Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-28T02:55:51.151Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE LINEAR COMBINATION OF LAPLACE RANDOM VARIABLES

Published online by Cambridge University Press:  31 August 2005

Saralees Nadarajah  and
Samuel Kotz
Saralees Nadarajah
Affiliation:
Department of Statistics, University of Nebraska, Lincoln, NE 68583, E-mail: snadaraj@unlserve.unl.edu
Samuel Kotz
Affiliation:
Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC 20052, E-mail: kotz@gwu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The distribution of the linear combination αX + βY is derived when X and Y are independent Laplace random variables. Extensive tabulations of the associated percentage points are also given. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing, and other areas of informational sciences.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 4 , October 2005 , pp. 463 - 470
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Albert, J. (2002). Sums of uniformly distributed variables: A combinatorial approach. College Mathematical Journal 33: 201–206.Google Scholar
Ali, M.M. (1982). Distribution of linear combinations of exponential variates. Communications in Statistics—Theory and Methods 11: 1453–1463.Google Scholar
Chapman, D.G. (1950). Some two-sample tests. Annals of Mathematical Statistics 21: 601–606.Google Scholar
Christopeit, N. & Helmes, K. (1979). A convergence theorem for random linear combinations of independent normal random variables. Annals of Statistics 7: 795–800.Google Scholar
Davies, R.B. (1980). Algorithm AS 155: The distribution of a linear combination of chi-squared random variables. Applied Statistics 29: 323–333.Google Scholar
Dobson, A.J., Kulasmaa, K., & Scherer, J. (1991). Confidence intervals for weighted sums of Poisson parameters. Statistics in Medicine 10: 457–462.Google Scholar
Farebrother, R.W. (1984). Algorithm AS 204: The distribution of a positive linear combination of chi-squared random variables. Applied Statistics 33: 332–339.Google Scholar
Fisher, R.A. (1935). The fiducial argument in statistical inference. Annals of Eugenics 6: 391–398.Google Scholar
Hitezenko, P. (1998). A note on a distribution of weighted sums of iid Rayleigh random variables. Sankhya A 60: 171–175.Google Scholar
Hu, C.-Y. & Lin, G.D. (2001). An inequality for the weighted sums of pairwise i.i.d. generalized Rayleigh random variables. Journal of Statistical Planning and Inference 92: 1–5.Google Scholar
Kamgar-Parsi, B., Kamgar-Parsi, B., & Brosh, M. (1995). Distribution and moments of weighted sum of uniform random variables with applications in reducing Monte Carlo simulations. Journal of Statistical Computation and Simulation 52: 399–414.Google Scholar
Moschopoulos, P.G. (1985). The distribution of the sum of independent gamma random variables. Annals of the Institute of Statistical Mathematics 37: 541–544.Google Scholar
Pham, T.G. & Turkkan, N. (1994). Reliability of a standby system with beta-distributed component lives. IEEE Transactions on Reliability 43: 71–75.Google Scholar
Pham-Gia, T. & Turkkan, N. (1993). Bayesian analysis of the difference of two proportions. Communications in Statistics—Theory and Methods 22: 1755–1771.Google Scholar
Provost, S.B. (1989). On sums of independent gamma random variables. Statistics 20: 583–591.Google Scholar
Williamson, R.C. (1991). The law of large numbers for fuzzy variables under a general triangular norm extension principle. Fuzzy Sets and Systems 41: 55–81.Google Scholar
Witkovsky, V. (2001). Computing the distribution of a linear combination of inverted gamma variables. Kybernetika 37: 79–90.Google Scholar