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References[1] Aldous, D.J. (1985). Exchangeability and related topics. Springer, École d’Été de Probabilités de SaintFlour XIII1983, Lecture Notes in Mathematics 1117, 1–198. MR0883646 [2] Aldous, D.J. (1985). More uses of exchangeability: representations of complex random structures. in Probability and Methematical Genetics – papers in honour of Sir John Kingman, Cambridge University Press 35–63. MR2744234 [3] Alfsen, E.M. (1971). Compact convex sets and boundary integrals. Springer, Berlin. MR0445271 [4] Arnold, B.C. (1975). A characterization of the exponential distribution by multivariate geometric compounding. Sankhy: The Indian Journal of Statistics 37:1 164–173. MR0440792 [5] Assaf, D. and Langberg, N.A. and Savits, T.H. and Shaked, M. (1984). Multivariate phasetype distributions. Operations Research 32:3 688–702. MR0756014 [6] Barlow, R.E. and Proschan, F. (1975). Statistical theory of reliability and life testing. Rinehart and Winston, New York. MR0438625 [7] Beirlant, J. and Goegebeur, Y. and Teugels, J. and Segers, J. (2004). Statistics of extremes: theory and applications. John Wiley & Sons, Chichester. MR2108013 [8] Berg, C. and Christensen, J.P.R. and Ressel, P. (1984). Harmonic analysis on semigroups. Springer, Berlin. MR0747302 [9] Bernhart, G. and Mai, J.F. and Scherer, M. (2015). On the construction of lowparametric families of minstable multivariate exponential distributions in large dimensions. Dependence Modeling 3 29–46. MR3418655 [10] Bernstein, S. (1929). Sur les fonctions absolument monotones. Acta Mathematica 52 1–66. MR1555269 [11] Bezgina, E. and Burkschat, M. (2019). On total positivity of exchangeable random variables obtained by symmetrization, with applications to failuredependent lifetimes. Journal of Multivariate Analysis 169 95–109. MR3875589 [12] Billingsley, P. (1995). Probability and measure. Wiley Series in Probability and Statistics, Wiley, New York. MR1324786 [13] Brigo, D. and Mai, J.F. and Scherer, M. (2016). Markov multivariate survival indicators for default simulation as a new characterization of the Marshall–Olkin law Statistics and Probability Letters 114 60–66. MR3491973 [14] Capéraà, P. and Fougères, A.L. and Genest, C. (2000). Bivariate distributions with given extreme value attractor. Journal of Multivariate Analysis 72 30–49. MR1747422 [15] Charpentier, A. and Fougères, A.L. and Genest, C. and Nešlehová, J.G. (2014). Multivariate Archimax copulas. Journal of Multivariate Analysis 126 118–136. MR3173086 [16] Cossette, H. and Gadoury, S.P. and Marceauand, E. and Mtalai, I. (2017). Hierarchical Archimedean copulas through multivariate compound distributions. Insurance: Mathematics and Economics 76 1–13. MR3698183 [17] Daboni, L. (1982). Exchangeability and completely monotone functions. In: Exchangeability in Probability and Statistics, edited by G. Koch and F. Spizzichino, NorthHolland Publishing Company 39–45. MR0675963 [18] de Finetti, B. (1931). Funzione caratteristica di un fenomeno aleatorio. Atti della R. Academia Nazionale dei Lincei, Serie 6. Memorie, Classe di Scienze Fisiche, Mathematica e Naturale 4 251–299. [19] de Finetti, B. (1937). La prévision: ses lois logiques, ses sources subjectives. Annales de l’Institut Henri Poincaré 7 1–68. MR1508036 [20] Diaconis, P. and Freedman, D. (1987). A dozen de Finettistyle results in search of a theory. Annales de l’Institute Henri Poincaré 23 397–423. MR0898502 [21] Dickinson, P.J.C. and Gijben, L. (2014). On the computational complexity of membership problems for the completely positive cone and its dual. Computational Optimization and Applications 57:2 403–415. MR3165055 [22] Durante, F. and QuesadaMolina, J.J. and ÚbedaFlores, M. (2007). A method for constructing multivariate copulas. In: New Dimensions in Fuzzy Logic and Related Technologies – Proceedings of the 5th EUSFLAT Conference, volume 1, edited by M. Štěpnička et al. 191–195. [23] Durrett, R. (2010). Probability: theory and examples, 4th edition. Cambridge University Press, Cambridge. MR2722836 [24] Dykstra, R.L. and Hewett, J.E. and Thompson, Jr., W.A. (1973). Events which are almost independent. Annals of Statistics 1:4 674–681. MR0397815 [25] Embrechts, P. and Hofert, M. (2013). A note on generalized inverses. Mathematical Methods of Operations Research 77 423–432. MR3072795 [26] Esary, J.D. and Marshall, A.W. (1974). Multivariate distributions with exponential minimums. Annals of Statistics 2 84–98. MR0362704 [27] EsSebaiy, K. and Ouknine, Y. (2008). How rich is the class of processes which are infinitely divisible with respect to time. Statistics and Probability Letters 78 537–547. MR2400867 [28] Giesecke, K. (2003). A simple exponential model for dependent defaults. Journal of Fixed Income 13:3 74–83. [29] Gupta, A.K. and Nadarajah, S. (2004). Handbook of beta distributions and its applications. Marcel Dekker, New York. MR2079703 [30] Hewitt, E. and Savage, l.J. (1955). Symmetric measures on Cartesian products. Transactions of the American Mathematical Society 80 470–501. MR0076206 [31] Fang, K.T. and Kotz, S. and Ng, K.W. (1990). Symmetric multivariate and related distributions. Chapman and Hall, London. MR1071174 [32] Feller, W. (1966). An introduction to probability theory and its applications, volume II, 2nd edition. John Wiley and Sons, Inc., Hoboken. [33] Ferguson, T.S. (1973). A Bayesian analysis of some nonparametric problems. Annals of Statistics 1 209–230. MR0350949 [34] Ferguson, T.S. (1974). Prior distributions on spaces of probability measures. Annals of Statistics 2 615–629. MR0438568 [35] Frank, M.J. (1979). On the simultaneous associativity of F(x,y) and x + y − F(x,y). Aequationes Mathematicae 19 194–226. MR0556722 [36] Galambos, J. (1975). Order statistics of samples from multivariate distributions. Journal of the American Statistical Association 70 674–680. MR0405714 [37] Genest, C. and Nešlehová, J.G. (2017). When Gumbel met Galambos. In: Copulas and Dependence Models With Applications: Contributions in Honor of Roger B. Nelsen (M. Úbeda Flores, E. de Amo Artero, F. Durante, J. Fernández Sánchez, Eds.), Springer, 83–93. MR3822198 [38] Genest, C. and Nešlehová, J.G. and Rivest, L.P. (2018). The class of multivariate maxid copulas with ℓ_{1}norm symmetric exponent measure. Bernoulli 24 3751–3790. MR3788188 [39] Genest, C. and Rivest, L.P. (1989). Characterization of Gumbel’s family of extreme value distributions. Statistics and Probability Letters 8 207–211. MR1024029 [40] Gnedin, A.V. (1995). On a class of exchangeable sequences. Statistics and Probability Letters 25 351–355. MR1363235 [41] Gumbel, E.J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association 55 698–707. MR0116403 [42] Gumbel, E.J. (1961). Bivariate logistic distributions. Journal of the American Statistical Association 56 335–349. MR0158451 [43] Hakassou, A. and Ouknine, Y. (2013). IDT processes and associated Lévy processes with explicit constructions. Stochastics 85:6 1073–1111. MR3176501 [44] Hausdorff, F. (1921). Summationsmethoden und Momentfolgen I. Mathematische Zeitschrift 9:34 74–109. MR1544453 [45] Hausdorff, F. (1923). Momentenproblem für ein endliches Intervall. Mathematische Zeitschrift 16 220–248. MR1544592 [46] Herbertsson, A. and Rootzén, H. (2008). Pricing kthtodefault swaps under default contagion: the matrixanalytic approach. Journal of Computational Finance 12 49–72. MR2504900 [47] Hering, C. and Hofert, M. and Mai, J.F. and Scherer, M. (2010). Constructing hierarchical Archimedean copulas with Lévy subordinators. Journal of Multivariate Analysis 101 1428–1433. MR2609503 [48] Hjort, N.L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Annals of Statistics 18:3 1259–1294. MR1062708 [49] Hofert, M. and Scherer, M. (2011). CDO pricing with nested Archimedean copulas. Quantitative Finance 11 775–787. MR2800641 [50] H. Joe (1997). Multivariate models and dependence concepts. Chapman & Hall/CRC, Boca Raton. MR1462613 [51] Kalbfleisch, J.D. (1978). Nonparametric Bayesian analysis of survival time data. Journal of the Royal Statistical Society Series B 40:2 214–221. MR0517442 [52] Kallenberg, O. (1982). A dynamical approach to exchangeability. In: Exchangeability in Probability and Statistics, edited by G. Koch and F. Spizzichino, NorthHolland Publishing Company, 87–96. MR0675967 [53] Karlin, S. and Shapley, L.S. (1953). Geometry of moment spaces. Memoirs of the American Mathematical Society 12:93. MR0059329 [54] Kimberling, C.H. (1974). A probabilistic interpretation of complete monotonicity. Aequationes Mathematicae 10 152–164. MR0353416 [55] Kingman, J.F.C. (1967). Completely random measures. Pacific Journal of Mathematics 21:1 59–78. MR0210185 [56] Kingman, J.F.C. (1972). On random sequences with spherical symmetry. Biometrika 59 492–494. MR0343420 [57] Kingman, J.F.C. (1978). Uses of exchangeability. Annals of Probability 6:2 183–197. MR0494344 [58] Konstantopoulos, T. and Yuan, L. (2019). On the extendibility of finitely exchangeable probability measures. Transactions of the American Mathematical Society 371 7067–7092. MR3939570 [59] Kopp, C. and Molchanov, I. (2018). Series representations of timestable stochastic processes. Probability and Mathematical Statistics 38:2 299–315. MR3896713 [60] Liggett, T.M. and Steiff, J.E. and Tóth, B. (2007). Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem. Annals of Probability 35:3 867–914. MR2319710 [61] Lijoi, A. and Prünster, I. and Walker, S.G. (2008). Posterior analysis for some classes of nonparametric models. Journal of Nonparametric Statistics 20:5 447–457. MR2424252 [62] Lindskog, F. and McNeil, A.J. (2003). Common Poisson shock models: applications to insurance and credit risk modelling. ASTIN Bulletin 33:2 209–238. MR2035051 [63] Lukacs, E. (1955). A characterization of the gamma distribution. Annals of Mathematical Statistics 26 319–324. MR0069408 [64] Mai, J.F. (2018). Extremevalue copulas associated with the expected scaled maximum of independent random variables. Journal of Multivariate Analysis 166 50–61. MR3799634 [65] Mai, J.F. (2019). Simulation of hierarchical Archimedean copulas beyond the completely monotone case. Dependence Modeling 7 202–214. MR3977499 [66] Mai, J.F. (2020). Canonical spectral representation for exchangeable maxstable sequences. Extremes 23 151–169. MR4064608 [67] Mai, J.F. (2020). The de Finetti structure behind some normsymmetric multivariate densities with exponential decay. Dependence Modeling 8 210–220. MR4156799 [68] Mai, J.F. and Schenk, S. and Scherer, M. (2016). Exchangeable exogenous shock models. Bernoulli 22 1278–1299. MR3449814 [69] Mai, J.F. and Schenk, S. and Scherer, M. (2016). Analyzing model robustness via a distortion of the stochastic root: a Dirichlet prior approach. Statistics and Risk Modeling 32 177–195. MR3507979 [70] Mai, J.F. and Schenk, S. and Scherer, M. (2017). Two novel characterizations of selfdecomposability on the positive halfaxis. Journal of Theoretical Probability 30 365–383. MR3615092 [71] Mai, J.F. and Scherer, M. (2009). Lévyfrailty copulas. Journal of Multivariate Analysis 100 1567–1585. MR2514148 [72] Mai, J.F. and Scherer, M. (2011). Reparameterizing Marshall–Olkin copulas with applications to sampling. Journal of Statistical Computation and Simulation 81 59–78. MR2747378 [73] Mai, J.F. and Scherer, M. (2012). Hextendible copulas. Journal of Multivariate Analysis 110 151–160. MR2927515 [74] Mai, J.F. and Scherer, M. (2014). Characterization of extendible distributions with exponential minima via processes that are infinitely divisible with respect to time. Extremes 17 77–95. MR3179971 [75] Mai, J.F. and Scherer, M. (2017). Simulating copulas, 2nd edition. World Scientific Publishing, Singapore. MR3729417 [76] Mai, J.F. and Scherer, M. (2019). Subordinators which are infinitely divisible w.r.t. time: construction, properties, and simulation of maxstable sequences and infinitely divisible laws. ALEA: Latin American Journal of Probability and Mathematical Statistics 16:2 977–1005. MR3999795 [77] Mai, J.F. and Scherer, M. and Shenkman, N. (2013). Multivariate geometric laws, (logarithmically) monotone sequences, and infinitely divisible laws. Journal of Multivariate Analysis 115 457–480. MR3004570 [78] Mansuy, R. (2005). On processes which are infinitely divisible with respect to time. Working paper, arXiv:math/0504408. [79] Marshall, A.W. and Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association 62 30–44. MR0215400 [80] Marshall, A.W. and Olkin, I. (1979). Inequalities: theory of majorization and its applications. Academic Press, New York. MR0552278 [81] McNeil, A.J. and Frey, R. and Embrechts, P. (2005). Quantitative risk management. Princeton University Press, Princeton. MR2175089 [82] McNeil, A.J. (2008). Sampling nested Archimedean copulas. Journal of Statistical Computation and Simulation 78 567–581. MR2516827 [83] McNeil, A.J. and Nešlehová, J. (2009). Multivariate Archimedean copulas, dmonotone functions and l_{1}norm symmetric distributions. Annals of Statistics 37:5B 3059–3097. MR2541455 [84] McNeil, A.J. and Nešlehová, J. (2010). From Archimedean to Liouville copulas. Journal of Multivariate Analysis 101 1772–1790. MR2651954 [85] Molchanov, I. (2008). Convex geometry of maxstable distributions. Extremes 11:3 235–259. MR2429906 [86] Müller, A. and Stoyan, D. (2002). Comparison methods for stochastic models and risks. John Wiley and Sons, Chichester (2002). MR1889865 [87] Papangelou, F. (1989). On the Gaussian fluctuations of the critical CurieWeiss model in statistical mechanics. Probability Theory and Related Fields 83 265–278. MR1012501 [88] Pestman, W.R. (2009). Mathematical statistics, 2nd edition. De Gruyter, Berlin. MR2516478 [89] Puccetti, G. and Wang, R. (2015). Extremal dependence concepts. Statistical Science 30:4 485–517. MR3432838 [90] Rachev, S.T. and Rüschendorf, L. (1991). Approximate independence of distributions on spheres and their stability properties. Annals of Probability 19 1311–1337. MR1112418 [91] Resnick, S.I. (1987). Extreme values, regular variation and point processes. SpringerVerlag, Berlin. MR0900810 [92] Ressel, P. (1985). de Finetti type theorems: an analytical approach. Annals of Probability 13 898–922. MR0799427 [93] RyllNardzewski, C. (1957). On stationary sequences of random variables and the de Finetti equivalence. Colloquium Mathematicum 4 149–156. MR0088823 [94] Sato, K.I. (1999). Lévy processes and infinitely divisible distributions. Cambridge University Press, Cambridge. MR1739520 [95] Scarsini, M. (1985). Lower bounds for the distribution function of a kdimensional nextendible exchangeable process. Statistics and Probability Letters 3 57–62. MR0792789 [96] Schilling, R. and Song, R. and Vondracek, Z. (2010). Bernstein functions. De Gruyter, Berlin. MR2978140 [97] Schoenberg, I.J. (1938). Metric spaces and positive definite functions. Transactions of the American Mathematical Society 44 522–536. MR1501980 [98] Shaked, M. (1977). A concept of positive dependence for exchangeable random variables. Annals of Statistics 5 505–515. MR0436414 [99] Shaked, M. and Spizzichino, F. and Suter, F. (2002). Nonhomogeneous birth processes and ℓ_{∞}spherical densities, with applications in reliability theory. Probability in the Engineering and Informational Sciences 16 271–288. MR1914427 [100] Sibley, D.A. (1971). A metric for weak convergence of distribution functions. Rocky Mountain Journal of Mathematics 1:3 427–430. MR0314089 [101] Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 229–231. MR0125600 [102] Sloot, H. (2020). The deFinetti representation of generalised Marshall–Olkin sequences. Dependence Modeling 8:1 107–118. MR4121354 [103] Spizzichino, F. (1982). Extendibility of symmetric probability distributions and related bounds. In: Exchangeability in Probability and Statistics, edited by G. Koch and F. Spizzichino, NorthHolland Publishing Company, 313–320. MR0675986 [104] Steutel, F.W. and van Harn, K. (2003). Infinite divisibility of probability distributions on the real line. CRC Press, Boca Raton. MR2011862 [105] Taleb, N.N. (2020). Statistical consequences of fat tails. STEM Academic Press. [106] Williamson, R.E. (1956). Multiply monotone functions and their Laplace transforms. Duke Mathematical Journal 23 189–207. MR0077581 [107] Zhu, W. and Wang, C.W. and Tan, K.S. (2016). Structure and estimation of Lévy subordinated hierarchical Archimedean copulas (LSHAC): theory and empirical tests. Journal of Banking and Finance 69 20–36. 

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