastic deformation and fracturing. Continuum mechanics can effectively deal with plastic deformation by using a yield function and the flow rule. At the same time, it has some limitations in dealing with the fracture problem since it is a theory based on the continuous field hypothesis. The lattice model can simulate the fracture problem very well, but it is inadequate for dealing with plastic deformation. Based on the discretized virtual internal bond model (DVIB), this paper proposes a lattice model that can account for plasticity. DVIB is a lattice method that considers material to comprise bond cells. Each bond cell may have any geometry with a finite number of bonds. The two-body or multi-body potential can characterize the strain energy of a bond cell. The two-body potential leads to the fixed Poisson ratio, while the multi-body potential can overcome the limitation of the fixed Poisson ratio. In the present paper, the modified Stillinger-Weber (SW), a multi-body potential, is employed to characterize the bond cell energy. The SW potential is composed of two parts. One part is the two-body potential that describes the interatomic interactions between particles. Another is the three-body potential that represents the bond angle interactions between particles. Because the SW interaction can represent the bond stretch and bond angle contribution, the SW potential-based DVIB (SW-DVIB) can represent the various Poisson ratios. To embed the plasticity in the SW-DVIB, the plasticity is considered in the two-body part of the SW potential. It is done by reducing the bond stiffness to a lower level once the bond reaches the yielding point. While before the bond reaches the yielding point, the bond is elastic. When the bond deformation exceeds the yielding point, the bond stiffness is softened to a lower value. When unloaded, irreversible deformation occurs. With the bond length increasing to a critical value, termed the failure bond length, the bond fails. The critical failure bond length is related to the cell size and the macro fracture energy. By this means, the fracture energy is conserved so that the cell size sensitivity problem is relieved to a great extent. In addition, the plasticity and the fracture are also unified at the bond level. To make the DVIB able to simulate different Poisson ratios, the three-body part of the SW potential is kept elasto-brittle. The bond angle can bear the moment before the bond angle increment is smaller than a critical value. By this method, the SW-DVIB can simulate the plastic deformation and the fracturing process of material with various Poisson ratios. The elastoplastic SW-DVIB is used to simulate the plastic deformation of a material, the plastic fracturing process, and the tunnel plastic deformation. It has been shown that the current SW-DVIB method is straightforward in simulating both elastoplastic deformation and plastic fracture.

Keywords: lattice model, discretized virtual internal bond, elastoplastic deformation, fracture, modified stillinger-weber potential

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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This study analyzed a queueing system with blocking and no waiting line. The customers arrive according to a Poisson process and the service times follow exponential distribution. There are two non-identical servers in the system. The queue discipline is FCFS, and the customers select the servers on fastest server first (FSF) basis. The service times are exponentially distributed with parameters μ1 and μ2 at servers I and II, respectively. Besides, the catastrophes occur in a Poisson manner with rate γ in the system. When server I is busy or blocked, the customer who arrives in the system leaves the system without being served. Such customers are called lost customers. The probability of losing a customer was computed for the system. The explicit time dependent probabilities of system size are obtained and a numerical example is presented in order to show the managerial insights of the model. Finally, the probability that arriving customer finds system busy and average number of server busy in steady state are obtained numerically.

Keywords: queueing system, blocking, poisson process, heterogeneous servers, queue discipline FCFS, busy period

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Authors: Jihad S. Daba, J. P. Dubois

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Understanding the statistics of non-isotropic scattering multipath channels that fade randomly with respect to time, frequency, and space in a mobile environment is very crucial for the accurate detection of received signals in wireless and cellular communication systems. In this paper, we derive stochastic models for the probability density function (PDF) of the shift in the carrier frequency caused by the Doppler Effect on the received illuminating signal in the presence of a dominant line of sight. Our derivation is based on a generalized Clarke’s and a two-wave partially developed scattering models, where the statistical distribution of the frequency shift is shown to be consistent with the power spectral density of the Doppler shifted signal.

Keywords: Doppler shift, filtered Poisson process, generalized Clark’s model, non-isotropic scattering, partially developed scattering, Rician distribution

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Authors: Zhou Jianhong

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Model averaging is a desirable approach to deal with model uncertainty, which, however, has rarely been explored for Poisson regression. In this paper, we propose a model averaging procedure based on an unbiased estimator of the expected Kullback-Leibler distance for the Poisson regression. Simulation study shows that the proposed model average estimator outperforms some other commonly used model selection and model average estimators in some situations. Our proposed methods are further applied to a real data example and the advantage of this method is demonstrated again.

Keywords: model averaging, poission regression, Kullback-Leibler distance, statistics

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Authors: Sujit Kumar Pradhan, Anil Kumar, Vijay Kumar

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The testing process of the software during the software development time is a crucial step as it makes the software more efficient and dependable. To estimate software’s reliability through the mean value function, many software reliability growth models (SRGMs) were developed under the assumption that operating and testing environments are the same. Practically, it is not true because when the software works in a natural field environment, the reliability of the software differs. This article discussed an SRGM comprising change-point and imperfect debugging in a simulated testing environment. Later on, we extended it in a multi-release direction. Initially, the software was released to the market with few features. According to the market’s demand, the software company upgraded the current version by adding new features as time passed. Therefore, we have proposed a generalized multi-release SRGM where change-point and imperfect debugging concepts have been addressed in a simulated testing environment. The failure-increasing rate concept has been adopted to determine the change point for each software release. Based on nine goodness-of-fit criteria, the proposed model is validated on two real datasets. The results demonstrate that the proposed model fits the datasets better. We have also discussed the optimal release time of the software through a cost model by assuming that the testing and debugging costs are time-dependent.

Keywords: software reliability growth models, non-homogeneous Poisson process, multi-release software, mean value function, change-point, environmental factors

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Authors: Luh Eka Suryani, Purhadi

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Poisson regression is a non-linear regression model with response variable in the form of count data that follows Poisson distribution. Modeling for a pair of count data that show high correlation can be analyzed by Poisson Bivariate Regression. Data, the number of infant mortality and maternal mortality, are count data that can be analyzed by Poisson Bivariate Regression. The Poisson regression assumption is an equidispersion where the mean and variance values are equal. However, the actual count data has a variance value which can be greater or less than the mean value (overdispersion and underdispersion). Violations of this assumption can be overcome by applying Generalized Poisson Regression. Characteristics of each regency can affect the number of cases occurred. This issue can be overcome by spatial analysis called geographically weighted regression. This study analyzes the number of infant mortality and maternal mortality based on conditions in East Java in 2016 using Geographically Weighted Bivariate Generalized Poisson Regression (GWBGPR) method. Modeling is done with adaptive bisquare Kernel weighting which produces 3 regency groups based on infant mortality rate and 5 regency groups based on maternal mortality rate. Variables that significantly influence the number of infant and maternal mortality are the percentages of pregnant women visit health workers at least 4 times during pregnancy, pregnant women get Fe3 tablets, obstetric complication handled, clean household and healthy behavior, and married women with the first marriage age under 18 years.

Keywords: adaptive bisquare kernel, GWBGPR, infant mortality, maternal mortality, overdispersion

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Authors: Prayas Sharma

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This paper proposed a generalized class of estimators, an exponential class of estimators based on the adaption of Sharma and Singh (2015) and Solanki and Singh (2013), and a simple difference estimator for estimating unknown population mean in the case of Poisson distributed population in simple random sampling without replacement. The expressions for mean square errors of the proposed classes of estimators are derived from the first order of approximation. It is shown that the adapted version of Solanki and Singh (2013), the exponential class of estimator, is always more efficient than the usual estimator, ratio, product, exponential ratio, and exponential product type estimators and equally efficient to simple difference estimator. Moreover, the adapted version of Sharma and Singh's (2015) estimator is always more efficient than all the estimators available in the literature. In addition, theoretical findings are supported by an empirical study to show the superiority of the constructed estimators over others with an application to earthquake data of Turkey.

Keywords: auxiliary attribute, point bi-serial, mean square error, simple random sampling, Poisson distribution

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Authors: Emmanuel Iyamuremye

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Extreme rainfall events have caused significant damage to agriculture, ecology, and infrastructure, disruption of human activities, injury, and loss of life. They also have significant social, economic, and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur, hence mitigating the consequences. Extreme value theory has been used widely in modeling extreme rainfall and in various disciplines, such as financial markets, the insurance industry, failure cases. Climatic extremes have been analyzed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions, which provides evidence of the importance of modeling extreme rainfall from different regions of the world. In this paper, we focused on Peak Over Thresholds approach, where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research also considers the use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Kigali. The results indicate that the proposed Poisson-GP distribution provides a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. The research also found a slow increase in return levels for maximum monthly rainfall for higher return periods, and further, the intervals are increasingly wider as the return period is increasing.

Keywords: exceedances, extreme value theory, generalized Pareto distribution, Poisson generalized Pareto distribution

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Authors: Rapelang E. Simon, Thebeetsile A. Olebetse, Joseph R. Maritinkole, Ruth O. Moleleke

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The P and S wave seismic velocity ratios (Vp/Vs) of some aftershocks are investigated using the method ofWadati diagrams. These aftershocks occurred after the 3rdApril 2017 Botswana’s Mw 6.5 earthquake and were recorded by the Network of Autonomously Recording Seismographs (NARS)-Botswana temporary network deployed from 2013 to 2018. In this paper, P and S wave data with good signal-to-noise ratiofrom twenty events of local magnitude greater or equal to 4.0are analysed with the Seisan software and used to infer properties of the upper crust in Botswana. The Vp/Vsratiosare determined from the travel-times of body waves and then converted to Poisson’s ratio, which is useful in determining the physical state of the subsurface materials. The Vp/Vs ratios of the upper crust in Botswana show regional variations from 1.70 to 1.77, with an average of 1.73. The Poisson’s ratios range from 0.24to 0.27 with an average of 0.25 and correlate well with the geological structures in Botswana.

Keywords: Botswana, earthquake, poisson's ratio, seismic velocity, Vp/Vs ratio

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Authors: Golnaz Shahtahmassebi, Jose Maria Sarabia

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In this talk, we introduce a new class of conjugate prior distributions obtained from conditional specification methodology. We illustrate the application of such distribution in Bayesian change point detection in Poisson processes. We obtain the posterior distribution of model parameters using a general bivariate distribution with gamma conditionals. Simulation from the posterior is readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.

Keywords: change point, bayesian inference, Gibbs sampler, conditional specification, gamma conditional distributions

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Authors: Y. Sunecher, N. Mamode Khan, V. Jowaheer

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This paper considers the modelling of a non-stationary bivariate integer-valued autoregressive moving average of order one (BINARMA(1,1)) with correlated Poisson innovations. The BINARMA(1,1) model is specified using the binomial thinning operator and by assuming that the cross-correlation between the two series is induced by the innovation terms only. Based on these assumptions, the non-stationary marginal and joint moments of the BINARMA(1,1) are derived iteratively by using some initial stationary moments. As regards to the estimation of parameters of the proposed model, the conditional maximum likelihood (CML) estimation method is derived based on thinning and convolution properties. The forecasting equations of the BINARMA(1,1) model are also derived. A simulation study is also proposed where BINARMA(1,1) count data are generated using a multivariate Poisson R code for the innovation terms. The performance of the BINARMA(1,1) model is then assessed through a simulation experiment and the mean estimates of the model parameters obtained are all efficient, based on their standard errors. The proposed model is then used to analyse a real-life accident data on the motorway in Mauritius, based on some covariates: policemen, daily patrol, speed cameras, traffic lights and roundabouts. The BINARMA(1,1) model is applied on the accident data and the CML estimates clearly indicate a significant impact of the covariates on the number of accidents on the motorway in Mauritius. The forecasting equations also provide reliable one-step ahead forecasts.

Keywords: non-stationary, BINARMA(1, 1) model, Poisson innovations, conditional maximum likelihood, CML

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Authors: Ishapathik Das, Sumen Sen, N. Rao Chaganty, Pooja Sengupta

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Dependent multivariate count data occur in several research studies. These data can be modeled by a multivariate Poisson or Negative binomial distribution constructed using copulas. However, when some of the counts are inflated, that is, the number of observations in some cells are much larger than other cells, then the copula based multivariate Poisson (or Negative binomial) distribution may not fit well and it is not an appropriate statistical model for the data. There is a need to modify or adjust the multivariate distribution to account for the inflated frequencies. In this article, we consider the situation where the frequencies of two cells are higher compared to the other cells, and develop a doubly inflated multivariate Poisson distribution function using multivariate Gaussian copula. We also discuss procedures for regression on covariates for the doubly inflated multivariate count data. For illustrating the proposed methodologies, we present a real data containing bivariate count observations with inflations in two cells. Several models and linear predictors with log link functions are considered, and we discuss maximum likelihood estimation to estimate unknown parameters of the models.

Keywords: copula, Gaussian copula, multivariate distributions, inflated distributios

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Authors: S. Suman, G. N. Singh

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The present manuscript addresses the estimation procedure of population parameter using Poisson probability distribution when characteristic under study possesses a rare sensitive attribute. The generalized form of unrelated randomized response model is suggested in order to acquire the truthful responses from respondents. The resultant estimators have been proposed for two situations when the information on an unrelated rare non-sensitive characteristic is known as well as unknown. The properties of the proposed estimators are derived, and the measure of confidentiality of respondent is also suggested for respondents. Empirical studies are carried out in the support of discussed theory.

Keywords: Poisson distribution, randomized response model, rare sensitive attribute, non-sensitive attribute

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Authors: Y. N. Phang, E. F. Loh

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Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling over-dispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling over-dispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling over-dispersed medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling over-dispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian, and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling over-dispersed medical count data when ZIP and ZINB are inadequate.

Keywords: zero inflated, inverse trinomial distribution, Poisson inverse Gaussian distribution, strict arcsine distribution, Pearson’s goodness of fit

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Authors: Riky Tri Hartagung, Mohammad Syamsu Rosid

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The lithology prediction process, as well as the fluid content is the most important part in the reservoir characterization. One of the methods used in this process is the simultaneous seismic inversion method. In the Posseidon field, Browse Basin, Australia, the parameters generated through simultaneous seismic inversion are not able to characterize the reservoir accurately because of the overlapping impedance values between hydrocarbon sand, water sand, and shale, which causes a high level of ambiguity in the interpretation. The Poisson Impedance inversion provides a solution to this problem by rotating the impedance a few degrees, which is obtained through the coefficient c. Coefficient c is obtained through the Target Correlation Coefficient Analysis (TCCA) by finding the optimum correlation coefficient between Poisson Impedance and the target log, namely gamma ray, effective porosity, and resistivity. Correlation of each of these target logs will produce Lithology Impedance (LI) which is sensitive to lithology sand, Porosity Impedance (ϕI) which is sensitive to porous sand, and Fluid Impedance (FI) which is sensitive to fluid content. The results show that PI gives better results in separating hydrocarbon saturated reservoir zones. Based on the results of the LI-GR crossplot, the ϕI-effective porosity crossplot, and the FI-Sw crossplot with optimum correlations of 0.74, 0.91, and 0.82 respectively, it shows that the lithology of hidrocarbon-saturated porous sand is at the value of LI ≤ 2800 (m/s)(g *cc), ϕI ≤ 5500 (m/s)(g*cc), and FI ≤ 4000 (m/s)(g*cc). The presence of low values of LI, ϕI, and FI correlates accurately with the presence of hydrocarbons in the well. Each value of c is then applied to the seismic data. The results show that the PI inversion gives a good distribution of Hydrocarbon-saturated porous sand lithology. The distribution of hydrocarbon saturated porous sand on the seismic inversion section is seen in the northeast – southwest direction, which is estimated as the direction of gas distribution.

Keywords: reservoir characterization, poisson impedance, browse basin, poseidon field

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Authors: Ya-Mei Chang

Abstract:

This research is intended to apply spatio-temporal point process methods to the dengue fever data in Tainan. The spatio-temporal intensity function of the dataset is assumed to be separable. The kernel estimation is a widely used approach to estimate intensity functions. The intensity function is very helpful to study the relation of the spatio-temporal point process and some covariates. The covariate effects might be nonlinear. An nonparametric smoothing estimator is used to detect the nonlinearity of the covariate effects. A fitted parametric model could describe the influence of the covariates to the dengue fever. The correlation between the data points is detected by the K-function. The result of this research could provide useful information to help the government or the stakeholders making decisions.

Keywords: dengue fever, spatial point process, kernel estimation, covariate effect

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