The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lo...The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.展开更多
In this paper, a mathematical model about the optimal booking level problem in airline overbooking rnanageanent is proposed. Firstly, the normal distribution is employed to approximate Poisson requests and binomial go...In this paper, a mathematical model about the optimal booking level problem in airline overbooking rnanageanent is proposed. Firstly, the normal distribution is employed to approximate Poisson requests and binomial goshows. By calculating the mean loss, a model to describe the relationship between booking level and flight revenue is established. Then, an equation is deduced to decide the optimal booking level. Finally, a numerical example is utilized to illustrate the proposed model and discuss the impact of refund rate on the optimal booking level and the mean loss.展开更多
基金supported by the National Natural Science Foundation of China (51279186,51479183)the 111 Project (B14028)The first author thanks the Chinese Scholarship Council for funding his research in University of Washington
文摘The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.
文摘In this paper, a mathematical model about the optimal booking level problem in airline overbooking rnanageanent is proposed. Firstly, the normal distribution is employed to approximate Poisson requests and binomial goshows. By calculating the mean loss, a model to describe the relationship between booking level and flight revenue is established. Then, an equation is deduced to decide the optimal booking level. Finally, a numerical example is utilized to illustrate the proposed model and discuss the impact of refund rate on the optimal booking level and the mean loss.
