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Evaluations of COVID-19 epidemic models with multiple susceptible compartments using exponential and non-exponential distribution for disease stages

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Infectious Disease Modelling 2022年第4期7卷 795-810页

作者： Yan Chen Haitao Song Shengqiang Liu School of Mathematical Sciences Tiangong UniversityTianjin300387China Complex Systems Research Center Shanxi UniversityTaiyuan030006China

Mathematical models have wide applications in studying COVID-19 epidemic transmission dynamics,however,most mathematical models do not take into account the heterogeneity of susceptible populations and the non-exponential distribution infectious *** paper attempts to investigate whether non-exponentially distributed infectious period can better characterize the transmission process in heterogeneous susceptible populations and how it impacts the control *** this purpose,we establish two COVID-19 epidemic models with heterogeneous susceptible populations based on different assumptions for infectious period:the first one is an exponential distribution model(EDM),and the other one is a gamma distribution model(GDM);explicit formula of peak time of the EDM is presented via our analytical *** data fitting with the COVID-19(Omicron)epidemic in Spain and Norway,it seems that Spain is more suitable for EDM while Norway is more suitable for ***,we use EDM and GDM to evaluate the impaction of control strategies such as reduction of transmission rates,and increase of primary course rate(PCR)and booster dose rate(BDR).

关键词： Mathematical models COVID-19 exponential distribution Gamma distribution Peak time

Robust and Efficient Reliability Estimation for exponential distribution

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Computers, Materials & Continua 2021年第11期69卷 2807-2824页

作者： Muhammad Aslam Mohd Safari Nurulkamal Masseran Muhammad Hilmi Abdul Majid Department of Mathematics Faculty of ScienceUniversiti Putra MalaysiaUPM Serdang43400SelangorMalaysia Department of Mathematical Sciences Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaUKM Bangi43600SelangorMalaysia

In modeling reliability data,the exponential distribution is commonly used due to its *** estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be ***,the maximum likelihood estimator is highly sensitive in the presence of contamination or *** this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform *** examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were *** new estimator offers reasonable protection against outliers besides being simple to ***,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of ***,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.

关键词： exponential distribution M-estimator probability integral transform statistic robust estimation reliability

Monotone Empirical Bayes Test for the exponential distribution

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Northeastern Mathematical Journal 2006年第3期22卷 265-274页

作者：王立春 Institute of Applied Mathematics Chinese Academy of Sciences

We study the two-action problem in the exponential distribution via empirical Bayes （EB） approach. Based on type Ⅱ censored samples, we construct an EB test rule and obtain an optimal rate of convergence which much... 详细信息

关键词： empirical Bayes exponential distribution rate of convergence

A Concise Proof of the Relation between Poisson Process and exponential distribution

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Systems Science and Systems Engineering 1999年第4期9卷 40-43页

作者： TANG Ying\|hui,\ TANG Xiao\|wo Dept. of Appl. Math., Mgt.College, Univer. of Electronic Science and Technology of China, Chengdu 610054, China

Using the memoryless property of the exponential distribution, we have proved again that the relation between the Poisson process and the exponential distribution, that is, the stochastic process {N(t), t≥0} is said to be a Poisson process with arrival rate λ(>0) if and only if the sequence of interarrival times {τ n,n≥1} are independent and identically distributed according to an exponential distribution with parameter λ, where N(t) denotes the arrival number in (0,t\].. It′s noting that the proof provided in this paper is concise and intuitive.

关键词： exponential distribution memoryless property Poisson process

On Size-Biased Double Weighted exponential distribution (SDWED)

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Open Journal of Statistics 2016年第5期6卷 917-930页

作者： Zahida Perveen Zulfiqar Ahmed Munir Ahmad Lahore Garrison University Main Campus Sector C Phase VI DHA Lahore Pakistan GIFT University Gujranwala Pakistan National College of Business Administration and Economics Lahore Pakistan

This paper introduces a new distribution based on the exponential distribution, known as Size-biased Double Weighted exponential distribution (SDWED). Some characteristics of the new distribution are obtained. Plots for the cumulative distribution function, pdf and hazard function, tables with values of skewness and kurtosis are provided. As a motivation, the statistical application of the results to a problem of ball bearing data has been provided. It is observed that the new distribution is skewed to the right and bears most of the properties of skewed distribution. It is found that our newly proposed distribution fits better than size-biased Rayleigh and Maxwell distributions and many other distributions. Since many researchers have studied the procedure of the weighted distributions in the estates of forest, biomedicine and biostatistics etc., we hope in numerous fields of theoretical and applied sciences, the findings of this paper will be useful for the practitioners.

关键词： exponential distribution Moments Moment Ratios Estimation

An exponential distribution-based Model for Equipment Remaining Life Prediction

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An Exponential Distribution-based Model for Equipment Remain...

CONSISTENCY　OF　MLE　OF　THE　PARAMETER　OF　exponential　LIFETIME　distribution　FOR　RANDOM　CENSORING　MODEL　WITH　INCOMPLETE　INFORMATION

2012 National Conference on Information Technology and Computer Science

作者： MENG Xiao-Hong 503 Section of Xi'' an High-tech Institute,710025,Hongqing Town,Xi'' an,China WANG Wei 503 Section of Xi'' an High-tech Institute,710025,Hongqing Town,Xi'' an,China ZHOU Yong-Tao 503 Section of Xi'' an High-tech Institute,710025,Hongqing Town,Xi'' an,China

The article proposed and established an exponential distribution-based model for equipment remaining life *** model is a general decision model for detectable continuous degradation *** modeling method and application example is *** with other models,the model has the basic characteristics of simple and *** has important practice value for maintenance decision of equipment parts fault caused by gradual loss.

关键词： exponential distribution remaining life equipment maintenance

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Applied Mathematics(A Journal of Chinese Universities) 1995年第4期10卷 379-386页

作者： YE ERHUA Department of Applied Mathematics Nanjing University of Aeronautics and Astronautics Nanjing

In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete informat... 详细信息

关键词： Random censoring test with incomplete information exponential distribution maximum likelihood estimator consistency.

Evaluation of GNSS Signal-in-Space Continuity:A Weibull-distribution-Based Method

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Chinese Journal of Electronics 2018年第3期27卷 634-640页

作者： LI Rui ZHENG Shuaiyong WANG Zhipeng TANG Yang SUN Si HUANG Zhigang School of Electronic and Information Engineering Beihang University Collaborative Innovation Center of Geospatial Technology

Signal-in-space(SIS) continuity is an important performance index of Global navigation satellite system(GNSS). However, the studies on the continuity of GNSS SIS are limited both at home and abroad, and are mainly based on the exponential distribution method. We first employ this method to analyze SIS failures of GPS and BDS, finding that this method is not flexile when describing the characteristic of GNSS SIS failures and the fitting characteristic of this method is not well. Therefore, we propose a method based on Weibull distribution to evaluate the performance of GNSS SIS continuity. Our method is compared with the models of exponential distribution, normal distribution, and Gamma distribution regarding the fitting characteristics of the interruption time interval of GPS SIS, the critical parameter of continuity. Results show that the fitting characteristic of the Weibull-distributionbased method is the best and can be used in various forms to describe reliability problem. Then our method is used to evalute the SIS continuity of BDS and GLONASS and its effectiveness and rationality are validated again. The contributions of our study lie in the development of a practical method for evaluating GNSS SIS continuity and a reference for GNSS performance.

关键词： GNSS SIS continuity Evaluation exponential distribution Weibull distribution

Improving Energy and Power Efficiency Using NComputing and Approaches for Predicting Reliability of Complex Computing Systems

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International Journal of Automation and computing 2010年第2期7卷 153-159页

作者： Hoang Pham Hoang Pham Jr. Department of Industrial and Systems Engineering Rutgers University Timothy Christian School

Opting to follow the computing-design philosophy that the best way to reduce power consumption and increase energy efficiency is to reduce waste, we propose an architecture with a very simple ready-implementation by using an NComputing device that can allow multi-users but only one computer is needed. This intuitively can save energy, space as well as cost. In this paper, we propose a simple and realistic NComputing architecture to study the energy and power-efficient consumption of desktop computer systems by using the NComputing device. We also propose new approaches to estimate the reliability of k-out-of-n systems based on the delta method. The k-out-of-n system consisting of n subsystems works if and only if at least k-of-the-n subsystems work. More specificly, we develop approaches to obtain the reliability estimation for the k-out-of-n systems which is composed of n independent and identically distributed subsystems where each subsystem （or energy-efficient usage application） can be assumed to follow a two-parameter exponential lifetime distribution function. The detailed derivations of reliability estimation of k-out-of-n systems based on the biased-corrected estimator, known as delta method, the uniformly minimum variance unbiased estimate （UMVUE） and maximum likelihood estimate （MLE） are discussed. An energy-management NComputing application is discussed to illustrate the reliability results in terms of the energy consumption usages of a computer system with qua（t-core, 8 GB of RAM, and a GeForce 9800GX-2 graphics card to perform various complex applications. The estimated reliability values of systems based on the UMVUE and the delta method differ only slightly. Often the UMVUE of reliability for a complex system is a lot more difficult to obtain, if not impossible. The delta method seems to be a simple and better approach to obtain the reliability estimation of complex systems. The results of this study also show that, in practice, the NComputing archite

关键词： Energy efficiency Ncomputing k-out-of-n system exponential distribution reliability estimation uniformly minimum variance unbiased estimate (UMVUE) maximum likelihood estimate (MLE).