Fitting bivariate losses with phase-type distributions

References

• Åhlström , L. , Olsson , M. and Nerman , O. 1999 . A parametric estimation procedure for relapse time distributions . Lifetime Data Analysis , 2 : 113 – 132 .
   Web of Science ®Google Scholar
• Assaf , D. and Levikson , B. 1982 . Closure of phase type distributions under operations arising in reliability theory . Annals of Probability , 10 : 265 – 269 .
   Web of Science ®Google Scholar
• Assaf , D. , Langberg , N. A. , Savits , T. H. and Shaked , M. 1984 . Multivariate phase-type distributions . Operation Research , 32 : 688 – 702 .
   Web of Science ®Google Scholar
• Asmussen , S. , Nerman , O. and Olsson , M. 1996 . Fitting phase-type distributions via the EM algorithm . Scandinavian Journal of Statistics , 23 : 419 – 441 .
   Web of Science ®Google Scholar
• Asmussen , S. 2000 . Ruin probabilities . Advanced Series on Statistical Science & Applied Probability, 2 . River Edge , NJ : World Scientific Publishing Co., Inc .
   Google Scholar
• Breuer , L. 2002 . An EM algorithm for batch Markovian arrival processes and its comparison to a simpler estimation procedure . Annals of Operations Research , 112 : 123 – 138 .
   Web of Science ®Google Scholar
• Cai , J. and Li , H. 2005a . Conditional tail expectations for multivariate phase-type distributions . Journal of Applied Probability , 42 : 810 – 825 .
   Web of Science ®Google Scholar
• Cai , J. and Li , H. 2005b . Multivariate risk model of phase type . Insurance: Mathematics and Economics , 36 : 137 – 152 .
   Web of Science ®Google Scholar
• Dempster , A. P. , Laird , N. M. and Rubin , D. B. 1977 . Maximum likelihood from incomplete data via the EM algorithm . Journal of Royal Statistical Society Series B , 39 : 1 – 38 .
   Google Scholar
• Drekic , S. , Dickson , D. C. M. , Stanford , D. A. and Willmot , G. E. 2004 . On the distribution of the deficit at ruin when claims are phase-type . Scandinavian Actuarial Journal , 2 : 105 – 120 .
   Google Scholar
• Frees , E. W. and Valdez , E. A. 1998 . Understanding relationships using copulas . North American Actuarial Journal , 2 : 1 – 25 .
   Google Scholar
• Kiefer , J. 1959 . K-sample analogues of the Kolmogorov-Smirnov and Cramr-V. Mises tests . The Annals of Mathematical Statistics , 30 : 420 – 447 .
   Google Scholar
• Klugman , S. A. , Panjer , H. H. and Willmot , G. E. 2004 . Loss models: from data to decision , 2nd ed , Hoboken , NJ : John Wiley & Sons .
   Google Scholar
• Klugman , S. A. and Parsa , R. 1999 . Fitting bivariate loss distributions with copulas . Insurance: Mathematics and Economics , 24 : 139 – 148 .
   Web of Science ®Google Scholar
• Kulkarni , V. G. 1989 . A new class of multivariate phase type distributions . Operation Research , 37 : 151 – 158 .
   Web of Science ®Google Scholar
• Li , H. 2003 . Association of multivariate phase-type distributions, with applications to shock models . Statistics & Probability Letters , 64 : 381 – 392 .
   Web of Science ®Google Scholar
• Li , S. and Garrido , J. 2004 . On ruin for the Erlang(n) risk process . Insurance: Mathematics and Economics , 34 : 391 – 408 .
   Web of Science ®Google Scholar
• Marshall , A. W. and Olkin , I. 1967 . A multivariate exponential distribution . Journal of the American Statistical Association , 62 : 30 – 44 .
   Web of Science ®Google Scholar
• Marshall , A. W. and Shaked , M. 1986 . Multivariate new better than used distributions . Mathematics of Operations Research , 11 : 110 – 116 .
   Web of Science ®Google Scholar
• Neuts , M. F. 1981 . Matrix-geometric solutions in stochastic models. An algorithmic approach , Baltimore , MD : Johns Hopkins University Press .
   Google Scholar
• Neuts , M. F. 1994 . Matrix-geometric solutions in stochastic models. An algorithmic approach , New York : Dover Publications Inc .
   Google Scholar
• O'Cinneide , C. A. 1989 . On nonuniqueness of representations of phase-type distributions. Communications in Statistics . Stochastic Models , 5 : 247 – 259 .
   Google Scholar
• Roberts , W. J. J. and Ephraim , Y. 2008 . An EM algorithm for ion-channel current estimation . IEEE Transactions on Signal Processing , 56 : 26 – 33 .
   Web of Science ®Google Scholar
• Roberts , W. J. J. , Ephraim , Y. and Dieguez , E. 2006 . On Rydén's EM algorithm for estimating MMPPs . IEEE Signal Processing Letters , 13 : 373 – 376 .
   Web of Science ®Google Scholar
• Ryden , T. 1996 . An EM algorithm for estimation in Markov-modulated Poisson processes . Computational Statistics & Data Analysis , 21 : 431 – 447 .
   Web of Science ®Google Scholar
• Stute , W. , Gonzáles , M. W. and Wenceslao , P. Q. M. 1993 . Bootstrap based goodness-of-fit tests . Metrika , 40 : 243 – 256 .
   Google Scholar
• Wu , C. F. J. 1983 . On the convergence properties of the EM algorithm . Annals of Statistics , 11 : 95 – 103 .
   Web of Science ®Google Scholar