The broadleaved-Korean pine mixed forest is a native vegetation in the Changbai Mountains, northeast China. The probability density functions including the normal, negative exponential, Weibull and finite mixture dist...The broadleaved-Korean pine mixed forest is a native vegetation in the Changbai Mountains, northeast China. The probability density functions including the normal, negative exponential, Weibull and finite mixture distribution, were used to describe the diameter distributions of the species groups and entire forest stand. There is a strong correlation between parameters and mean DBH except the shape parameters in the mixture distribution. The diameter classes of species and entire forest stand showed not negative exponential but normal and "S" distribution. The mixture function was better than normal and Weibull to describe the model distribution. The location parameter had an effect on the estimated frequency in the first diameter class, when the estimated location parameter was bigger than the lower limit of the first diameter class.展开更多
High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, vario...High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.展开更多
Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studie...Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studies have lately focused on finite mixture models as mixing distributions in the mixing mechanism. In the present work, we consider a Normal Variance Mean mix<span>ture model. The mixing distribution is a finite mixture of two special cases of</span><span> Generalised Inverse Gaussian distribution with indexes <span style="white-space:nowrap;">-1/2 and -3/2</span>. The </span><span>parameters of the mixed model are obtained via the Expectation-Maximization</span><span> (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.展开更多
<p> <span style="color:#000000;"><span style="color:#000000;">Normal Variance-Mean Mixture (NVMM) provide</span></span><span style="color:#000000;"><...<p> <span style="color:#000000;"><span style="color:#000000;">Normal Variance-Mean Mixture (NVMM) provide</span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">s</span></span></span><span><span><span><span style="color:#000000;"> a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, </span><i><span style="color:#000000;">i.e.</span></i><span style="color:#000000;"> daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. </span><span style="color:#000000;">The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-</span><span style="color:#000000;">Nielsen </span></span></span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">(1977)</span></span></span><span><span><span><span style="color:#000000;"> which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, </span><i><span style="color:#000000;">i.e</span></i></span></span></span><span style="color:#000000;"><span style="color:#000000;"><i><span style="color:#000000;">.</span></i></span></span><span><span><span><span style="color:#000000;">, the index parameter of the GIG is</span><span style="color:red;"> <img src="Edit_721a4317-7ef5-4796-9713-b9057bc426fc.bmp" alt="" /></span><span style="color:#000000;">. The NIG is very popular because of its analytical tractability. In the mixing mechanism</span></span></span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">,</span></span></span><span><span><span><span><span style="color:#000000;"> the mixing distribution characterizes the prior informa展开更多
The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim ...The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.展开更多
基金jointly supported by the National Natural Science Foundation of China(Grant Nos.70373044 and 30470302)China's Ministry of Science and Technology(04EFN216600328)the Northeast Rejuvenation Program of the Chinese Academy of Sciences.
文摘The broadleaved-Korean pine mixed forest is a native vegetation in the Changbai Mountains, northeast China. The probability density functions including the normal, negative exponential, Weibull and finite mixture distribution, were used to describe the diameter distributions of the species groups and entire forest stand. There is a strong correlation between parameters and mean DBH except the shape parameters in the mixture distribution. The diameter classes of species and entire forest stand showed not negative exponential but normal and "S" distribution. The mixture function was better than normal and Weibull to describe the model distribution. The location parameter had an effect on the estimated frequency in the first diameter class, when the estimated location parameter was bigger than the lower limit of the first diameter class.
文摘High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.
文摘Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studies have lately focused on finite mixture models as mixing distributions in the mixing mechanism. In the present work, we consider a Normal Variance Mean mix<span>ture model. The mixing distribution is a finite mixture of two special cases of</span><span> Generalised Inverse Gaussian distribution with indexes <span style="white-space:nowrap;">-1/2 and -3/2</span>. The </span><span>parameters of the mixed model are obtained via the Expectation-Maximization</span><span> (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.
文摘<p> <span style="color:#000000;"><span style="color:#000000;">Normal Variance-Mean Mixture (NVMM) provide</span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">s</span></span></span><span><span><span><span style="color:#000000;"> a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, </span><i><span style="color:#000000;">i.e.</span></i><span style="color:#000000;"> daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. </span><span style="color:#000000;">The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-</span><span style="color:#000000;">Nielsen </span></span></span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">(1977)</span></span></span><span><span><span><span style="color:#000000;"> which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, </span><i><span style="color:#000000;">i.e</span></i></span></span></span><span style="color:#000000;"><span style="color:#000000;"><i><span style="color:#000000;">.</span></i></span></span><span><span><span><span style="color:#000000;">, the index parameter of the GIG is</span><span style="color:red;"> <img src="Edit_721a4317-7ef5-4796-9713-b9057bc426fc.bmp" alt="" /></span><span style="color:#000000;">. The NIG is very popular because of its analytical tractability. In the mixing mechanism</span></span></span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">,</span></span></span><span><span><span><span><span style="color:#000000;"> the mixing distribution characterizes the prior informa
基金Supported by National Natural Science Foundation of China(11471104)Natural Science Foundation of Henan Educational Committee(2011B110018)Program for Innovative Research Team(in Science and Technology)in University of Henan Province(14IRTSTHN023)
文摘The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.
