Parameters Estimation of Nakagami Probability Distribution Using Methods of L.Moments

Ishfaq Ahmad, Shafiq -ul-Rehman


In communications theory, Nakagami distribution (NKD) is used to model scattered signals that reach a receiver from different paths. In order to use NKD to model a given set of data, we will have to estimate its parameters from the given data. Method of L-Moments (MLM) is being compared with Method of Moments (MOM) for estimating the parameters of NKD. In this study, we have derived its first two L-moments in closed form and estimated its parameters using simulated data. This study shows that estimates based on MLM are better than MOM, not only in small samples but also in large samples. For evaluation purpose, we calculated Root Mean Square Error (RMSE) and Bias using Monte Carlo simulations.

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M. Nakagami, “The m-distribution-A general formula of intensity distribution of rapid fading,” Statistical Method of Radio Propagation, 1960.

S. Sarkar, et al., “Adequacy of Nakagami-m distribution function to derive GIUH,” Journal of Hydrologic Engineering, vol. 14, no. 10,

, pp. 1070-1079.

S. Sarkar, et al., “Performance investigation of Nakagami-m distribution to derive flood hydrograph by genetic algorithm optimization

approach,” Journal of Hydrologic Engineering, vol. 15, no. 8, 2010, pp. 658-666.

P. Tsui, et al., “Use of Nakagami distribution and logarithmic compression in ultrasonic tissue characterization,” Journal of Medical

and Biological Engineering, vol. 26, no. 2, 2006, pp. 69.

E. Carcole and H. Sato, “Statistics of the fluctuations of the amplitude of coda waves of local earthquakes,” Proc. Seismological Society of Japan, 2009 Fall Meeting, C31-13, Kyoto, Japan, 2009.

H. Nakahara and E. Carcolé, “Maximum likelihood method for estimating coda Q and the Nakagami-m parameter,” Bulletin of the

Seismological Society of America, vol. 100, no. 6, 2010, pp. 3174-3182.

U. Charash, “Reception through Nakagami fading multipath channels with random delays,” IEEE Transactions on Communications, vol. 27, no. 4, 1979, pp. 657-670.

H. Nakahara and E. Carcolé, “Maximum likelihood method for estimating coda Q and the Nakagami-m parameter-I,” Bulletin of the

Seismological Society of America, vol. 100, no. 6, 2010, pp. 3174-3182.

J. Cheng and N.C. Beaulieu, “Maximum likelihood based estimation of the Nakagami m parameter,” IEEE Communications letters, vol. 5, no. 3, 2001, pp. 101-103.

J. Cheng and N.C. Beaulieu, “Generalized moment estimators for the Nakagami fading parameter,” IEEE communications letters, vol. 6, no. 4, 2002, pp. 144-146.

A. Abidi and M. Kaveh, “Performance comparison of three different estimator for the Nakagami m parameter using Monte Carlo simulations,” IEEE Commun. Lett, vol. 4, no. 4, 2000, pp. 119-121.

J. Gaeddert and A. Annamalai, “Further results on Nakagami-m parameter estimation,” Proc. Vehicular Technology Conference, 2004.

VTC2004-Fall. 2004 IEEE 60th, IEEE, 2004,

pp. 4255-4259.

N.C. Beaulieu and Y. Chen, “A MAP estimator for the m parameter in Nakagami fading ultra-wide bandwidth indoor channels,” IEEE transactions on wireless communications, vol. 6, no. 3, 2007, pp. 840-

J.R. Hosking, “L-moments: analysis and estimation of distributions using linear combinations of order statistics,” Journal of the Royal Statistical Society. Series B (Methodological), 1990, pp. 105-124.

P. Royston, “Figure 7; R. M. Vogel and N. M. Fennessey, Water Resources Research, 29 (1993), Figures 3 and 4.

W.H. Asquith, “L-moments and TL-moments of the generalized lambda distribution,” Computational Statistics & Data Analysis, vol.

, no. 9, 2007, pp. 4484-4496.



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