scholarly journals Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks

1976 ◽  
Vol 73 (1) ◽  
pp. 11-13 ◽  
Author(s):  
A. V. Peterson
Keyword(s):  
Distribution Function ◽  
Competing Risks ◽  
Joint Distribution ◽  
Distribution Functions ◽  
Joint Distribution Function

scholarly journals Measures of concordance determined byD4-invariant copulas

2004 ◽  
Vol 2004 (70) ◽  
pp. 3867-3875 ◽  
Author(s):  
H. H. Edwards ◽  
P. Mikusiński ◽  
M. D. Taylor
Keyword(s):  
Distribution Function ◽  
Mass Distribution ◽  
Random Vector ◽  
Joint Distribution ◽  
Distribution Functions ◽  
Joint Distribution Function ◽  
Unit Square ◽  
Special Cases ◽  
Measures Of Concordance ◽  
Measure Of Association

A continuous random vector(X,Y)uniquely determines a copulaC:[0,1]2→[0,1]such that when the distribution functions ofXandYare properly composed intoC, the joint distribution function of(X,Y)results. A copula is said to beD4-invariant if its mass distribution is invariant with respect to the symmetries of the unit square. AD4-invariant copula leads naturally to a family of measures of concordance having a particular form, and all copulas generating this family areD4-invariant. The construction examined here includes Spearman’s rho and Gini’s measure of association as special cases.

scholarly journals Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 64 ◽  
Author(s):  
Guilin Liu ◽  
Baiyu Chen ◽  
Song Jiang ◽  
Hanliang Fu ◽  
Liping Wang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Maximum Entropy ◽  
Wave Height ◽  
Joint Distribution ◽  
Height Function ◽  
Copula Function ◽  
Wave Period ◽  
Ocean Engineering ◽  
Joint Distribution Function ◽  
Design Wave Height

Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period.

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