Hazard risk assessment of tropical cyclones based on joint probability theory

The main hazard-causing factors of tropical cyclones are strong wind,heavy rainfall,and storm surge.Evaluation of the hazard-causing degree of a tropical cyclone requires a joint intensity analysis of these hazard-causing factors.According to the maximum hourly mean wind speed,total rainfall,and maximum tide level at various observation stations in Hong Kong during these tropical cyclones,three hazard-causing indices for tropical cyclones are introduced:the strong-wind index(VI),total-rainfall index(RI),and tide-level index(LI).Through a joint probability analysis of VI,RI,and LI for a tropical cyclone affecting Hong Kong,the joint return period is calculated to evaluate its joint hazard-causing intensity.A limit state function of Hong Kong’s resistance to tropical cyclones is developed and used to evaluate the regional risk of tropical cyclones affecting Hong Kong.The results indicate that the joint return period of VI,RI,and LI can reflect the joint hazard-causing intensity of strong wind,heavy rain,and storm surge caused by tropical cyclones;if the overall design return periods of the regional structures decrease,the regional ability to defend against tropical cyclone disasters is degraded.

Stochastic ordering of medians in exchangeable trivariate normal vectors

In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.