İki Bağımsız Log-Normal Dağıtılmış Rastgele Değişkenin Toplamının Logaritması Olan Rastgele Değişkenin Parametrelerinin Hızlı Hesaplanması
Öz
Bu çalışmada, iki log-normal dağılımlı rasgele değişkenin logaritması olan rasgele değişkenin ortalama ve varyansını hesaplamak için iki hızlı metot sunulmuştur. Ortalama ve varyansın sadece bir boyutlu nümerik integral metodu ile hesaplanabileceği gösterilmiştir. Önerilen algoritmanın hızı temel algoritmanın hızı ile karşılaştırılmıştır. Benzetim sonuçları önerilen ilk yöntemin çalışma zamanını ortalama %43,98 azalttığını göstermiştir. Benzetim sonuçları ayrıca önerilen ikinci metodun 0,325’ten büyük varyanslar için birinci yöntemden daha hızlı olduğunu göstermiştir..
Anahtar Kelimeler
Log-normal dağılımlı rasgele değişkenlerin toplamı Paralel model kombinasyonu Nümerik integral Gürbüzlük
Kaynakça
- 1. Schwartz, S., Yeh, Y., 1982. On the Distribution Function and Moments of Power Sums with Lognormal Components. Bell Syst. Tech. Journal, 61, 1441–1462.
- 2. Li, X., Wu, Z., Chakravarthy, V.D., Wu, Z., 2011. A Low-complexity Approximation to Lognormal Sum Distributions via Transformed Log Skewnormal Distribution. IEEE Transactions on Vechular Technology, 60(8), 4040–4045.
- 3. Gales, M.J.F., Young, S.J., 1993. Cepstral Parameter Compensation for Hmm Recognition in Noise. Speech Communications, 12, 231–240.
- 4. Gales, M.J.F., Young, S.J., 1995. A Fast and Flexible Implementation of Parallel Model Combination. In Proceedings of ICASSP, Detroit Michigan USA, 133–136.
- 5. Gales, M.J.F., Young, S.J., 1996. Robust Continuous Speech Recognition Using Parallel Model Compensation. IEEE Transactions on Acoustics, Speech, and Signal Processing, 4(5), 352–359.
- 6. Gales, M.J.F., Young, S.J., 1995. Robust Speech Recognition in Additive and Convolutional Noise Using Parallel Model Combination. Computer Speech and Language, 9, 289–307.
- 7. Fenton, L.F., 1960. The Sum of Lognormal Probability Distributions in Scatter Transmission Systems. IRE Transactions on Communications Systems, 8, 57–67.
- 8. Neelesh, B., Wu, B.J., Molisch, A.F., Zhang, J., 2007. Approximating a Sum of Random Variables with a Lognormal. IEEE Transactions on Wireless Communications, 6(7), 2690–2699.
- 9. Milevsky, M., Posner, S., 1998. Asian Options, the Sum of Lognormals and the Reciprocal Gamma Distribution. Journal of Financial and Quantative Analysis, 33(3), 409–422.
- 10. Romeo, M., Da Costa, V., Bardou, F., 2003. Broad Distribution Effects in Sums of Lognormal Random Variables. The European Physical Journal B, 32(4), 513–525.
- 11. Gong, Y., 1995. Speech Recognition in Noisy Environments: a Survey. Speech Communications, 16, 261–291.
- 12. Abramowitz, M., Stegen, I.A., 1965. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. New York, USA: Dover, Publications.
- 13. Oppenheim, A.V., Schafer, R.W., 1989. Discrete-Time Signal Processing. Englewood Cliffs, New Jersey, USA: Prentice-Hall, Inc.
- 14. Kincaid, D., Cheney, W., 1996. Numerical Analysis. California, USA: Brooks/Cole Publishing Company.
Fast Computation of Parameters of the Random Variable that is Logarithm of Sum of Two Independent Log-normally Distributed Random Variables
Öz
In this paper, two fast methods are proposed for computation of mean and variance of a random variable which is logarithm of two log-normally distributed random variables. It is shown that mean and variance can be computed using only one dimensional numerical integration method. The speed of the proposedalgorithms is compared with the baseline algorithm. Simulation results showed that the first proposed method decreases the execution time by an average of 43.98 %. Simulation results also showed that the second proposed method is faster than the first proposed method for the variances greater than 0.325.
Anahtar Kelimeler
Sum of log-normally distributed random variables Parallel model combination Numerical integration Robustness.
Kaynakça
- 1. Schwartz, S., Yeh, Y., 1982. On the Distribution Function and Moments of Power Sums with Lognormal Components. Bell Syst. Tech. Journal, 61, 1441–1462.
- 2. Li, X., Wu, Z., Chakravarthy, V.D., Wu, Z., 2011. A Low-complexity Approximation to Lognormal Sum Distributions via Transformed Log Skewnormal Distribution. IEEE Transactions on Vechular Technology, 60(8), 4040–4045.
- 3. Gales, M.J.F., Young, S.J., 1993. Cepstral Parameter Compensation for Hmm Recognition in Noise. Speech Communications, 12, 231–240.
- 4. Gales, M.J.F., Young, S.J., 1995. A Fast and Flexible Implementation of Parallel Model Combination. In Proceedings of ICASSP, Detroit Michigan USA, 133–136.
- 5. Gales, M.J.F., Young, S.J., 1996. Robust Continuous Speech Recognition Using Parallel Model Compensation. IEEE Transactions on Acoustics, Speech, and Signal Processing, 4(5), 352–359.
- 6. Gales, M.J.F., Young, S.J., 1995. Robust Speech Recognition in Additive and Convolutional Noise Using Parallel Model Combination. Computer Speech and Language, 9, 289–307.
- 7. Fenton, L.F., 1960. The Sum of Lognormal Probability Distributions in Scatter Transmission Systems. IRE Transactions on Communications Systems, 8, 57–67.
- 8. Neelesh, B., Wu, B.J., Molisch, A.F., Zhang, J., 2007. Approximating a Sum of Random Variables with a Lognormal. IEEE Transactions on Wireless Communications, 6(7), 2690–2699.
- 9. Milevsky, M., Posner, S., 1998. Asian Options, the Sum of Lognormals and the Reciprocal Gamma Distribution. Journal of Financial and Quantative Analysis, 33(3), 409–422.
- 10. Romeo, M., Da Costa, V., Bardou, F., 2003. Broad Distribution Effects in Sums of Lognormal Random Variables. The European Physical Journal B, 32(4), 513–525.
- 11. Gong, Y., 1995. Speech Recognition in Noisy Environments: a Survey. Speech Communications, 16, 261–291.
- 12. Abramowitz, M., Stegen, I.A., 1965. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. New York, USA: Dover, Publications.
- 13. Oppenheim, A.V., Schafer, R.W., 1989. Discrete-Time Signal Processing. Englewood Cliffs, New Jersey, USA: Prentice-Hall, Inc.
- 14. Kincaid, D., Cheney, W., 1996. Numerical Analysis. California, USA: Brooks/Cole Publishing Company.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 29 Mart 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 37 Sayı: 1 |
