T. Askey, S. Banciu, E. Casseau, D. Menard, and T. Michel, A Case Study Of The Stochastic Modeling Approach For Range Estimation, Proc. DASIP Conf, pp.301-308, 2010.

A. Banciu, E. Casseau, D. Menard, and T. Michel, Stochastic modeling for floating-point to fixed-point conversion, 2011 IEEE Workshop on Signal Processing Systems (SiPS), 2011.
DOI : 10.1109/SiPS.2011.6088971
URL : https://hal.archives-ouvertes.fr/hal-00746791

M. Barberis and N. Shah, Migrating signal processing applications from floating-point to fixed-point, 2004.

A. Benedetti and P. Perona, Bit-width optimization for configurable DSPs by multi-interval analysis, Proc. Asilomar Conf. Signals, Syst. And Comp, pp.355-359, 2000.

S. Blinnikov and R. Moessner, Expansions for nearly Gaussian distributions, Astronomy and Astrophysics Supplement Series, vol.130, issue.1, pp.193-205, 1998.
DOI : 10.1051/aas:1998221

R. Cameron and W. Martin, The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals, The Annals of Mathematics, vol.48, issue.2, p.385, 1947.
DOI : 10.2307/1969178

J. Carletta, R. Veillette, F. Krach, and Z. Fang, Determining appropriate precisions for signals in fixed-point IIR filters, Proceedings of the 40th conference on Design automation , DAC '03, pp.656-661, 2003.
DOI : 10.1145/775832.775998

C. Carreras and J. A. Lopez, Bit-width selection for data-path implementations, Proceedings 12th International Symposium on System Synthesis, pp.114-119, 1999.
DOI : 10.1109/ISSS.1999.814269

C. Chatfield, The Analysis of Time Series: An Introduction, 1989.

A. Chapoutot, L. Didier, and F. Villers, Range Estimation of Floating- Point Variables in Simulink Models, NSV-II : Second InternationalWorkshop on Numerical Software Verification, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00816115

M. Clark, M. Mulligan, D. Jackson, and D. Linebarger, Accelerating Fixed- Point Design for MB-OFDM UWB Systems, CommsDesign, 2005.

J. A. Clarke, G. A. Constantinides, and P. Y. Cheung, Wordlength Selection for Power Minimization via Nonlinear Optimization, ACM Trans. Ob Des
DOI : 10.1145/1529255.1529261

J. Cong, Evaluation of Static Analysis Techniques for Fixed-Point Precision Optimization, 2009 17th IEEE Symposium on Field Programmable Custom Computing Machines, pp.231-234, 2009.
DOI : 10.1109/FCCM.2009.35

B. J. Debusschere, H. N. Najm, P. P. Pebay, O. M. Knio, R. G. Ghanem et al., Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes, SIAM Journal on Scientific Computing, vol.26, issue.2, p.698719, 2004.
DOI : 10.1137/S1064827503427741

L. Didier, A statistical method of range estimation for embedded applications, 13th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations -SCAN2008, pp.34-35, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01303656

O. Ditlevsen and H. O. Madsen, Structural Reliability Methods, 2007.

A. Dutfoy and R. Lebrun, Modelisation de la dependence par la theorie des copules: une generalization de la transformation de Nataf, 18eme Congres Francais de Mecanique, 2007.

C. F. Fang, R. B. Rutenbar, M. Puschel, and T. Chen, Toward efficient static analysis of finite-precision effects in DSP applications via affine arithmetic modeling, Proceedings of the 40th conference on Design automation , DAC '03, pp.496-501, 2003.
DOI : 10.1145/775832.775960

C. F. Fang, T. Chen, and R. A. Rutenbar, Floating-point error analysis based on affine arithmetic, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)., p.561564, 2003.
DOI : 10.1109/ICASSP.2003.1202428

R. V. Fields and . Jr, Numerical methods to estimate the coefficients of polynomial chaos expansion, 15th ASCE Engineering Mechanics Conference, 2002.

L. H. De-figuereido and J. Stolfi, Self-Validated numerical methods and applications, Brazilian Mathematics Colloquium monographs, 1997.

L. H. De-figuereido and J. Stolfi, Affine Arithmetic: Concepts and Applications, Numerical Algorithms, vol.37, issue.1-4, pp.137-158, 2004.
DOI : 10.1023/B:NUMA.0000049462.70970.b6

R. G. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

R. G. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach, 2003.
DOI : 10.1007/978-1-4612-3094-6

T. Grtker, E. Multhaup, and O. Mauss, Evaluation of HW/SW Tradeoffs Using Behavioral Synthesis, 7th International Conference on Signal Processing Applications and Technology (ICSPAT96), 1996.

J. Emil, Statistics of Extremes, 1958.

N. Hervé, D. Menard, and O. Sentieys, Data wordlength optimization for FPGA synthesis, IEEE Workshop on Signal Processing Systems Design and Implementation, 2005., p.623628, 2005.
DOI : 10.1109/SIPS.2005.1579941

T. Hill, AccelDSPs synthesis tool floating-point to fixedpoint conversion of matlab algorithms targeting FPGAs, 2006.

S. Hussain, Peak to Average Power Ratio Analysis and Reduction of Cognitive Radio Signals, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00426930

L. B. Jackson, On the Interaction of Roundoff Noise and Dynamic Range in Digital Filters*, Bell System Technical Journal, vol.49, issue.2, pp.159-184, 1970.
DOI : 10.1002/j.1538-7305.1970.tb01763.x

H. Keding, M. Willems, M. Coors, and H. Meyr, FRIDGE: A fixedpoint design and simulation environment, CMConf. on Design,Automation and Test in Europe, p.429435, 1998.

S. Kim and W. Sung, A floating-point to fixed-point assembly program translator for the TMS320C25, IEEE Trans. Circuits Syst. II, vol.41, pp.730-739, 1994.

S. Kim and W. Sung, Fixed-Point-Simulation Utility for C and C++ Based Digital Signal Processing Programs, Twenty-eighth Annual Asilomar Conference on Signals, Systems, and Computer, 1994.

S. Kim, K. Kum, and S. Wonyang, Fixed-Point Optimization Utility for C and C++ Based Digital Signal Processing Programs, IEEE Transaction on Circuits and Systems II, vol.45, issue.11, 1998.

S. Kim and W. Sung, Fixed-Point Error Analysis and Word Length Optimization of 8x8 IDCT Architectures, IEEE Transactions on Circuits and Systems for Video Technology, vol.8, issue.8, p.935940, 1998.

K. Kum and W. Sung, Combined word-length optimization and high level synthesis of digital signal processing systems, IEEE Trans. On CAD Of Integr

N. Lagaros, G. Stefanou, and M. Papadrakakis, An enhanced hybrid method for the simulation of highly skewed non-Gaussian stochastic fields, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.45-47, pp.4824-4844, 2005.
DOI : 10.1016/j.cma.2004.12.009

D. Lee, Accuracy-Guaranteed Bit-Width Optimization, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.25, issue.10, 2006.
DOI : 10.1109/TCAD.2006.873887
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.385.6194

C. Li and A. Der-kiureghian, Optimal Discretization of Random Fields, Journal of Engineering Mechanics, vol.119, issue.6, p.11361154, 1993.
DOI : 10.1061/(ASCE)0733-9399(1993)119:6(1136)

M. Lò-eve, Probability Theory, 1977.

J. A. Lopez, Fast characterization of the noise bounds derived from coefficient and signal quantization, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03., pp.309-312, 2003.
DOI : 10.1109/ISCAS.2003.1205835

J. A. Lopez, C. Carreras, and O. Nieto-taladriz, Improved Interval-Based Characterization of Fixed-Point LTI Systems With Feedback Loops, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.26, issue.11, pp.1923-1933, 2007.
DOI : 10.1109/TCAD.2007.896306

D. Menard and O. Sentieys, Automatic Evaluation of the Accuracy of Fixedpoint Algorithms, Design, Automation and Test in Europe 2002 (DATE02), 2002.
URL : https://hal.archives-ouvertes.fr/inria-00482931

D. Menard and O. Sentieys, A methodology for evaluating the precision of fixed-point systems, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP02), 2002.
URL : https://hal.archives-ouvertes.fr/inria-00482913

D. Menard, Methodologie de compilation d'algorithmes de traitement du signal pour les processeurs en virgule fixe, sous contrainte de precision, 2002.
URL : https://hal.archives-ouvertes.fr/tel-00609159

D. Menard, D. Chillet, and O. Sentieys, Floating-to-Fixed-Point Conversion for Digital Signal Processors, EURASIP Journal on Applied Signal Processing, vol.37, issue.8, 2006.
DOI : 10.1155/ASP/2006/96421
URL : https://hal.archives-ouvertes.fr/inria-00459212

D. Menard, R. Rocher, and O. Sentieys, Analytical Fixed-Point Accuracy Evaluation in Linear Time-Invariant Systems, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.55, issue.10, 2008.
DOI : 10.1109/TCSI.2008.923279
URL : https://hal.archives-ouvertes.fr/inria-00459231

R. E. Moore, Interval Analysis, 1966.

A. Nataf, Determination des distributions dont les marges sont donnees, Comptes rendus de lAcademie des Sciences, pp.42-43, 1962.

R. B. Nelsen, An Introduction to Copulas, 1999.
DOI : 10.1007/978-1-4757-3076-0

B. Van-den-nieuwenhof, Stochastic Finite Elements For Elastodynamics: Random field and shape uncertainty modelling using direct and modal perturbation-based approaches, RE Transactions on Circuit Theory, 2003.

H. Ochiai and H. Imai, On the distribution of the peak-to-average power ratio in OFDM signals, IEEE Transactions on Communications, vol.49, issue.2, pp.282-289, 2001.
DOI : 10.1109/26.905885

E. Ozer, A. P. Nisbet, and D. Gregg, Stochastic bit-width approximation using extreme value theory for customizable processors, CC 2004, p.250264, 2004.

E. Ozer, A. P. Nisbet, and D. Gregg, A stochastic bitwidth estimation technique for compact and low-power custom processors, ACM Transactions on Embedded Computing Systems, vol.7, issue.3, pp.1-30, 2008.
DOI : 10.1145/1347375.1347387

K. Parashar, R. Rocher, D. Menard, and O. Sentieys, Analytical approach for analyzing quantization noise effects on decision operators, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.1554-1557, 2010.
DOI : 10.1109/ICASSP.2010.5495520
URL : https://hal.archives-ouvertes.fr/inria-00534522

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

J. G. Proakis, Digital Communications, 2000.

M. Rosenblatt, Remarks on multivariate transformation The Annals of Mathematical Statistics. v23 i3, pp.470-472, 1952.

C. Shi and R. W. Brodersen, An automated floating-point to fixed-point conversion methodology, Proc. IEEE Int. Conf. on Acoust., Speech, and Signal Processing (ICASSP03), pp.529-532, 2003.

C. Shi and R. W. Brodersen, A perturbation theory on statistical quantization effects in fixed-point DSP with non-stationary inputs, IEEE International Symposium on Circuits and Systems (ISCAS04), 2004.

A. Singhee, C. F. Fang, J. D. Ma, and R. A. Rutenbar, Probabilistic intervalvalued computation : Toward a practical surrogate for statistics inside CAD tools, Proc. IEEE/ACM Des. Autom. Conf. (DAC), pp.167-172, 2006.

A. Singhee, C. F. Fang, J. D. Ma, and R. A. Rutenbar, Probabilistic interval-valued computation, Proceedings of the 43rd annual conference on Design automation , DAC '06, pp.2317-2330, 2008.
DOI : 10.1145/1146909.1146955

B. Pinon, Une introduction Scilab, ESIAL Nancy, 2006.

B. Sudret and A. Der-kiureghian, Stochastic finite elements and reliability : A state-of-the-art report, 2000.

B. Sudret, M. Berveiller, and M. Lemaire, A stochastic finite element procedure for moment and reliability analysis, Revue europ??enne de m??canique num??rique, vol.15, issue.7-8, pp.7-8, 2006.
DOI : 10.3166/remn.15.825-866

W. Sung and K. Kum, Simulation-based word-length optimization method for fixed-point digital signal processing systems, IEEE Transactions on Signal Processing, vol.43, issue.12, pp.3087-3090, 1995.
DOI : 10.1109/78.476465

B. Widrow, A Study of Rough Amplitude Quantization by Means of Nyquist Sampling Theory, IRE Transactions on Circuit Theory, vol.3, issue.4, p.266276, 1956.
DOI : 10.1109/TCT.1956.1086334

B. Widrow, Statistical analysis of amplitude-quantized sampled-data systems, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry, vol.79, issue.6, pp.555-568, 1960.
DOI : 10.1109/TAI.1961.6371702

B. Widrow, I. Kollar, and M. Liu, Statistical theory of quantization, IEEE Transactions on Instrumentation and Measurement, vol.45, issue.2, 1996.
DOI : 10.1109/19.492748

B. Widrow and I. Kollar, Quantization Noise: Round Off Error in Digital Computation, Signal Processing, Control and Communications, 2008.
DOI : 10.1017/CBO9780511754661

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268

B. Wu, J. Zhu, and F. Najm, An analytical approach for dynamic range estimation, Proceedings of the 41st annual conference on Design automation , DAC '04, 2004.
DOI : 10.1145/996566.996699

B. Wu, J. Zhu, and F. Najm, Dynamic Range Estimation, Computer-Aided Design of Integrated Circuits and Systems IEEE Transactions on, vol.5, issue.9, p.16181636, 2006.

D. Xiu and G. E. Karniadakis, The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.24, issue.2, p.619644, 2002.
DOI : 10.1137/S1064827501387826

L. Zhang, Y. Zhang, and W. Zhou, Floating-point to Fixed-point Transformation Using Extreme Value Theory, 2009 Eighth IEEE/ACIS International Conference on Computer and Information Science, pp.271-276, 2009.
DOI : 10.1109/ICIS.2009.38