J. Alvarez, M. Amadis, G. Boros, D. Karp, V. H. Moll et al., An extension of a criterion for unimodality. The Electronic Journal of Combinatorics, pp.30-155, 2001.

J. Alvarez, M. Amadis, and L. Rosales, Unimodality and log-concavity of polynomials, The Summer Institute in Mathematics for Undergraduates (SIMU). (Cited on page 161, 2000.

A. Arzt, Score following with dynamic time warping: an automatic pageturner, 2008.

A. Arzt and G. Widmer, Simple tempo models for real-time music tracking, Proceedings of the Seventh Sound and Music Computing Conference, 2010.

A. Arzt and G. Widmer, Towards effective 'any-time' music tracking, Proceedings of the Fifth Starting AI Researchers' Symposium (STAIRS 2010), pp.24-36, 2010.

A. Arzt, G. Widmer, and S. Dixon, Automatic page turning for musicians via real-time machine listening, Proceedings of the 18th European Conference on Artificial Intelligence, pp.241-245, 2008.

M. Banciu and P. Mirchandani, Technical Note???New Results Concerning Probability Distributions with Increasing Generalized Failure Rates, Operations Research, vol.61, issue.4, pp.925-931, 2013.
DOI : 10.1287/opre.2013.1198

S. Basu and A. Dasgupta, The mean, median, and mode of unimodal distributions: A characterization, Theory of Probability & Its Applications, pp.210-223, 1997.

H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, p.63, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00643354

E. M. Bertin, I. Cuculescu, and R. Theodorescu, Unimodality of Probability Measures Mathematics and its Applications, 1997.

P. J. Bickel and E. L. Lehmann, Descriptive Statistics for Nonparametric Models II. Location, The Annals of Statistics, vol.3, issue.5, pp.1045-1069, 1975.
DOI : 10.1214/aos/1176343240

J. A. Bilmes, Timing is of the essence: Perceptual and computational techniques for representing, learning, and reproducing expressive timing in percussive rhythm. Master's thesis, Massachusetts Institute of Technology, 1993.

S. Bloch-mercier, Monotone Markov processes with respect to the reversed hazard rate ordering: an application to reliability, Journal of Applied Probability, vol.97, issue.01, pp.195-208, 2001.
DOI : 10.1287/moor.12.3.562

URL : https://hal.archives-ouvertes.fr/hal-00693742

H. W. Block and T. H. Savits, Laplace Transforms for Classes of Life Distributions, The Annals of Probability, vol.8, issue.3, 1980.
DOI : 10.1214/aop/1176994721

L. Bondesson, Generalized Gamma Convolutions and Related Classes of Distributions and Densities. Lecture Notes in Statistics, 1992.

G. Boros and V. H. Moll, A criterion for unimodality. The Electronic Journal of Combinatorics, p.10, 1999.

F. Brenti, Unimodal, Log-Concave and Pólya Frequency Sequences in Combinatorics . Memoirs of the AMS Series, pp.149-162, 1989.
DOI : 10.1090/memo/0413

URL : http://dspace.mit.edu/bitstream/1721.1/103188/1/20051018-MIT.pdf

M. Brown and N. R. Chaganty, On the first passage time distribution for a class of Markov chains. The Annals of Probability, pp.1000-1008, 1983.

J. Cai and G. E. Willmot, Monotonicity and aging properties of random sums, Statistics & Probability Letters, vol.73, issue.4, pp.381-392, 2005.
DOI : 10.1016/j.spl.2005.04.013

P. Cano, A. Loscos, and J. Bonada, Score-performance matching using HMMs, Proceedings of the 1999 International Computer Music Conference, 1999.

O. Cappé, E. Moulines, and T. And-ryden, Inference in Hidden Markov Models . Springer Series in Statistics, 2005.

W. Y. Chen, A. L. Yang, and E. L. Zhou, Ratio monotonicity of polynomials derived from nondecreasing sequences, The Electronic Journal of Combinatorics, vol.17, issue.156, pp.37-155, 2010.

W. Y. Chen and C. C. Gu, The reverse ultra log-concavity of the Boros-Moll polynomials, Proceedings of the, pp.3991-3998, 2009.
DOI : 10.1090/S0002-9939-09-09976-6

A. Cont, Realtime Audio to Score Alignment for Polyphonic Music Instruments, using Sparse Non-Negative Constraints and Hierarchical HMMS, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, pp.245-248, 2006.
DOI : 10.1109/ICASSP.2006.1661258

URL : https://hal.archives-ouvertes.fr/hal-00723224

A. Cont, Antescofo: Anticipatory synchronization and control of interactive parameters in computer music, Proceedings of the 2008 International Computer Music Conference, pp.33-40, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00694803

A. Cont, A Coupled Duration-Focused Architecture for Real-Time Music-to-Score Alignment, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.6, pp.974-987, 2010.
DOI : 10.1109/TPAMI.2009.106

URL : https://hal.archives-ouvertes.fr/hal-00479737

A. Cont, D. Schwarz, N. Schnell, R. , and C. , Evaluation of real-time audio-to-score alignment, Proceedings of the 8th International Society for Music Information Retrieval, pp.315-316, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00839068

R. Cont and P. Tankov, Financial Modelling with Jump Processes. Financial Mathematics Series, p.193, 0199.
DOI : 10.1201/9780203485217

URL : https://hal.archives-ouvertes.fr/hal-00002693

I. Cuculescu and R. Theodorescu, Multiplicative Strong Unimodality, Australian <html_ent glyph="@amp;" ascii="&"/> New Zealand Journal of Statistics, vol.40, issue.2, pp.205-214, 1998.
DOI : 10.1111/1467-842X.00023

P. Cuvillier, Time-coherency of Bayesian priors on transient semi-Markov chains for audio-to-score alignment, Bayesian Inference and Maximum Entropy Methods in Science and Engineering, pp.255-262, 2014.
DOI : 10.1063/1.4905986

URL : https://hal.archives-ouvertes.fr/hal-01080235

P. Cuvillier and A. Cont, Coherent time modeling of Semi-Markov models with application to real-time audio-to-score alignment, 2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), 2014.
DOI : 10.1109/MLSP.2014.6958908

URL : https://hal.archives-ouvertes.fr/hal-01058366

R. B. Dannenberg, An on-line algorithm for real-time accompaniment, Proceedings of the 1984 International Computer Music Conference (ICMC 1984), pp.193-198, 1984.

H. Davenport and G. Pólya, On the product of two power series, Journal canadien de math??matiques, vol.1, issue.1, pp.1-5, 1949.
DOI : 10.4153/CJM-1949-001-1

J. Devaney and D. P. Ellis, Handling asynchrony in audio-score alignment, Proceedings of the 2009 International Computer Music Conference, pp.29-32, 2009.
DOI : 10.1080/09298215.2014.890630

S. Dixon, An on-line time warping algorithm for tracking musical performances, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI-05), pp.1727-1728, 2005.

Z. Duan and B. Pardo, Soundprism: An Online System for Score-Informed Source Separation of Music Audio, IEEE Journal of Selected Topics in Signal Processing, vol.5, issue.6, pp.1205-1215, 2011.
DOI : 10.1109/JSTSP.2011.2159701

Z. Duan and B. Pardo, A state space model for online polyphonic audioscore alignment, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.197-200, 2011.

R. Durbin, S. R. Eddy, A. Krogh, and G. Mitchison, Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids, 1998.
DOI : 10.1017/CBO9780511790492

F. Esscher, On the probability function in the collective theory of risk, Scandinavian Actuarial Journal, vol.15, issue.231, pp.175-195, 1932.

H. Finner and M. Roters, Log-concavity and inequalities for chi-square, F and beta distributions with applications in multiple comparisons, Statistica Sinica, vol.7, issue.3, pp.771-787, 1997.

G. Forst, A characterization of self-decomposable probabilities on the halfline, pp.349-352, 1979.

B. E. Fristedt and L. F. Gray, A Modern Approach to Probability Theory, Birkhäuser, 1997.
DOI : 10.1007/978-1-4899-2837-5

B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables. Translated from the Russian, 1954.

R. Gong, P. Cuvillier, N. Obin, and A. Cont, Real-time audio-to-score alignment of singing voice based on melody and lyric information, Proceedings of the 16th Annual Conference of the International Speech Communication Association, pp.3312-3316, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01164550

L. Grubb, R. B. Dannenberg, B. Hayes-roth, and R. E. Korf, Automated accompaniment of musical ensembles, Proceedings of the 12th National Conference on Artificial Intelligence (AAAI-94), pp.94-99, 1994.

Y. Guédon, Estimating Hidden Semi-Markov Chains From Discrete Sequences, Journal of Computational and Graphical Statistics, vol.12, issue.3, 2003.
DOI : 10.1198/1061860032030

Y. Guédon, Hidden hybrid Markov/semi-Markov chains, Computational Statistics & Data Analysis, vol.49, issue.3, pp.663-688, 2005.
DOI : 10.1016/j.csda.2004.05.033

Y. Guédon and C. Cocozza-thivent, Explicit state occupancy modelling by hidden semi-Markov models: application of Derin's scheme, Computer Speech & Language, vol.4, issue.2, pp.167-192, 1990.
DOI : 10.1016/0885-2308(90)90003-O

A. Gut, Probability: A Graduate Course Springer Texts in Statistics, 2005.

B. G. Hansen, On log-concave and log-convex infinitely divisible sequences and densities. The Annals of Probability, pp.1832-1839, 1988.
DOI : 10.1214/aop/1176991600

URL : https://pure.tue.nl/ws/files/2273512/Metis199948.pdf

S. G. Hoggar, Chromatic polynomials and logarithmic concavity, Journal of Combinatorial Theory, Series B, vol.16, issue.3, pp.248-254, 1974.
DOI : 10.1016/0095-8956(74)90071-9

URL : http://doi.org/10.1016/0095-8956(74)90071-9

P. Holgate, The modality of some compound Poisson distributions, Biometrika, vol.57, issue.3, pp.666-667, 1970.
DOI : 10.1093/biomet/57.3.666

I. A. Ibragimov, On the composition of unimodal distributions. Theory of Probability & Its Applications, pp.255-260, 1956.

K. Joag-dev, S. Kochar, and F. Proschan, A general composition theorem and its applications to certain partial orderings of distributions, Statistics & Probability Letters, vol.22, issue.2, pp.111-119, 1995.
DOI : 10.1016/0167-7152(94)00056-E

C. Joder, Alignement temporel musique-sur-partition par modèles graphiques discriminatifs [Audio-to-Score Temporal Alignment with Discriminative Graphical Models], pp.27-32, 2011.

C. Joder, S. Essid, R. , and G. , A conditional random field viewpoint of symbolic audio-to-score matching, Proceedings of the international conference on Multimedia, MM '10, pp.871-874, 2010.
DOI : 10.1145/1873951.1874100

C. Joder, S. Essid, R. , and G. , An improved hierarchical approach for music-to-symbolic score alignment, Proceedings of the 11th International Society for Music Information Retrieval Conference, pp.39-45, 2010.
DOI : 10.1109/aspaa.2011.6082330

C. Joder, S. Essid, R. , and G. , Hidden Discrete Tempo Model: A tempo-aware timing model for audio-to-score alignment, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.397-400, 2011.
DOI : 10.1109/ICASSP.2011.5946424

N. L. Johnson, S. Kotz, and A. W. Kemp, Univariate Discrete Distributions, p.120, 0199.
DOI : 10.1002/0471715816

O. Johnson, Log-concavity and the maximum entropy property of the Poisson distribution, Stochastic Processes and their Applications, pp.791-802, 2007.
DOI : 10.1016/j.spa.2006.10.006

O. Johnson and C. Goldschmidt, Preservation of log-concavity on summation, ESAIM: Probability and Statistics, pp.206-215, 2006.
DOI : 10.1051/ps:2006008

O. Johnson, I. Kontoyiannis, and M. Madiman, Log-concavity, ultra-logconcavity , and a maximum entropy property of discrete compound Poisson measures, 2013.

S. Karlin and . Usa, Total positivity, volume I, p.206, 1968.

J. Keilson, Log-concavity and log-convexity in passage time densities of diffusion and birth-death processes, Journal of Applied Probability, vol.4, issue.02, pp.391-398, 1971.
DOI : 10.1090/S0002-9947-1957-0091566-1

J. Keilson and A. Kester, Unimodality preservation in Markov chains, Stochastic Processes and their Applications, pp.179-190, 1978.
DOI : 10.1016/0304-4149(78)90016-9

URL : http://doi.org/10.1016/0304-4149(78)90016-9

J. Keilson and U. Sumita, Uniform stochastic ordering and related inequalities, Canadian Journal of Statistics, vol.24, issue.3, 1982.
DOI : 10.2307/3556181

M. Kijima, Hazard rate and reversed hazard rate monotonicities in continuous-time Markov chains, Journal of Applied Probability, vol.32, issue.03, pp.545-556, 1998.
DOI : 10.2307/3213979

A. Klapuri, A. J. Eronen, and J. Astola, Analysis of the meter of acoustic musical signals, IEEE Transactions on Audio, Speech and Language Processing, vol.14, issue.1, pp.342-355, 2006.
DOI : 10.1109/TSA.2005.854090

F. Korzeniowski, F. Krebs, A. Arzt, and G. Widmer, Tracking rests and tempo changes: Improved score following with particle filters, Proceedings of the 39th International Computer Music Conference, pp.93-99, 2013.

F. Korzeniowski and G. Widmer, Refined spectral template models for score following, Proceedings of the Sound and Music Computing Conference 2013, pp.376-382, 2013.

R. Lajugie, P. Bojanowski, P. Cuvillier, S. Arlot, and F. R. Bach, A weaklysupervised discriminative model for audio-to-score alignment, Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp.2484-2488, 2016.
DOI : 10.1109/icassp.2016.7472124

URL : https://hal.archives-ouvertes.fr/hal-01251018

E. L. Lehmann, Ordered Families of Distributions, The Annals of Mathematical Statistics, vol.26, issue.3, pp.399-419, 1955.
DOI : 10.1214/aoms/1177728487

E. L. Lehmann and J. P. Romano, Testing statistical hypotheses, 2005.

J. Lember and A. A. Koloydenko, Bridging Viterbi and posterior decoding: a generalized risk approach to hidden path inference based on hidden Markov models, Journal of Machine Learning Research, vol.15, issue.1, pp.1-58, 2014.

G. Leoni, A First Course in Sobolev Spaces. Graduate studies in mathematics, 2009.

S. E. Levinson, Continuously variable duration hidden Markov models for automatic speech recognition, Computer Speech & Language, vol.1, issue.1, pp.29-45, 1986.
DOI : 10.1016/S0885-2308(86)80009-2

T. M. Liggett, Ultra Logconcave Sequences and Negative Dependence, Journal of Combinatorial Theory, Series A, vol.79, issue.2, pp.315-325, 1997.
DOI : 10.1006/jcta.1997.2790

URL : http://doi.org/10.1006/jcta.1997.2790

A. Llamas and J. Martínez-bernal, Nested Log-Concavity, Communications in Algebra, vol.40, issue.5, pp.1968-1981, 2010.
DOI : 10.1016/j.ejc.2004.04.012

J. Lynch, G. Mimmack, and F. Proschan, Uniform stochastic orderings and total positivity, Canadian Journal of Statistics, vol.10, issue.1, pp.63-69, 1987.
DOI : 10.2307/3314862

M. M. Meerschaert and H. Scheffler, Triangular array limits for continuous time random walks, Stochastic Processes and their Applications, pp.1606-1633, 2008.
DOI : 10.1016/j.spa.2007.10.005

URL : http://doi.org/10.1016/j.spa.2007.10.005

A. Mijatovic, M. Vidmar, and S. Jacka, Markov chain approximations for transition densities of L??vy processes, Electronic Journal of Probability, vol.19, issue.0, pp.1-37, 2014.
DOI : 10.1214/EJP.v19-2208

N. Misra, H. Singh, and E. J. Harner, Stochastic comparisons of Poisson and binomial random variables with their mixtures, Statistics & Probability Letters, vol.65, issue.4, pp.279-290, 2003.
DOI : 10.1016/j.spl.2003.07.002

C. D. Mitchell and L. H. Jamieson, Modeling duration in a hidden Markov model with the exponential family, IEEE International Conference on Acoustics Speech and Signal Processing, pp.331-334, 1993.
DOI : 10.1109/ICASSP.1993.319304

M. G. Mittag-leffler, Sur la nouvelle fonction E ? (x) Comptes Rendus de l'Académie des sciences de Paris, pp.554-558, 1903.

N. Montecchio and A. Cont, A unified approach to real time audio-to-score and audio-to-audio alignment using sequential Montecarlo inference techniques, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.193-196, 2011.
DOI : 10.1109/ICASSP.2011.5946373

URL : https://hal.archives-ouvertes.fr/hal-00692579

N. Montecchio and N. Orio, A discrete filter bank approach to audio to score matching for polyphonic music, Proceedings of the 10th International Society for Music Information Retrieval Conference, pp.495-500, 2009.

M. Müller, H. Mattes, and F. Kurth, An efficient multiscale approach to audio synchronization, Proceedings of the 7th International Society for Music Information Retrieval, pp.192-197, 2006.

T. Nakamura, E. Nakamura, and S. Sagayama, Acoustic score following to musical performance with errors and arbitrary repeats and skips for automatic accompaniment, Proceedings of the Sound and Music Computing Conference 2013, pp.299-304, 2013.

A. K. Nanda and D. Sengupta, Discrete life distributions with decreasing reversed hazard. Sankhy¯ a: The Indian Journal of, Statistics, vol.67, issue.1, pp.106-125, 2003.

R. Nelson, Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling, 1995.
DOI : 10.1007/978-1-4757-2426-4

N. Orio and F. Déchelle, Score following using spectral analysis and hidden Markov models, Proceedings of the 2001 International Computer Music Conference, pp.151-154, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01161055

N. Orio and D. Schwarz, Alignment of monophonic and polyphonic music to a score, Proceedings of the 2001 International Computer Music Conference, pp.129-132, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01161134

N. Orio, L. Serge, D. Schwarz, and N. Schnell, Score following: State of the art and new developments, Proceedings of the 2003 International Conference on New Interfaces for Musical Expression (NIME-03), pp.36-41, 2003.

T. Otsuka, K. Nakadai, T. Takahashi, T. Ogata, and H. G. Okuno, Real-Time Audio-to-Score Alignment Using Particle Filter for Coplayer Music Robots, EURASIP Journal on Advances in Signal Processing, vol.19, issue.2-3, pp.20111-20124, 2011.
DOI : 10.1162/comj.2009.33.4.69

B. Pardo and W. P. Birmingham, Modeling form for on-line following of musical performances, Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI-05) and the Seventeenth Innovative Applications of Artificial Intelligence Conference (IAAI-05), pp.1018-1023, 2005.

C. Park and W. J. Padgett, Accelerated Degradation Models for Failure Based on Geometric Brownian Motion and Gamma Processes, Lifetime Data Analysis, vol.37, issue.4, pp.511-527, 2005.
DOI : 10.1007/s10985-005-5237-8

P. H. Peeling, A. T. Cemgil, and S. J. Godsill, A probabilistic framework for matching music representations, Proceedings of the 8th International Conference on Music Information Retrieval, pp.267-272, 2007.

R. Pemantle, Towards a theory of negative dependence, Journal of Mathematical Physics, vol.36, issue.3, pp.1371-1390, 2000.
DOI : 10.1063/1.533200

R. N. Pillai, On Mittag-Leffler functions and related distributions, Annals of the Institute of Statistical Mathematics, vol.29, issue.1, pp.157-161, 1990.
DOI : 10.1007/BF00050786

J. L. Powell, Estimation of semiparametric models, Handbook of Econometrics, pp.2443-2521, 1994.

P. S. Puri and C. M. Goldie, Poisson mixtures and quasi-infinite divisibility of distributions, Journal of Applied Probability, vol.5, issue.01, pp.138-153, 1979.
DOI : 10.1017/S0305004100042225

L. R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE, pp.257-286, 1989.

C. Raphael, Automatic segmentation of acoustic musical signals using hidden Markov models, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.21, issue.4, pp.360-370, 1999.
DOI : 10.1109/34.761266

C. Raphael, Aligning music audio with symbolic scores using a hybrid graphical model, Machine Learning, pp.389-409, 2006.
DOI : 10.1007/s10994-006-8415-3

A. Rényi, A characterization of Poisson processes, Magyar Tudományos Akadémia Matematikai Kutató Intézetének Közleményei, vol.1, pp.519-527, 1957.

K. Sato, Self-similar processes with independent increments. Probability Theory and Related Fields, pp.285-300, 0198.
DOI : 10.1007/bf01198788

K. Sato, Lévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics, p.149, 0199.

D. Schwarz, N. Orio, and N. Schnell, Robust polyphonic Midi score following with hidden Markov models, Proceedings of the 2004 International Computer Music Conference, pp.442-445, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01161328

M. Shaked, H. S. Li, N. Balakrishnan, C. B. Read, and B. Vidakovic, Aging first-passage times, Encyclopedia of Statistical Sciences, pp.60-67, 2006.
DOI : 10.1002/0471667196.ess0247.pub2

M. Shaked and J. G. Shanthikumar, On the First-Passage Times of Pure Jump Processes, Journal of Applied Probability, vol.25, issue.3, pp.501-509, 1988.
DOI : 10.2307/3213979

M. Shaked and J. G. Shanthikumar, Stochastic Orders, p.89, 2007.
DOI : 10.1007/978-0-387-34675-5

URL : https://hal.archives-ouvertes.fr/hal-00539122

J. G. Shanthikumar, DFR property of first-passage times and its preservation under geometric compounding. The Annals of Probability, pp.397-406, 1988.

T. Simon, Multiplicative strong unimodality for positive stable laws, Proceedings of the American Mathematical Society, vol.139, issue.7, pp.2587-2595, 2011.
DOI : 10.1090/S0002-9939-2010-10697-4

URL : https://hal.archives-ouvertes.fr/hal-00460134

T. Simon, Comparing Fr??chet and positive stable laws, Electronic Journal of Probability, vol.19, issue.0, pp.1-25, 2014.
DOI : 10.1214/EJP.v19-3058

URL : http://arxiv.org/abs/1310.1888

T. Simon, Total positivity in stable semigroups. Constructive Approximation, pp.103-120, 2016.
DOI : 10.1007/s00365-016-9337-3

F. W. Steutel and K. Van-harn, Discrete analogues of self-decomposability and stability. The Annals of Probability, pp.893-899, 0198.

F. W. Steutel and K. Van-harn, Infinite Divisibility of Probability Distributions on the Real Line, Pure and Applied Mathematics. Marcel Dekker, vol.20033319, issue.152, 2004.
DOI : 10.1201/9780203014127

Y. Sun, A. Baricz, and S. Zhou, On the Monotonicity, Log-Concavity, and Tight Bounds of the Generalized Marcum and Nuttall <formula formulatype="inline"> <tex Notation="TeX">$Q$</tex></formula>-Functions, IEEE Transactions on Information Theory, vol.56, issue.3, pp.1166-1186, 2010.
DOI : 10.1109/TIT.2009.2039048

H. Takeda, T. Nishimoto, and S. Sagayama, Rhythm and Tempo Analysis Toward Automatic Music Transcription, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07, pp.1317-1320, 2007.
DOI : 10.1109/ICASSP.2007.367320

M. Veillette and M. S. Taqqu, Using differential equations to obtain joint moments of first-passage times of increasing L??vy processes, Statistics & Probability Letters, vol.80, issue.7-8, pp.697-705, 2010.
DOI : 10.1016/j.spl.2010.01.002

P. Vellaisamy and A. Kumar, First-exit times of an inverse Gaussian process. ArXiv e-prints, 2011.

B. Vercoe, The synthetic performer in the context of live performance, Proceedings of the 1984 International Computer Music Conference (ICMC 1984), pp.199-200, 1984.

B. Vercoe and M. Puckette, Synthetic rehearsal: Training the synthetic performer, Proceedings of the 1985 International Computer Music Conference, pp.275-278, 1985.

E. J. Veres-ferrer and J. M. Pavía, La elasticidad: una nueva herramienta para caracterizar distribuciones de probabilidad, pp.145-158, 2012.

E. J. Veres-ferrer and J. M. Pavía, Elasticity function of a discrete random variable and its properties, Communications in Statistics - Theory and Methods, vol.13, 2016.
DOI : 10.1142/S0218539302000822

O. P. Vinogradov, The Definition of Distribution Functions with Increasing Hazard Rate in Terms of the Laplace Transform, Theory of Probability & Its Applications, pp.811-813, 1974.
DOI : 10.1137/1118108

Y. Wang and Y. Yeh, Proof of a conjecture on unimodality, European Journal of Combinatorics, vol.26, issue.5, pp.617-627, 2005.
DOI : 10.1016/j.ejc.2004.04.012

Z. Wang and X. Xiao, Duration-Distribution-Based HMM for Speech Recognition, Frontiers of Electrical and Electronic Engineering in China, vol.7, issue.1, pp.26-30, 2006.
DOI : 10.1007/s11460-005-0010-z

T. Watanabe, On the Strong Unimodality of L??vy Processes, Nagoya Mathematical Journal, vol.15, pp.195-199, 1991.
DOI : 10.1080/01621459.1971.10482273

T. Watanabe, On Yamazato's property of unimodal one-sided L??vy processes, Kodai Mathematical Journal, vol.15, issue.1, 1992.
DOI : 10.2996/kmj/1138039526

W. Whitt, Uniform conditional variability ordering of probability distributions, Journal of Applied Probability, vol.42, issue.03, pp.619-633, 1985.
DOI : 10.1214/aos/1176345075

M. Yamazato, Unimodality of infinitely divisible distribution functions of class L. The Annals of Probability, pp.523-531, 1978.

M. Yamazato, On strongly unimodal infinitely divisible distributions. The Annals of Probability, pp.589-601, 1982.
DOI : 10.1214/aop/1176993769

S. Yu, Hidden semi-Markov models, Artificial Intelligence, vol.174, issue.2, pp.215-243, 2010.
DOI : 10.1016/j.artint.2009.11.011

S. Yu and H. Kobayashi, A hidden semi-Markov model with missing data and multiple observation sequences for mobility tracking, Signal Processing, vol.83, issue.2, pp.235-250, 2003.
DOI : 10.1016/S0165-1684(02)00378-X

Y. Yu, On the Entropy of Compound Distributions on Nonnegative Integers, IEEE Transactions on Information Theory, vol.55, issue.8, pp.3645-3650, 2009.
DOI : 10.1109/TIT.2009.2023725

Y. Yu, Stochastic ordering of exponential family distributions and their mixtures, Journal of Applied Probability, vol.46, issue.1, pp.244-254, 2009.
DOI : 10.1239/jap/1238592127

Y. Yu, On log-concavity of the generalized Marcum Q function. ArXiv e-prints, p.154, 2011.

Y. Yu, On normal variance-mean mixtures. ArXiv e-prints, 2011.
DOI : 10.1016/j.spl.2016.07.024

URL : http://arxiv.org/abs/1106.2333