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Article
Publication date: 17 October 2008

Fan Aihua, Wang Zhongzhi and Ding Fangqing

The purpose of this paper is to give some limit theorems on ε‐neighborhood and ε‐increasing runs of continuous‐valued dependent random sequence. In the main result no assumptions…

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Abstract

Purpose

The purpose of this paper is to give some limit theorems on ε‐neighborhood and ε‐increasing runs of continuous‐valued dependent random sequence. In the main result no assumptions are made concerning the random variables. As corollary a result on independent case is obtained.

Design/methodology/approach

The crucial part of the proof is to construct a non‐negative supper‐martingale depending on a parameter by using the moment generating function, and then applying the Doob's martingale convergence theorem.

Findings

The upper and lower bounds of the deviations from the sums of arbitrary continuous‐valued random variables from the reference distributions are obtained.

Research limitations/implications

The computation of asymptotic log‐likelihood ratio h(P|Q) is the main limitations, and it is difficult to obtain the rigorous bounds of the deviations.

Practical implications

A useful method to study the property for runs of dependent random sequence.

Originality/value

The new approach of study strong limit behavior for dependent random sequence.

Details

Kybernetes, vol. 37 no. 9/10
Type: Research Article
ISSN: 0368-492X

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Book part
Publication date: 1 September 2021

Feng Yang, Zhen Bi, Fangqing Wei and Zhimin Huang

In China, more than 80,000 people have been diagnosed with COVID-19, and more than 3,000 people have lost their lives. It seems that there will be more deaths since the epidemic…

Abstract

In China, more than 80,000 people have been diagnosed with COVID-19, and more than 3,000 people have lost their lives. It seems that there will be more deaths since the epidemic is not over. All the Chinese provinces have reported the COVID-19 cases. This chapter aims to explore the trend of COVID-19 treatment efficiency in Chinese provinces using the data released daily by China Center for Disease Control and Prevention. Since China Center for Disease Control and Prevention began to release data daily from January 24 to March 12, we have more than 40 groups of daily data for 31 provinces in China mainland. In the calculation, we take the daily data of each province as a sample and then we have more than 1,200 samples in this study.

We use additive two-stage data envelopment analysis as an efficiency evaluation tool to calculate the COVID-19 treatment efficiency. In our framework, the first stage is to understand the infection rate and the second stage is to evaluate the treatment efficiency. In the first stage for the tth day, we use total population (p) and number of people infected in the previous day (inft−1) as the inputs and cumulative number of people infected in the current day (inft) as the output. In the second stage for the tth day, we use cumulative number of people infected in the current day (inft) as the input and cumulative death in the current day (deatht) and cumulative recovery in the current day (recovt) as the outputs. Some techniques on how to deal with undesirable outputs such as inft and deatht are employed in this study.

After we have the infection rate and treatment efficiency for the samples more than 1,200, we analyze the COVID-19 treatment efficiency and its development trend from January 24 to March 12 in 34 regions of China from static and dynamic aspects. The results show that, on the whole, the overall efficiency and phased efficiency of COVID-19 treatment efficiency in all regions of China are relatively high, which reflects the key factor for the Chinese government to quickly control the epidemic in the short term. Relatively speaking, the average efficiency value in the infection stage (first stage) is lower than the average efficiency value in the healing stage (second stage), which shows that the focus of anti-epidemic in China should be early detection and prevention rather than treatment process. In terms of trend, the total efficiency of COVID-19 treatment in each region shows a trend of “increasing first and then decreasing.” Our analysis indicates that in the initial stage, the continuous increase of various resources leads to the rise of the total efficiency, while in the later stage, the rapid decline of the number of infected people leads to the decrease of the total efficiency. Based on the results of the efficiency analysis, this study provides corresponding management implications and policy suggestions, hoping to provide some enlightenment and suggestions for the anti-epidemic work of other countries in the severe environment where the epidemic is spreading rapidly.

Details

Advances in Business and Management Forecasting
Type: Book
ISBN: 978-1-83982-091-5

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