Sangüesa, Carmen (2008) Uniforms Error Bounds in Continuous Approximations of Nonnegative Random Variables Using Laplace Transforms. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
- Published Version
In this work we deal with approximations for distribution functions of nonnegative random variables. More specifically, we construct continuous approximants using an acceleration technique over a well-know inversion formula for Laplace transforms. We give uniform error bounds using a
representation of these approximations in terms of gamma-type operators. We apply our results to certain mixtures of Erlang distributions which contain the class of continuous phase-type distributions.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 1/08|
|Corporate Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||Uniform distance; Laplace transform; gamma distribution; phase-type distribution|
|Deposited By:||DIANE MICHAUD|
|Deposited On:||03 Jun 2010 20:13|
|Last Modified:||08 Dec 2010 23:20|
Adell, J. A. and de la Cal, J. (1993). On the uniform convergence of normalized Poisson mixtures to their mixing distribution, Statist. Probab. Lett. 18, 227-232.
Adell, J. A. and de la Cal, J. (1994). Approximating gamma distributions by normalized negative binomial distributions, J. Appl. Probab. 31, 391-400.
Adell J. A. and Sangüesa C. (1999). Direct and converse inequalities for positive linear operators on the positive semi-axis, J. Austral. Math. Soc. Ser. A 66, 90-103.
Alzer, H. (1997) On some inequalities for the gamma and psi functions, Math. Comp., 66, 373-389.
Asmussen, S. (2000). Ruin probabilities, World Scientific, Singapore.
Embrechts, P., Grübel, R. and Pitts, S. M. (1993) Some applications of the fast Fourier transform algorithm in insurance mathematics, Statist. Neerlandica, 47, 59-75.
Feller, W. (1971). An Introduction to Probability Theory and its Applications, Vol II, 2nd. edition. Wiley, New York.
Grübel, R. and Hermesmeier, R. (2000). Computation of compound distributions II: discretization errors and Richardson extrapolation. Astin Bull. 30, 309-331.
Hipp, C. (2006). Speedy convolution algorithms and Panjer recursions for phase-type distributions. Insurance Math. Econom. 38, 176
Latouche, G. and Ramaswami, V. (1999). Introduction to Matrix Analytic Methods in Stochastic Modelling, ASA-SIAM, Philadelphia.
Maier, R.S. (1991) The algebraic construction of phase-type distributions, Comm. Statist. Stochastic Models, 7, 573-602.
O'Cinneide, C. A. (1999) Phase-type distributions: open problems and a few properties., Comm. Statist. Stochastic Models, 15, 731-757.
Qi, F., Cui, R., Chen, C., Guo, B. (2005) Some completely monotonic functions involving polygamma functions and an application. J. Math. Anal. Appl. 310 , 303-308.
Sangüesa, C. (2007). Error bounds in approximations of compound distributions using gamma-type operators, To appear in Insurance Math. Econom.
Sundt, B. (2002). Recursive evaluation of aggregate claims distributions, Insurance Math. Econom. 30, 297-322.
Willmot, G. E. and Woo, J. K. (2007). On the class of Erlang mixtures with risk theoretical applications, N. Am. Actuar. J. 11, 99-105
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