In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become i...In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.展开更多
Gamma Mixture Model(GaMM)is a useful tool for representing complex distributions.However,estimating the parameters of GaMM faces challenges due to the lack of closed-form solution for the shape parameter.Existing para...Gamma Mixture Model(GaMM)is a useful tool for representing complex distributions.However,estimating the parameters of GaMM faces challenges due to the lack of closed-form solution for the shape parameter.Existing parameter estimation methods face limitations stemming from their reliance on approximate computations,which degrade estimation accuracy,as well as the inherent complexity of numerical calculations,leading to computational inefficiency.To address these limitations and fully consider the multimodal nature of big data,this paper proposes a Mode-Partitioned GaMM(MP-GaMM)estimation method for large-scale multimodal data.The MP-GaMM method explores the spatial distribution characteristics of the data through clustering to partition the data into distinct modes,addresses mode overlap with a tune-up strategy,and employs closed-form estimator for parameter estimation of each mode in parallel.Experimental results demonstrate the rationality and effectiveness of the proposed MP-GaMM method,which outperforms existing methods in both accuracy and computational efficiency.Specifically,MP-GaMM exhibits lower error metrics,higher log-likelihood values and shorter runtime,indicating its capability to provide a more accurate estimation of the model parameters,and more precise characterization of the multimodal nature of large-scale data.展开更多
文摘In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.
基金supported by the Natural Science Foundation of Guangdong Province(No.2023A1515011667)the Basic Research Foundation of Shenzhen(No.JCYJ20210324093609026)+1 种基金Guangdong Basic and Applied Basic Research Foundation(No.2023B1515120020)the Science and Technology Major Project of Shenzhen(No.KJZD20230923114809020).
文摘Gamma Mixture Model(GaMM)is a useful tool for representing complex distributions.However,estimating the parameters of GaMM faces challenges due to the lack of closed-form solution for the shape parameter.Existing parameter estimation methods face limitations stemming from their reliance on approximate computations,which degrade estimation accuracy,as well as the inherent complexity of numerical calculations,leading to computational inefficiency.To address these limitations and fully consider the multimodal nature of big data,this paper proposes a Mode-Partitioned GaMM(MP-GaMM)estimation method for large-scale multimodal data.The MP-GaMM method explores the spatial distribution characteristics of the data through clustering to partition the data into distinct modes,addresses mode overlap with a tune-up strategy,and employs closed-form estimator for parameter estimation of each mode in parallel.Experimental results demonstrate the rationality and effectiveness of the proposed MP-GaMM method,which outperforms existing methods in both accuracy and computational efficiency.Specifically,MP-GaMM exhibits lower error metrics,higher log-likelihood values and shorter runtime,indicating its capability to provide a more accurate estimation of the model parameters,and more precise characterization of the multimodal nature of large-scale data.
