Examine generalized lambda distribution fitting performance: An application to extreme share return in Malaysia


  • Muhammad Fadhil Marsani Department of Mathematical Sciences, Faculty Sciences, Universiti Teknologi Malaysia
  • Ani Shabri Department of Mathematical Sciences, Faculty Sciences, Universiti Teknologi Malaysia
  • Nur Amalina Mat Jan Universiti Teknologi Malaysia




Extreme share returns, kuala lumpur composite index (KLCI), l-moment, risk management, value at risk (VaR)


Understand the extreme volatility in the market is important for the investor to make a correct prediction. This paper evaluated the performance of generalized lambda distribution (GLD) by comparing with the popular probability distribution namely generalized extreme value (GEV), Generalized logistic (GLO), generalized Pareto (GPA), and Pearson (PE3) using Kuala Lumpur composite index stock return data. The parameter for each distribution estimated using the L-moment method. Based on k-sample Anderson darling goodness of fit test, GLD performs well in weekly maximum and minimum period. Evidence for preferring GLD as an alternative to extreme value theory distribution also described.

Author Biographies

Muhammad Fadhil Marsani, Department of Mathematical Sciences, Faculty Sciences, Universiti Teknologi Malaysia

Muhammad Fadhil Bin Marsani was born on December 22, 1991. He obtained a Bachelor of Science degree in Applied Science Mathematics and Economics from the University Science Malaysia, and a Masters of Science degree in Statistics from Universiti Kebangsaan Malaysia, in 2015. Presently, he is a Ph.D. student with Universiti Teknologi Malaysia, in the Department of Mathematical Sciences. His Research Interests is in Statistical Economics Modeling.

Ani Shabri, Department of Mathematical Sciences, Faculty Sciences, Universiti Teknologi Malaysia

Dr. Ani Shabri is Lecturer in Statistics from Department of Mathematical Sciences, Faculty of Science. His Research Interests is in Time series forecasting and Flood Frequency Analysis.

PhD in Statistics (UKM)
M.Sc. in Statistics (UTM)
B.Sc. in Science Mathematics (UTM)


Broussard, J. P., Booth, G. G. 1998. The behavior of extreme values in Germany's stock index futures: An application to intradaily margin setting. European Journal of Operational Research. 104, 393-402.

Carvalhal, A., Mendes, B. V. 2003. Value-at-risk and extreme returns in Asian stock markets. International Journal of Business. 8(1), 1-24.

Chalabi, Y., Scott, D. J., Würtz, D. 2010. The generalized lambda distribution as an alternative to model financial returns. Eidgenössische Technische Hochschule and University of Auckland, Zurich and Auckland. Retrieved from Rmetrics

Research Collection website: https://www.rmetrics.org/sites/default/files/glambda_0.pdf.

Chen, N.-F., Roll, R., Ross, S. A. 1986. Economic forces and the stock market. The Journal of Business. 59, 383-403.

Corlu, C. G., Meterelliyoz, M. 2014. Estimating the parameters of the generalized lambda distribution: Which method performs best? Communications in Statistics-Simulation and Computation. 45(7), 2276-2296.

Corlu, C. G., Meterelliyoz, M., Tiniç, M. 2016. Empirical distributions of daily equity index returns: A comparison. Expert Systems with Applications. 54, 170-192.

Corrado, C. J. 2001. Option pricing based on the generalized lambda distribution. Journal of Futures Market, 21(3), 213-236.

Danielsson, J., De Vries, C. 1997. Beyond the sample: Extreme

quantile and probability estimation. Tinbergen Institute Discussion Paper, 98-016/2.

Danielsson, J., Hartmann, P., De Vries, C. 1998. The Cost of Conservatism:Extreme Returns, Value-at-Risk, and the Basle ‘Multiplication Factor’. Risk. 11(1), 101-103.

Embrechts, P., Resnick, S. I., Samorodnitsky, G. 1999. Extreme value theory as a risk management tool. North American Actuarial Journal. 3, 30-41.

Fama, E. F. 1965. The behavior of stock-market prices. The journal of Business. 38, 34-105.

Fournier, B., Rupin, N., Bigerelle, M., Najjar, D., Iost, A. 2006. Application of the generalized lambda distributions in a statistical process control methodology. Journal of Process Control. 16, 1087-1098.

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

Gray, J. B., French, D. W. 1990. Empirical comparisons of distributional models for stock index returns. Journal of Business Finance & Accounting. 17, 451-459.

Greenwood, J. A., Landwehr, J. M., Matalas, N. C., 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.

Harris, R. D. F., Küçüközmen, C. C. 2001. The empirical distribution of UK and US stock returns. Journal of Business Finance & Accounting. 28, 715-740.

Hasan, H., Radi, N. F. A., Kassim, S., Baskoro, E. T., Suprijanto, D. 2012. Modeling the distribution of extreme share return in Malaysia using Generalized Extreme Value (GEV) distribution. In AIP Conference Proceedings. 82-89.

Hosking, J. R. 1986. The theory of probability weighted moments, Research Report RC12210, IBM Research Division, Yorktown Heights, N.Y.

Hosking, J. R. 1990. L-moments: analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society. Series B (Methodological). 52(1), 105-124.

Hussain, S. I., Li, S. 2015. Modeling the distribution of extreme returns in the Chinese stock market. Journal of International Financial Markets, Institutions and Money. 34, 263-276.

Jondeau, E., Rockinger, M. 2003. Testing for differences in the tails of stock-market returns. Journal of Empirical Finance. 10, 559-581.

Karvanen, J., Nuutinen, A. 2008. Characterizing the generalized lambda distribution by L-moments. Computational Statistics & Data Analysis. 52, 1971-1983.

Longin, F. M. 1996. The asymptotic distribution of extreme stock market returns. Journal of Business. 69, 383-408.

Longin, F. M. 2000. From value at risk to stress testing: The extreme value approach. Journal of Banking & Finance. 24, 1097-1130.

Mcdonald, J. B., Xu, Y. J. 1995. A generalization of the beta distribution with applications. Journal of Econometrics. 66, 133-152.

Mcneil, A. J. 1998. Calculating quantile risk measures for financial return series using extreme value theory. Retreived from ETH Zürich Research Collection website: https://www.research-collection.ethz.ch/handle/20.500. 11850/146132.

Mcneil, A. J., Frey, R. 2000. Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Journal of Empirical Finance. 7, 271-300.

Öztürk, A., Dale, R. 1982. A study of fitting the generalized lambda distribution to solar radiation data. Journal of Applied Meteorology. 21, 995-1004.

Pal, S. 2004. Evaluation of nonnormal process capability indices using generalized lambda distribution. Quality Engineering. 17, 77-85.

Peiró, A. 1994. The distribution of stock returns: International evidence. Applied Financial Economics. 4, 431-439.

Ramberg, J. S., Schmeiser, B. W. 1974. An approximate method for generating asymmetric random variables. Communications of the ACM. 17, 78-82.

Scholz, F. W., Stephens, M. A. 1987. K-sample Anderson–Darling tests. Journal of the American Statistical Association. 82, 918-924.

Tarsitano, A. 2004. Fitting the generalized lambda distribution to income data. In COMPSTAT’2004 Symposium. 1861-1867.

Theodossiou, P. 1998. Financial data and the skewed generalized t distribution. Management Science. 44, 1650-1661.

Tolikas, K. 2014. Unexpected tails in risk measurement: Some international evidence. Journal of Banking & Finance. 40, 476-493.

Tolikas, K. 2008. Value-at-risk and extreme value distributions for financial returns. The Journal of Risk. 10, 31-77.

Tolikas, K., Brown, R. A. 2006. The distribution of the extreme daily share returns in the Athens stock exchange. European Journal of Finance. 12, 1-22.

Tolikas, K., Gettinby, G. D. 2009. Modelling the distribution of the extreme share returns in Singapore. Journal of Empirical Finance. 16, 254-263.

Tukey, J. W. 1962. The future of data analysis. The Annals of Mathematical Statistics. 33, 1-67.

Viglione, A., Laio, F., Claps, P. 2007. A comparison of homogeneity tests for regional frequency analysis. Water Resources Research. 43.

Zin, W. Z. W., Safari, M. a. M., Jaaman, S. H., Yie, W. L. S. 2014. Probability distribution of extreme share returns in Malaysia. In AIP Conference Proceedings. 325-333.