On the Effects of Plotting Positions to the Probability Weighted Moments Method for the Generalized Logistic Distribution

- Journal title : Communications for Statistical Applications and Methods
- Volume 14, Issue 3, 2007, pp.561-576
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2007.14.3.561

Title & Authors

On the Effects of Plotting Positions to the Probability Weighted Moments Method for the Generalized Logistic Distribution

Kim, Myung-Suk;

Kim, Myung-Suk;

Abstract

Five plotting positions are applied to the computation of probability weighted moments (PWM) on the parameters of the generalized logistic distribution. Over a range of parameter values with some finite sample sizes, the effects of five plotting positions are investigated via Monte Carlo simulation studies. Our simulation results indicate that the Landwehr plotting position frequently tends to document smaller biases than others in the location and scale parameter estimations. On the other hand, the Weibull plotting position often tends to cause larger biases than others. The plotting position (i - 0.35)/n seems to report smaller root mean square errors (RMSE) than other plotting positions in the negative shape parameter estimation under small samples. In comparison to the maximum likelihood (ML) method under the small sample, the PWM do not seem to be better than the ML estimators in the location and scale parameter estimations documenting larger RMSE. However, the PWM outperform the ML estimators in the shape parameter estimation when its magnitude is near zero. Sensitivity of right tail quantile estimation regarding five plotting positions is also examined, but superiority or inferiority of any plotting position is not observed.

Keywords

Generalized logistic distribution;plotting position;probability weighted moments;quantile;shape parameter;

Language

English

Cited by

References

2.

Gettinby, G. D., Sinclair, C. D., Power, D. M. and Brown, R. A. (2004). An analysis of the distribution of extreme share returns in the UK from 1975 to 2000. Journal of Business Fianance & Accounting, 31, 607-646

3.

Gettinby, G. D., Sinclair, C. D., Power, D. M. and Brown, R. A. (2006). An analysis of the distribution of extremes in indices of share returns in the US, UK and Japan from 1963 to 2000. International Journal of Finance & Economics, 11, 97-113

4.

Greenwood, J. A., Landwehr, J. M., Matalas, N. C. and Wallis, J. R. (1979). Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research, 15, 1049-1054

5.

Haktanir, T. and Bozduman, A. (1995). A study on sensitivity of the probability-weighted moments method on the choice of the plotting position formula. Journal of Hydrology, 168, 265-281

6.

Hosking, J. R. M. (1990). L-moments: analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society, Ser. B, 52, 105-124

7.

Hosking, J. R. M., Wallis, J. R. and Wood, E. F. (1985). Estimation ofthe generalized extreme value distribution by the method of probability-weighted moments. Technometrics, 27, 251-261

8.

Hosking, J. R. M. and Wallis, J. R. (1987). Parameter and quantile estimation for the generalized Pareto distribution. Technometrics, 29, 339-349

9.

Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quarterly Journal of the Royal Meteorological Society, 81, 158-171

10.

Landwehr, J. M., Matalas, N. C. and Wallis, J. R. (1979a). Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Water Resources Research, 15, 1055-1064