The Linear Combination of Logistic and Gumbel Random Variables

• Autorzy: Nadarajah S. , Kotz S.
• Języki publikacji: EN

Abstrakty

EN

The exact distribution of the linear combination aX +bY is derived when X and Y are independent logistic and Gumbel random variables. A measure of entropy of the linear combination is investigated. Computer programs are provided for generating tabulations of the percentage points associated with the linear combination. The work is motivated by problems in automation, control, fuzzy sets, neurocomputing and other areas of computer science.

Słowa kluczowe

EN

entropy; gumbel distribution; linear combinations of random variables; logistic distribution

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2006
• Tom: Vol. 74, nr 2,3
• Strony: 341--350
• Opis fizyczny: bibliogr. 20 poz.

Twórcy

autor

Nadarajah S.

autor

Kotz S.

• Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA,

Bibliografia

• [1] Albert, J.: Sums of uniformly distributed variables: a combinatorial approach, College Mathematics Journal, 33, 2002, 201-206.
• [2] Ali, M. M., Obaidullah,M.: Distribution of linear combination of exponential variates, Communications in Statistics-Theory and Methods, 11, 1982, 1453-1463.
• [3] Chapman, D. G.: Some two-sample tests, Annals of Mathematical Statistics, 21, 1950, 601-606.
• [4] Christopeit, N., Helmes, K.: A convergence theorem for randomlinear combinations of independent normal random variables, Annals of Statistics, 7, 1979, 795-800.
• [5] Davies, R. B.: Algorithm AS 155: The distribution of a linear combination of X2 random variables, Applied Statistics, 29, 1980, 323-333.
• [6] Dobson, A. J., Kulasmaa, K., Scherer, J.: Confidence intervals for weighted sums of Poisson parameters, Statistics in Medicine, 10, 1991, 457-462.
• [7] Farebrother, R. W.: Algorithm AS 204: The distribution of a positive linear combination of X2 random variables, Applied Statistics, 33, 1984, 332-339.
• [8] Fisher, R. A.: The fiducial argument in statistical inference, Annals of Eugenics, 6, 1935, 391-398.
• [9] Gradshteyn, I. S., Ryzhik, I. M.: Table of Integrals, Series, and Products, sixth edition, Academic Press, San Deigo, CA, 2000.
• [10] Hitczenko, P.: A note on a distribution of weighted sums of i.i.d. Rayleigh random variables, Sankhy¯a, A, 60, 1998, 171-175.
• [11] Hu, C. -Y., Lin, G. D.: An inequality for the weighted sums of pairwise i.i.d. generalized Rayleigh random variables, Journal of Statistical Planning and Inference, 92, 2001, 1-5.
• [12] Kamgar-Parsi, B., Kamgar-Parsi, B., Brosh, M.: Distribution and moments of weighted sum of uniform randomvariables with applications in reducingMonte Carlo simulations, Journal of Statistical Computation and Simulation, 52, 1995, 399-414.
• [13] Moschopoulos, P. G.: The distribution of the sum of independent gamma random variables, Annals of the Institute of Statistical Mathematics, 37, 1985, 541-544.
• [14] Pham, T. G. and Turkkan, N.: Reliability of a standby system with beta-distributed component lives, IEEE Transactions on Reliability, 43, 1994, 71-75.
• [15] Pham-Gia, T., Turkkan, N.: Bayesian analysis of the difference of two proportions, Communications in Statistics-Theory and Methods, 22, 1993, 1755-1771.
• [16] Provost, S. B.: On sums of independent gamma random variables, Statistics, 20, 1989, 583-591.
• [17] Prudnikov, A. P., Brychkov, Y. A., Marichev, O. I.: Integrals and Series, volumes 1, 2 and 3, Gordon and Breach Science Publishers, Amsterdam, 1986.
• [18] Rényi, A.: On measures of entropy and information, in: Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. I, University of California Press, Berkeley, 1961, 547-561.
• [19] Shannon, C. E.: A mathematical theory of communication, Bell System Technical Journal 27, 1948, 379-432.
• [20] Witkovský, V.: Computing the distribution of a linear combination of inverted gamma variables, Kybernetika, 37, 2001, 79-90.