Extreme Value Distributions on Closing Quotations and Returns of Islamabad Stock Exchange

Main Article Content

Muhammad Anas
Nasir Jamal
Muhammad Hanif
Usman Shahzad


This study is an experimental test done on the secondary data of banking sector of Islamabad Stock Exchange for year 2017 and applied different techniques on the given data record by using Generalized Extreme Value Distribution (GEV), Gumble Distribution (GBL), Generalized Pareto Distribution (GPD), Exponential Distribution (EXP), Gamma Distribution (GAM), Weibull Distribution (WBL) on the data of four banks Habib Bank, Allied Bank, Bank Alfalah and Askari Bank. This data is concerning the closing quotations and returns of four banks registered in Islamabad Stock Exchange. We try to fit different distributions on the data and founnd the best fit distribution.

We estimated the parameters of each distribution and also find the standard deviations of each distribution by using R Language and find which distribution is the best fit distribution on the basis of standard deviation distribution. We analyzed that shape wise GEV is the most suitable distribution, scale wise EXP distribution the best and location wise the best one is Gumbal distribution. This article shows that the overall GEV is the best distribution to model correctly the data.

GEV distribution, EXP distribution, GBL distribution, WBL distribution, GPD, R-language.

Article Details

How to Cite
Anas, M., Jamal, N., Hanif, M., & Shahzad, U. (2019). Extreme Value Distributions on Closing Quotations and Returns of Islamabad Stock Exchange. Asian Journal of Advanced Research and Reports, 5(4), 1-9. https://doi.org/10.9734/ajarr/2019/v5i430140
Original Research Article


Whitt W. The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution. Queueing Systems. 2000;36(1-3):71-87.

Krishnamoorthy K, Mathew T, Mukherjee S. Normal-based methods for a gamma distribution. Technometrics. 2008;50(1):69-78.

Chen P, Ye ZS. Estimation of field reliability based on aggregate lifetime data. Technimetrics, to Appear; 2016.

DOI: 10.1080/00401706.2015.1096827

Lawless Meeker WQ, Escobar LA. Statistical methods for reliability data. John Wiley & Sons: New York; 1998.

Vaseghi SV. Advanced digital signal processing and noise reduction. John Wiley & Sons: New York; 2008.

Pickands J. Statistical inference using extreme order statistics. Annals of Statistics. 1975;3:119–131.

Davison AC, Smith RL. Models for exceedence over high thresholds (with discussion). Journal of the Royal Statistical Society. 1990;52:393–442.

Combes C, Dussauchoy A. Generalized extreme value distribution for fitting opening/closing asset prices and returns in stock-exchange. Operational Research. 2006;6(1):3-26.

Onen F, Bagatur T. Prediction of flood frequency factor for Gumbel distribution using regression and GEP model. Arabian Journal for Science and Engineering. 2017;42(9):3895-3906.

Ye ZS, Chen N. Closed-form estimators for the gamma distribution derived from likelihood equations. The American Statistician. 2017;71(2):177-181.

Al-Fawzan MA. Methods for estimating the parameters of the Weibull distribution. King Abdulaziz City for Science and Technology, Saudi Arabia; 2000.

Angadi AB, Angadi AB, Gull KC. International Journal of Advanced Research in Computer Science and Software Engineering. 2013;3(6).

Calderon Vela A, Rodríguez G. Extreme value theory: An application to the Peruvian stock market returns; 2014.

Chen M, Zhang Z, Cui C. On the bias of the maximum likelihood estimators of parameters of the Weibull distribution. Mathematical and Computational Applications. 2017;22(1):19.

Kwaśnicka H, Ciosmak M. Intelligen techniques in stock analysis. In Intelligent Information Systems. Physica, Heidelberg. 2001;195-208.

Hosking JR, Wallis JR. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics. 1987;29(3):339-349.

Ilie N, Hickel R. Macro-, micro-and nano-mechanical investigations on silorane and methacrylate-based composites. Dental Materials. 2009;25(6):810-819.

Nadarajah S, Kotz S. The beta Gumbel distribution. Mathematical Problems in Engineering. 2004;4:323-332.

Lazoglou G, Anagnostopoulou C. An overview of statistical methods for studying the extreme rainfalls in Mediterranean. In Multidisciplinary Digital Publishing Institute Proceedings. 2017;1(5):681.