Final outcome probabilities for SIR epidemic model

Abstract

We consider an SIR stochastic epidemic model in which new infections occur at rate f(x, y), where x and y are, respectively, the number of susceptibles and infectives at the time of infection and f is a positive sequence of real functions. A simple explicit formula for the final size distribution is obtained. Some efficient recursive methods are proved for the exact calculation of this distribution. In addition, we give a Gaussian approximation for the final distribution using a diffusion process approximation.     

The Beta Exponential-Geometric Distribution

A new four-parameter distribution with decreasing, increasing, and upside-down bathtub failure rate called the beta exponential-geometric distribution is proposed. The new distribution, generated from the logit of a beta random variable, extends the exponential-geometric distribution of Adamidis and Loukas (1998 Adamidis , K. , Loukas , S. ( 1998 ). A lifetime distribution with decreasing failure rate . Statistics and Probability Letters 39 : 35 – 42 .[Crossref], [Web of Science ®] , [Google Scholar]) and some other distributions. A comprehensive mathematical treatment of this distribution is provided. Some expressions for the moment generating function, moments, order statistics, and Rényi entropy of the new distribution are derived. Estimation of the stress-strength parameter is also obtained. The model parameters are estimated by the maximum likelihood method and Fisher information matrix is discussed. Finally, an application to a real data set is illustrated.     

A robust R control chart based on a two-step estimator of the process dispersion

ABSTRACT

Control charts are the frequently used tools for monitoring and controlling the processes. Classical control charts are sensitive to existing contaminated data which may be presented in the data collected from the processes. Thus, these charts are not able to control the processes precisely when the data are contaminated. Robust control charts are those which are less sensitive to contamination. Some robust control charts for monitoring the process variability were proposed in the past which are robust to some sorts of contamination. In this paper a new robust R control chart is proposed which is less sensitive to wide range of contaminations, i.e. general and local contaminations. Simulation studies are performed to compare the performance of the proposed control chart with some classical and robust control charts, using ARL and MSD as criteria for comparisons purposes. The simulation results show a very good performance of the proposed chart when both types of contaminations exist.     

Predicting losses of residential structures in the state of Florida by the public hurricane loss evaluation model

As an environmental phenomenon, hurricanes cause significant property damage and loss of life in coastal areas almost every year. Although a number of commercial loss projection models have been developed to predict the property losses, only a handful of studies are available in the public domain to predict damage for hurricane prone areas. The state of Florida has developed an open, public model for the purpose of probabilistic assessment of risk to insured residential property associated with wind damage from hurricanes. The model comprises three components; viz. the atmospheric science component, the engineering component and the actuarial science component. The atmospheric component includes modeling the track and intensity life cycle of each simulated hurricane within the Florida threat area. Based on historical hurricane statistics, thousands of storms are simulated allowing determination of the wind risk for all residential Zip Code locations in Florida. The wind risk information is then provided to the engineering and actuarial components to model damage and average annual loss, respectively. The actuarial team finds the county-wise loss and the total loss for the entire state of Florida. The computer team then compiles all information from atmospheric science, engineering and actuarial components, processes all hurricane related data and completes the project. The model was submitted to the Florida Commission on Hurricane Loss Projection Methodology for approval and went through a rigorous review and was revised as per the suggestions of the commission. The final model was approved for use by the insurance companies in Florida by the commission. At every stage of the process, statistical procedures were used to model various parameters and validate the model. This paper presents a brief summary of the main components of the model (meteorology, vulnerability and actuarial) and then focuses on the statistical validation of the same.     

Authors’ responses to the discussion on “Predicting losses of residential structures in the state of Florida by the Public Hurricane Loss Evaluation Model”

Hurricanes threaten the Florida coast line every year and are capable of causing catastrophic losses. The Public Hurricane Loss Model was developed in response to the need for having an open transparent model to predict the above losses. The results were summarized in the paper “Predicting Losses of Residential Structures in the State of Florida by the Public Hurricane Loss Model” which was subsequently a subject of discussion by experts in Meteorology, Engineering, Actuarial Sciences and Statistics. The present paper presents a response to the discussions on the above mentioned article.     

The Intervening Role of Innovative Climate: A Study of Middle Managers in Manufacturing Organizations in Iran

Based on a developed model, this study deals with an investigation on whether innovative climate is a variable that moderates the relationship among middle managers' technological innovation and organizational factors such as structure, strategic posture, and environment. We used path analysis framework to study this relationship. The respondents (N=158, n=96) were all the managers of large or medium manufacturing companies with headquarters in the province of Tehran in Iran. The study found that innovative climate has an intervening role in the relationship among organizational structure, strategic posture and environment, and middle managers' technological innovation. The results have implications for the executive and human resource management practices.     

The frequency of sexual abuse and depression in a sample of street children of one of deprived districts of Tehran

The purpose of this study was to determine the frequency of sexual abuse and depression among street children who live in a deprived district of Tehran. The researchers used the K-SADS questionnaire and a clinical interview were used to evaluate depression and sexual abuse in 87 street children in Tehran. Eighteen (20.9%) of the children had been sexually abused. Depressed children were 3.2 times more likely to be sexually abused than non-depressed children. Furthermore, 26 girls (86.7%) and 27 boys (48.2%) suffered from depression. The frequency of depression demonstrated a significant association with the father's or breadwinner's history of imprisonment or unemployment. Interventional programs providing education and support should be implemented for street children.