Poisson Distribution Results for v-Spirallike Functions of Orderγ

The main objective of this organized paper is to establish the Poisson distribution conditions for the v-spirallike function classes S(γ;ψ)and K(γ;ψ).We also investigate an integral operator associated with the Poisson distribution.

Improvement on MLE of the Means of Independent Poisson Distribution

In this paper, we consider the simultaneous estimation of the pa rameters (means) of the independent Poisson distribution by using the following loss functions:L0(θ,T)=ni=1(Ti-θi)2, L1(θ,T)=ni=1(Ti-θi)2/θiWe develop an estimator which is better than the maximum likelihood estimator X simultaneously under L0(θ,T) and L1(θ,T). Our estimator possesses substantially smaller risk than the usual estimator X to estimate the param eters (means) of the independent Poisson distribution.

Improved Estimation of Rare Sensitive Attribute in a Stratified Sampling Using Poisson Distribution

In this study, we propose a two stage randomized response model. Improved unbiased estimators of the mean number of persons possessing a rare sensitive attribute under two different situations are proposed. The proposed estimators are evaluated using a relative efficiency comparison. It is shown that our estimators are efficient as compared to existing estimators when the parameter of rare unrelated attribute is known and in unknown case, depending on the probability of selecting a question.

The Poisson Distribution Is Applied to Improve the Estimation of Individual Cell and Micropopulation Lag Phases

Many articles dealing with individual cell lag phase determination assume that growth, when observed, comes from one cell. This assumption is not in agreement with the Poisson distribution, which uses the probability of growth in a sample to predict how many samples contain one, two, or some other number of cells. This article analyses and compares different approaches to improve the accuracy of lag phase estimation of individual cells and micropopulations. It argues that if the highest initial load, as predicted by the Poisson distribution, is assigned to the sample with the shortest lag phase, the second highest to the sample with the second shortest lag phase and so on, the resulting lag phase distributions would be more accurate. This study also proposes the use of a robust test, permutation test, to compare lag phase distributions obtained in different situations.

Designing Bayesian Two-Sided Group Chain Sampling Plan for Gamma Prior Distribution

Acceptance sampling is used to decide either the whole lot will be accepted or rejected,based on inspection of randomly sampled items from the same lot.As an alternative to traditional sampling plans,it is possible to use Baye-sian approaches using previous knowledge on process variation.This study pre-sents a Bayesian two-sided group chain sampling plan(BTSGChSP)by using various combinations of design parameters.In BTSGChSP,inspection is based on preceding as well as succeeding lots.Poisson function is used to derive the probability of lot acceptance based on defective and non-defective products.Gamma distribution is considered as a suitable prior for Poisson distribution.Four quality regions are found,namely:(i)quality decision region(QDR),(ii)probabil-istic quality region(PQR),(iii)limiting quality region(LQR)and(iv)indifference quality region(IQR).Producer’s risk and consumer’s risk are considered to esti-mate the quality regions,where acceptable quality level(AQL)is associated with producer’s risk and limiting quality level(LQL)is associated with consumer’s risk.Moreover,AQL and LQL are used in the selection of design parameters for BTSGChSP.The values based on all possible combinations of design parameters for BTSGChSP are presented and inflection points’values are found.Thefinding exposes that BTSGChSP is a better substitute for the existing plan for industrial practitioners.

A COMPOUND POISSON MODEL FOR LEARNING DISCRETE BAYESIAN NETWORKS

We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.

POISSON LIMIT THEOREM FOR COUNTABLE MARKOV CHAINS IN MARKOVIAN ENVIRONMENTS

A countable Markov chain in a Markovian environment is considered.A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved.In order to prove this theorem,the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown. It's well-known that a Markov process in a Markovian environment is generally not a standard Markov chain,so an example of Poisson approximation for a process which is not a Markov process is given.On the other hand,when the environmental process degenerates to a constant sequence,a Poisson limit theorem for countable Markov chains,which is the generalization of Pitskel's result for finite Markov chains is obtained.

Hypothesis testing of Poisson rates in COVID-19 offspring distributions

In the present study,we undertake the task of hypothesis testing in the context of Poissondistributed data.The primary objective of our investigation is to ascertain whether two distinct sets of discrete data share the same Poisson rate.We delve into a comprehensive review and comparative analysis of various frequentist and Bayesian methodologies specifically designed to address this problem.Among these are the conditional test,the likelihood ratio test,and the Bayes factor.Additionally,we employ the posterior predictive p-value in our analysis,coupled with its corresponding calibration procedures.As the culmination of our investigation,we apply these diverse methodologies to test both simulated datasets and real-world data.The latter consists of the offspring distributions linked to COVID-19 cases in two disparate geographies-Hong Kong and Rwanda.This allows us to provide a practical demonstration of the methodologies’applications and their potential implications in the field of epidemiology.

Assessment and sequencing of air target threat based on intuitionistic fuzzy entropy and dynamic VIKOR

In view of the fact that traditional air target threat assessment methods are difficult to reflect the combat characteristics of uncertain, dynamic and hybrid formation, an algorithm is proposed to solve the multi-target threat assessment problems. The target attribute weight is calculated by the intuitionistic fuzzy entropy(IFE) algorithm and the time series weight is gained by the Poisson distribution method based on multi-times data. Finally,assessment and sequencing of the air multi-target threat model based on IFE and dynamic Vlse Kriterijumska Optimizacija I Kompromisno Resenje(VIKOR) is established with an example which indicates that the method is reasonable and effective.

An Intelligent Fine-Tuned Forecasting Technique for Covid-19 Prediction Using Neuralprophet Model

COVID-19,being the virus of fear and anxiety,is one of the most recent and emergent of various respiratory disorders.It is similar to the MERS-COV and SARS-COV,the viruses that affected a large population of different countries in the year 2012 and 2002,respectively.Various standard models have been used for COVID-19 epidemic prediction but they suffered from low accuracy due to lesser data availability and a high level of uncertainty.The proposed approach used a machine learning-based time-series Facebook NeuralProphet model for prediction of the number of death as well as confirmed cases and compared it with Poisson Distribution,and Random Forest Model.The analysis upon dataset has been performed considering the time duration from January 1st 2020 to16th July 2021.The model has been developed to obtain the forecast values till September 2021.This study aimed to determine the pandemic prediction of COVID-19 in the second wave of coronavirus in India using the latest Time-Series model to observe and predict the coronavirus pandemic situation across the country.In India,the cases are rapidly increasing day-by-day since mid of Feb 2021.The prediction of death rate using the proposed model has a good ability to forecast the COVID-19 dataset essentially in the second wave.To empower the prediction for future validation,the proposed model works effectively.

Surface-enhanced resonance Raman scattering spectroscopy of single R6G molecules

Surface-enhanced resonance Raman scattering （SERRS） of Rhodamine 6G （R6G） adsorbed on colloidal silver clusters has been studied. Based on the great enhancement of the Raman signal and the quench of the fluorescence, the SERRS spectra of R6G were recorded for the samples of dye colloidal solution with different concentrations. Spectral inhomogeneity behaviours from single molecules in the dried sample films were observed with complementary evidences, such as spectral polarization, spectral diffusion, intensity fluctuation of vibrational lines and even ＂breathing＂ of the molecules. Sequential spectra observed from a liquid sample with an average of 0.3 dye molecules in the probed volume exhibited the expected Poisson distribution for actually measuring 0, 1 or 2 molecules. Difference between the SERRS spectra of R6G excited by linearly and circularly polarized light were experimentally measured.

Multi-Threat Real-Time Separating System

This paper describes a multi-threat real-time separating system for broadband anti-radiation missile seeker. It presents a method, with a dual-port memory as comparer, to perform PF and PW hardware real-time separation and to determine the time-of-arrival (TOA) by use of sequential difference histogram (SDIF). The method has been applied to practice, which has achieved good results.

CONDITIONAL RECURSIVE EQUATIONS ON EXCESS-OF-LOSS REINSURANCE

The rharginal recursive equations on excess-of-loss reinsurance treaty are investignted, under the assumption that the number of claims belongs to the family consisting of Poisson, binomial and negative binomial, and that the severity distribution has bounded continuous density function. On conditional of the numbers of claims associated with the reinsurer and the cedent, some recursive equations are obtained for the marginal distributions of the total payments of the reinsurer and the cedent.

A spatially-explicit count data regression for modeling the density of forest cockchafer(Melolontha hippocastani) larvae in the Hessian Ried(Germany)

Background： In this paper, a regression model for predicting the spatial distribution of forest cockchafer larvae in the Hessian Ried region （Germany） is presented. The forest cockchafer, a native biotic pest, is a major cause of damage in forests in this region particularly during the regeneration phase. The model developed in this study is based on a systematic sample inventory of forest cockchafer larvae by excavation across the Hessian Ried. These forest cockchafer larvae data were characterized by excess zeros and overdispersion. Methods： Using specific generalized additive regression models, different discrete distributions, including the Poisson, negative binomial and zero-inflated Poisson distributions, were compared. The methodology employed allowed the simultaneous estimation of non-linear model effects of causal covariates and, to account for spatial autocorrelation, of a 2-dimensional spatial trend function. In the validation of the models, both the Akaike information criterion （AIC） and more detailed graphical procedures based on randomized quantile residuals were used. Results： The negative binomial distribution was superior to the Poisson and the zero-inflated Poisson distributions, providing a near perfect fit to the data, which was proven in an extensive validation process. The causal predictors found to affect the density of larvae significantly were distance to water table and percentage of pure clay layer in the soil to a depth of I m. Model predictions showed that larva density increased with an increase in distance to the water table up to almost 4 m, after which it remained constant, and with a reduction in the percentage of pure clay layer. However this latter correlation was weak and requires further investigation. The 2-dimensional trend function indicated a strong spatial effect, and thus explained by far the highest proportion of variation in larva density. Conclusions： As such the model can be used to support forest practitioners in their decision making for regeneration and forest protection planning in the Hessian predicting future spatial patterns of the larva density is still comparatively weak. Ried. However, the application of the model for somewhat limited because the causal effects are

Adaptive Multi-Cost Routing Protocol to Enhance Lifetime for Wireless Body Area Network

Wireless Body Area Network(WBAN)technologies are emerging with extensive applications in several domains.Health is a fascinating domain of WBAN for smart monitoring of a patient’s condition.An important factor to consider in WBAN is a node’s lifetime.Improving the lifetime of nodes is critical to address many issues,such as utility and reliability.Existing routing protocols have addressed the energy conservation problem but considered only a few parameters,thus affecting their performance.Moreover,most of the existing schemes did not consider traffic prioritization which is critical in WBANs.In this paper,an adaptive multi-cost routing protocol is proposed with a multi-objective cost function considering minimum distance from sink,temperature of sensor nodes,priority of sensed data,and maximum residual energy on sensor nodes.The performance of the proposed protocol is compared with the existing schemes for the parameters:network lifetime,stability period,throughput,energy consumption,and path loss.It is evident from the obtained results that the proposed protocol improves network lifetime and stability period by 30%and 15%,respectively,as well as outperforms the existing protocols in terms of throughput,energy consumption,and path loss.

FEATURE-EXTRACT ANALYSIS OF SERIAL ANALYSIS OF GENE EXPRESSION DATA

Serial Analysis of Gene Expression (SAGE) is a powerful tool to analyze whole-genome expression profiles. SAGE data, characterized by large quantity and high dimensions, need reducing their dimensions and extract feature to improve the accuracy and efficiency when they are used for pattern recognition and clustering analysis. A Poisson Model-based Kernel (PMK) was proposed based on the Poisson distribution of the SAGE data. Kernel Principle Component Analysis (KPCA) with PMK was proposed and used in feature-extract analysis of mouse retinal SAGE data. The computa-tional results show that this algorithm can extract feature effectively and reduce dimensions of SAGE data.

Species Abundance in a Forest Community in South China：A Case of Poisson Lognormal Distribution

Case studies on Poisson lognormal distribution of species abundance have been rare, especially in forest communities. We propose a numerical method to fit the Poisson lognormal to the species abundance data at an evergreen mixed forest in the Dinghushan Biosphere Reserve, South China. Plants in the tree, shrub and herb layers in 25 quadrats of 20 m× 20 m, 5 m× 5 m, and 1 m× 1 m were surveyed. Results indicated that: (i) for each layer, the observed species abundance with a similarly small median, mode, and a variance larger than the mean was reverse J-shaped and followed well the zero-truncated Poisson lognormal; (ii) the coefficient of variation, skewness and kurtosis of abundance, and two Poisson lognormal parameters (& and μ) for shrub layer were closer to those for the herb layer than those for the tree layer; and (iii) from the tree to the shrub to the herb layer, the α and the coefficient of variation decreased, whereas diversity increased. We suggest that: (i) the species abundance distributions in the three layers reflects the overall community characteristics; (ii) the Poisson lognormal can describe the species abundance distribution in diverse communities with a few abundant species but many rare species; and (iii) 1/α should be an alternative measure of diversity.

Identifying accident black spots based on the accident spacing distribution

The identification of accident black spots is of great significance for the prevention of traffic accidents.Commonly used accident black spot identification methods divide road sections for the analysis of accident data,the direct result of which is the splitting of accident black spots,which affects the results.This paper is based on three years of traffic accident data from the Beijing-Harbin Expressway,including the time and location of traffic accidents,form of the accident fatalities,severe injuries,slight injuries,and property damage only(PDO).To avoid road division effects,an identification method based on the accident spacing distribution is established by using quality control theory.The results show that the average number of accidents per kilometer by the method proposed in this paper is 42,which is much higher than 10,identified by other identification methods.The method proposed in this paper improves the accuracy of the identification results.This method avoids the problem of road segmentation found in other common methods and can more accurately reflect the spatial distribution of traffic accidents.Thus making the identification of accidents more scientific and accurate.

Risk estimation based on mixed normal distribution model for diabetes-related hospitalization claims

Medical insurance service, the important part of national healthcare supporting system with a history dating back more than 100 years ago, remains a global challenge because of its high rates of compensation and difficulty in risk control. When developing the diabetes related, hospitalization insurance, we found that the risk loss of the diabetic inpatients does not follow a symmetrical unimodal distribution： in fact, it is hard to describe its risk loses distribution with a single probability distribution model. Therefore, we put forward a risk measurement method based on a mixed normal distributions model for medical insurance of inpatients with diabetes.

Implementation of upper limit calculation for a Poisson variable by Bayesian approach

The calculation of Bayesian confidence upper limit for a Poisson variable including both signal and background with and without systematic uncertainties has been formulated. A Fortran 77 routine, BPULE, has been developed to implement the calculation. The routine can account for systematic uncertainties in the background expectation and signal efficiency. The systematic uncertainties may be separately parameterized by a Gaussian, Log-Gaussian or flat probability density function （pdf）. Some technical details of BPULE have been discussed.