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The New Mixed Generalized Erlang Distribution
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作者 Therrar Kadri Yara Ghannam 《Applied Mathematics》 2023年第8期497-511,共8页
In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various discip... In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments. 展开更多
关键词 generalized Erlang distribution Mixed distribution Probability Density Function Cumulative distribution Function Moment generating Function Hazard Rate Function Reliability Function Moment of Order k
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Analysis of College Students’ Test Scores Based on Two-Component Mixed Generalized Normal Distribution
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作者 Luliang Wen Haiwu Rong Yanjun Qiu 《Journal of Data Analysis and Information Processing》 2023年第1期69-80,共12页
In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditiona... In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value. 展开更多
关键词 Two-Component Mixed generalized Normal distribution Two-Component Mixed Normal distribution ECM Algorithm Test Scores
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Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution 被引量:1
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作者 Tao Yin Changgen Peng +2 位作者 Weijie Tan Dequan Xu Hanlin Tang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第1期827-843,共17页
In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining ... In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party. 展开更多
关键词 Rate setting Tweedie distribution generalized linear models federated learning homomorphic encryption
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A Novel Defender-Attacker-Defender Model for Resilient Distributed Generator Planning with Network Reconfiguration and Demand Response
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作者 Wenlu Ji Teng Tu Nan Ma 《Energy Engineering》 EI 2024年第5期1223-1243,共21页
To improve the resilience of a distribution system against extreme weather,a fuel-based distributed generator(DG)allocation model is proposed in this study.In this model,the DGs are placed at the planning stage.When a... To improve the resilience of a distribution system against extreme weather,a fuel-based distributed generator(DG)allocation model is proposed in this study.In this model,the DGs are placed at the planning stage.When an extreme event occurs,the controllable generators form temporary microgrids(MGs)to restore the load maximally.Simultaneously,a demand response program(DRP)mitigates the imbalance between the power supply and demand during extreme events.To cope with the fault uncertainty,a robust optimization(RO)method is applied to reduce the long-term investment and short-term operation costs.The optimization is formulated as a tri-level defenderattacker-defender(DAD)framework.At the first level,decision-makers work out the DG allocation scheme;at the second level,the attacker finds the optimal attack strategy with maximum damage;and at the third level,restoration measures,namely distribution network reconfiguration(DNR)and demand response are performed.The problem is solved by the nested column and constraint generation(NC&CG)method and the model is validated using an IEEE 33-node system.Case studies validate the effectiveness and superiority of the proposed model according to the enhanced resilience and reduced cost. 展开更多
关键词 distribution system RESILIENCE defender-attacker-defender distributed generator demand response microgrids formation
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Brain Functional Network Generation Using Distribution-Regularized Adversarial Graph Autoencoder with Transformer for Dementia Diagnosis 被引量:1
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作者 Qiankun Zuo Junhua Hu +5 位作者 Yudong Zhang Junren Pan Changhong Jing Xuhang Chen Xiaobo Meng Jin Hong 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第12期2129-2147,共19页
The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlat... The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlation between abnormal connectivities and dementia disorders.However,it is challenging to access considerable amounts of brain functional network data,which hinders the widespread application of data-driven models in dementia diagnosis.In this study,a novel distribution-regularized adversarial graph auto-Encoder(DAGAE)with transformer is proposed to generate new fake brain functional networks to augment the brain functional network dataset,improving the dementia diagnosis accuracy of data-driven models.Specifically,the label distribution is estimated to regularize the latent space learned by the graph encoder,which canmake the learning process stable and the learned representation robust.Also,the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions.The typical topological properties and discriminative features can be preserved entirely.Furthermore,the generated brain functional networks improve the prediction performance using different classifiers,which can be applied to analyze other cognitive diseases.Attempts on the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset demonstrate that the proposed model can generate good brain functional networks.The classification results show adding generated data can achieve the best accuracy value of 85.33%,sensitivity value of 84.00%,specificity value of 86.67%.The proposed model also achieves superior performance compared with other related augmentedmodels.Overall,the proposedmodel effectively improves cognitive disease diagnosis by generating diverse brain functional networks. 展开更多
关键词 Adversarial graph encoder label distribution generative transformer functional brain connectivity graph convolutional network DEMENTIA
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Robust multi-task distributed estimation based on generalized maximum correntropy criterion
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作者 胡倩 陈枫 叶明 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第6期705-715,共11页
False data injection(FDI) attacks are common in the distributed estimation of multi-task network environments, so an attack detection strategy is designed by combining the generalized maximum correntropy criterion. Ba... False data injection(FDI) attacks are common in the distributed estimation of multi-task network environments, so an attack detection strategy is designed by combining the generalized maximum correntropy criterion. Based on this, we propose a diffusion least-mean-square algorithm based on the generalized maximum correntropy criterion(GMCC-DLMS)for multi-task networks. The algorithm achieves gratifying estimation results. Even more, compared to the related work,it has better robustness when the number of attacked nodes increases. Moreover, the assumption about the number of attacked nodes is relaxed, which is applicable to multi-task environments. In addition, the performance of the proposed GMCC-DLMS algorithm is analyzed in the mean and mean-square senses. Finally, simulation experiments confirm the performance and effectiveness against FDI attacks of the algorithm. 展开更多
关键词 distributed estimation generalized correntropy multi-task networks adaptive filtering
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Statistical analysis of generalized exponential distribution under progressive censoring with binomial removals 被引量:11
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作者 Weian Yan Yimin Shi +1 位作者 Baowei Song Zhaoyong Mao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第4期707-714,共8页
The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximu... The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation. 展开更多
关键词 binomial removal progressive censoring maximumlikelihood estimator expected experiment time generalized exponential distribution.
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SPECTRUM DISTRIBUTION OF THE SEDOND ORDER GENERALIZED DISTRIBUTED PARAMETER SYSTEMS 被引量:2
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作者 葛照强 朱广田 马勇镐 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第10期1224-1232,共9页
Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expr... Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system. 展开更多
关键词 second order generalized distributed parameter system spectrum distribution Hilbert space generalized inverse one of bounded linear operatiors
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GENERALIZED OPERATORS AND OPERATOR-VALUED DISTRIBUTIONS IN QUANTUM FIELD THEORY 被引量:2
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作者 黄志远 王湘君 王才士 《Acta Mathematica Scientia》 SCIE CSCD 2003年第2期145-154,共10页
The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
关键词 White noise analysis quantum fields generalized operator operator-valued distribution
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GENERALIZED PARETO DISTRIBUTION FIT TO MEDICAL INSURANCE CLAIMS DATA 被引量:2
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作者 Ouyang Zisheng Xie Chi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第1期21-29,共9页
How to choose an optimal threshold is a key problem in the generalized Pareto distribution (GPD) model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily... How to choose an optimal threshold is a key problem in the generalized Pareto distribution (GPD) model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data. 展开更多
关键词 generalized Pareto distribution high quantile probable maximum loss.
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The exponentiated generalized power Lindley distribution: Properties and applications 被引量:1
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作者 S.M.T.K. MirMostafaee Morad Alizadeh +1 位作者 Emrah Altun Saralees Nadarajah 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2019年第2期127-148,共22页
In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of th... In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of the density and hazard rate functions, the quantile function, moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived. Moreover, we discuss the parameter estimation of the new distribution using the maximum likelihood and diagonally weighted least squares methods. A simulation study is performed to evaluate the estimators. We use two real data sets to illustrate the applicability of the new model. Empirical findings show that the proposed model provides better fits than some other well-known extensions of Lindley distributions. 展开更多
关键词 Anderson-Darling test statistic Exponentiated generalized class of distributionS Lambert function Maximum LIKELIHOOD method POWER Lindley distribution
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Prediction Based on Generalized Order Statistics from a Mixture of Rayleigh Distributions Using MCMC Algorithm 被引量:2
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作者 Tahani A. Abushal Areej M. Al-Zaydi 《Open Journal of Statistics》 2012年第3期356-367,共12页
This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distribut... This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper. 展开更多
关键词 MIXTURE distributionS RAYLEIGH distribution generalized Order STATISTICS RECORD VALUES MCMC
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Influence of Generalized (r, q) Distribution Function on Electrostatic Waves 被引量:2
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作者 M.N.S. Qureshi SHI Jian-Kui MA Shi-Zhuang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第3期550-554,共5页
Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau... Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma (Langmuir) waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized (r, q) distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices. 展开更多
关键词 generalized (r q) distribution function electrostatic waves DAMPING
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Importance of Generalized Logistic Distribution in Extreme Value Modeling 被引量:1
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作者 K. Nidhin C. Chandran 《Applied Mathematics》 2013年第3期560-573,共14页
We consider a problem from stock market modeling, precisely, choice of adequate distribution of modeling extremal behavior of stock market data. Generalized extreme value (GEV) distribution and generalized Pareto (GP)... We consider a problem from stock market modeling, precisely, choice of adequate distribution of modeling extremal behavior of stock market data. Generalized extreme value (GEV) distribution and generalized Pareto (GP) distribution are the classical distributions for this problem. However, from 2004, [1] and many other researchers have been empirically showing that generalized logistic (GL) distribution is a better model than GEV and GP distributions in modeling extreme movement of stock market data. In this paper, we show that these results are not accidental. We prove the theoretical importance of GL distribution in extreme value modeling. For proving this, we introduce a general multivariate limit theorem and deduce some important multivariate theorems in probability as special cases. By using the theorem, we derive a limit theorem in extreme value theory, where GL distribution plays central role instead of GEV distribution. The proof of this result is parallel to the proof of classical extremal types theorem, in the sense that, it possess important characteristic in classical extreme value theory, for e.g. distributional property, stability, convergence and multivariate extension etc. 展开更多
关键词 Financial Risk MODELING STOCK Market Analysis generalized Logistic distribution generalized Extreme Value distribution TAIL EQUIVALENCE Maximum Stability Random Sample size Limit distribution
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Generalized Pareto Distribution Model and Its Application to Hydrocarbon Resource Structure Prediction of the Huanghua Depression 被引量:1
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作者 Liu Xiaoping Jin Zhijun +1 位作者 Chen Shanyong Liu Lifang 《Petroleum Science》 SCIE CAS CSCD 2006年第2期22-27,共6页
The generalized Pareto distribution model is a kind of hydrocarbon pool size probability statistical method for resource assessment. By introducing the time variable, resource conversion rate and the geological variab... The generalized Pareto distribution model is a kind of hydrocarbon pool size probability statistical method for resource assessment. By introducing the time variable, resource conversion rate and the geological variable, resource density, such model can describe not only different types of basins, but also any exploration samples at different phases of exploration, up to the parent population. It is a dynamic distribution model with profound geological significance and wide applicability. Its basic principle and the process of resource assessment are described in this paper. The petroleum accumulation system is an appropriate assessment unit for such method. The hydrocarbon resource structure of the Huanghua Depression in Bohai Bay Basin was predicted by using this model. The prediction results accord with the knowledge of exploration in the Huanghua Depression, and point out the remaining resources potential and structure of different petroleum accumulation systems, which are of great significance for guiding future exploration in the Huanghua Depression. 展开更多
关键词 generalized Pareto distribution model hydrocarbon resource assessment hydrocarbon resource structure Huanghua depression
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Likelihood and Quadratic Distance Methods for the Generalized Asymmetric Laplace Distribution for Financial Data 被引量:1
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作者 Andrew Luong 《Open Journal of Statistics》 2017年第2期347-368,共22页
Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct ... Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models. 展开更多
关键词 M-ESTIMATORS CUMULANT generating Function CHI-SQUARE Tests generalized Hyperbolic distribution SIMPLEX Pattern Search Variance Gamma Minimum Distance VALUE at RISK Entropic VALUE at RISK European Call Option
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Evaluating Traffic Congestion Using the Traffic Occupancy and Speed Distribution Relationship: An Application of Bayesian Dirichlet Process Mixtures of Generalized Linear Model 被引量:1
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作者 Emmanuel Kidando Ren Moses +1 位作者 Eren E. Ozguven Thobias Sando 《Journal of Transportation Technologies》 2017年第3期318-335,共18页
Accurate classification and prediction of future traffic conditions are essential for developing effective strategies for congestion mitigation on the highway systems. Speed distribution is one of the traffic stream p... Accurate classification and prediction of future traffic conditions are essential for developing effective strategies for congestion mitigation on the highway systems. Speed distribution is one of the traffic stream parameters, which has been used to quantify the traffic conditions. Previous studies have shown that multi-modal probability distribution of speeds gives excellent results when simultaneously evaluating congested and free-flow traffic conditions. However, most of these previous analytical studies do not incorporate the influencing factors in characterizing these conditions. This study evaluates the impact of traffic occupancy on the multi-state speed distribution using the Bayesian Dirichlet Process Mixtures of Generalized Linear Models (DPM-GLM). Further, the study estimates the speed cut-point values of traffic states, which separate them into homogeneous groups using Bayesian change-point detection (BCD) technique. The study used 2015 archived one-year traffic data collected on Florida’s Interstate 295 freeway corridor. Information criteria results revealed three traffic states, which were identified as free-flow, transitional flow condition (congestion onset/offset), and the congested condition. The findings of the DPM-GLM indicated that in all estimated states, the traffic speed decreases when traffic occupancy increases. Comparison of the influence of traffic occupancy between traffic states showed that traffic occupancy has more impact on the free-flow and the congested state than on the transitional flow condition. With respect to estimating the threshold speed value, the results of the BCD model revealed promising findings in characterizing levels of traffic congestion. 展开更多
关键词 TRAFFIC Congestion Multistate SPEED distribution TRAFFIC OCCUPANCY Dirichlet Process Mixtures of generalized Linear Model BAYESIAN CHANGE-POINT Detection
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Entropy Bayesian Analysis for the Generalized Inverse Exponential Distribution Based on URRSS 被引量:1
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作者 Amer I.Al-Omari Amal S.Hassan +2 位作者 Heba F.Nagy Ayed R.A.Al-Anzi Loai Alzoubi 《Computers, Materials & Continua》 SCIE EI 2021年第12期3795-3811,共17页
This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and up... This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results. 展开更多
关键词 Shannon entropy generalized inverse exponential distribution Bayesian estimators loss function ranked set sampling markov chain
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Bayesian Joint Modelling of Survival Time and Longitudinal CD4 Cell Counts Using Accelerated Failure Time and Generalized Error Distributions 被引量:1
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作者 Markos Abiso Erango Ayele Taye Goshu 《Open Journal of Modelling and Simulation》 2019年第1期79-95,共17页
Survival of HIV/AIDS patients is crucially dependent on comprehensive and targeted medical interventions such as supply of antiretroviral therapy and monitoring disease progression with CD4 T-cell counts. Statistical ... Survival of HIV/AIDS patients is crucially dependent on comprehensive and targeted medical interventions such as supply of antiretroviral therapy and monitoring disease progression with CD4 T-cell counts. Statistical modelling approaches are helpful towards this goal. This study aims at developing Bayesian joint models with assumed generalized error distribution (GED) for the longitudinal CD4 data and two accelerated failure time distributions, Lognormal and loglogistic, for the survival time of HIV/AIDS patients. Data are obtained from patients under antiretroviral therapy follow-up at Shashemene referral hospital during January 2006-January 2012 and at Bale Robe general hospital during January 2008-March 2015. The Bayesian joint models are defined through latent variables and association parameters and with specified non-informative prior distributions for the model parameters. Simulations are conducted using Gibbs sampler algorithm implemented in the WinBUGS software. The results of the analyses of the two different data sets show that distributions of measurement errors of the longitudinal CD4 variable follow the generalized error distribution with fatter tails than the normal distribution. The Bayesian joint GED loglogistic models fit better to the data sets compared to the lognormal cases. Findings reveal that patients’ health can be improved over time. Compared to the males, female patients gain more CD4 counts. Survival time of a patient is negatively affected by TB infection. Moreover, increase in number of opportunistic infection implies decline of CD4 counts. Patients’ age negatively affects the disease marker with no effects on survival time. Improving weight may improve survival time of patients. Bayesian joint models with GED and AFT distributions are found to be useful in modelling the longitudinal and survival processes. Thus we recommend the generalized error distributions for measurement errors of the longitudinal data under the Bayesian joint modelling. Further studies may investigate the models with various types of shared random effects and more covariates with predictions. 展开更多
关键词 ACCELERATED Failure Time BAYESIAN Joint Model CD4 Cell COUNT generalized Error distribution HIV/AIDS Longitudinal Survival Analysis
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The Chapman-Richards Distribution and its Relationship to the Generalized Beta
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作者 Jeffrey H.Gove Thomas B.Lynch Mark J.Ducey 《Forest Ecosystems》 SCIE CSCD 2019年第3期219-235,共17页
Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptio... Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptions of the Chapman-Richards growth function, constant mortality and recruitment into the mathematical form of the distribution. Therefore, unlike 'assumed' distribution models, it is intrinsically linked with the underlying vital rates for the forest area under consideration. Methods: It is shown that the Chapman-Richards distribution can be recast as a subset of the generalized beta distribution of the first kind, a rich family of assumed probability distribution models with known properties. These known properties for the generalized beta are then immediately available for the Chapman-Richards distribution, such as the form of the compatible basal area-size distribution. A simple two-stage procedure is proposed for the estimation of the model parameters and simulation experiments are conducted to validate the procedure for four different possible distribution shapes. Results: The simulations explore the efficacy of the two-stage estimation procedure;these cover the estimation of the growth equation and mortality-recruitment derives from the equilibrium assumption. The parameter estimates are shown to depend on both the sample size and the amount of noise imparted to the synthetic measurements. The results vary somewhat by distribution shape, with the smaller, noisier samples providing less reliable estimates of the vital rates and final distribution forms. Conclusions: The Chapman-Richards distribution in its original form, or recast as a generalized beta form, presents a potentially useful model integrating vital rates and stand diameters into a flexible family of resultant distributions shapes. The data requirements are modest, and parameter estimation is straightforward provided the minimal recommended sample sizes are obtained. 展开更多
关键词 Diameter distributionS Chapman-Richards growth generalized BETA distribution of the first KIND Maximum LIKELIHOOD McKendrick-Von Foerster equation Physiologically structured population model Size-structured distributionS
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