Abstract (
)
Download PDF (
)
Knowledge map
Save
Multiple discrete data are very common in the manufacturing industry. Most control charts are built based on the assumption of the multivariate Poisson model with a single common covariance term, which allows only equal covariance. However, this assumption may not be realistic, for the cases observed in different
regions sometimes are dependent with different covariance. Besides, these control charts cannot provide fault diagnosis information. This article presents GMP-CUSUM chart based on the multivariate Poisson model with two-way covariance structure. Using Monte Carlo simulation, we compare the average running chain length (ARL) of traditional MP control chart and the new control chart considering various factors. The results show that the latter model is more suitable for modeling multivariate discrete data and the new control chart increases sensitivity to process shifts. When applied to raw data directly, the proposed method is powerful yet simple to use in practice.
Abstract (
)
Download PDF (
)
Knowledge map
Save
In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong L^p-convergence version and a strongly quasi sure convergence version of the law of large numbers.
Abstract (
)
Download PDF (
)
Knowledge map
Save
We employ a linear Bayes procedure to estimate the unknown parameter of the uniform distribution R(-\theta,\theta) and propose a linear approximate Bayes estimator (LABE) for \theta, which has a closed analytic solution form and is convenient to use. Numerical simulations indicate that the proposed LABE is close to the ordinary Bayes estimator (BE), which is calculated by numerical integration and the so-called brute-force method as well. Furthermore, we compare the proposed LABE with the Lindley's approximation. The superiorities of the LABE over the classical estimators are also established in terms of the mean squared
error (MSE) criterion.
Abstract (
)
Download PDF (
)
Knowledge map
Save
In this paper, we consider the classical compound Poisson risk model with two-step premium rate. Using an alternative approach, we find the explicit expressions for the Laplace transforms of joint occupation times over disjoint intervals for this model. The Laplace transforms are expressed in terms of scale functions of L\'{e}vy processes.
Abstract (
)
Download PDF (
)
Knowledge map
Save
In the discrete-time Sparre Andersen risk model with investments and dividend payments, the company controls the dividend payments and the proportions of venture investments in order to maximize the cumulative expected discounted dividends prior to ruin. The paper gets the algorithm of the optimal dividend strategy by analyzing a Hamilton-Jacobi-Bellman equation and transforming the value function. Furthermore, the existence of the optimal solution of the transformation function is proved by using compression mapping and fixed point principle. In order to make the calculation easier, this paper also proposes an
innovative random simulation method for the optimal strategy, and proves that the simulation result is the consistent estimate of the real value. Finally, the random simulation method in the Matlab is used for numerical analysis in an example, which shows the innovative simulation method is a very good and helpful method for making dividend payment and investment decisions.
Abstract (
)
Download PDF (
)
Knowledge map
Save
In this paper, we propose a novel and efficient method for detecting distribution changes in a picture. We design an approach based on the parametric change-points detection problem and apply it into region detection problem. The number of change-points is determined by the Schwartz information criterion and the location of the change-points is estimated via a modified pruned exact linear time algorithm. Furthermore, we propose a new merging method to merge the regions in the same distribution after finishing the estimation of change-points. Under some mild conditions, we prove our estimation of change-points and regions is consistent. In the simulation studies, the new method performs well in both estimation and computation time compared to other method.
Abstract (
)
Download PDF (
)
Knowledge map
Save
Using the transmission dynamics model, the number of confirmed cases, cured cases and dead cases announced by the National Health Commission, we got the following three conclusions: First, the joint prevention and control mechanism adopted by the Chinese government has played a very significant role in the prevention and control of Corona virus diseases 2019 (COVID-19). The basic regeneration number (R_0) in Hubei province has gradually decreased from 3.86 before February 3 to 0.42 after February 8; and R_0 of Zhejiang province, Guangdong province, Henan province, Hunan province, Jiangxi province, Anhui province, Beijing city and Shanghai city (six provinces and two cities) decreased from 3.68 before January 30 to 0.18 after February 4. Second, the infectivity of
asymptomatic and symptomatic cases was almost the same before confirmed diagnosis. The difficulty in the prevention and control of the COVID-19
lies in the isolation and timely treatment of asymptomatic cases. Although the number of asymptomatic cases in Hubei province has gradually dropped
from 23,068 to 2,935 on February 29, the situation of epidemic prevention and control in Hubei province remains very grim. The number of asymptomatic
cases in six provinces and two cities has fallen to between 5 and 21 on February 29, and the epidemic of COVID-19 in these regions has been effectively controlled. Third, selecting the time to relax traffic control measure in Hubei province requires caution. The transmission dynamic model predicts that if the traffic control measures are lifted in mid-May or mid-June, and approximately 100,000 asymptomatic cases are allowed to be imported from Hubei province to six provinces and two cities, the cumulative number of infected people will increase by 5.5 or 1.3 after 1.5 months. However, if the traffic control measures are lifted in mid-March or mid-April, the cumulative number of infected people will increase by 93 or 22 after 1.5 months.
