W-Peakedness: A Simulation based Study

Suboohi Safdar, Dr. Ejaz Ahmed


Kurtosis is a commonly used descriptive statistics. Kurtosis “Coefficient of excess” is critically reviewed in different aspects and is called as, measuring the fatness of the tails of the density functions, concentration towards the central value, scattering away from the target point or degree of peakedness of probability distribution. Kurtosis is referred to the shape of the distribution but many distributions having same kurtosis value may have different shapes while Kurtosis may exist when peak of a distribution is not in existence. Through extensive study of kurtosis on several distributions, Wu (2002) introduced a new measure called “W-Peakedness” that offers a fine capture of distribution shape to provide an intuitive measure of peakedness of the distribution which is inversely proportional to the standard deviation of the distribution. In this paper the work is extended for different others continuous probability distributions. Empirical results through simulation illustrate the proposed method to evaluate kurtosis by W-peakedness

Full Text:



Ahmed, S. A., Haq M and Khursheed A (1990), “Measure of peakedness in Pareto model”, The Philippine Statistician, 39, 61-70

Blanda, K.P. (1987), “Kurtosis comparison of the Cauchy and double exponential distribution”, Communication in Statistics- Theory and methods, 16, 579-592

Balanda, K. P. and MacGillivary, H. L. (1990). “Kurtosis and spread”, The Canadian Journal of Statistics, 18, 17-30.

Blest, D. C. (2003). “A new measure of kurtosis adjusted for skewness”, Australian and New Zealand Journal of Statistics, 45, 175-179.

Dane, W.Wu (USA) (2002). “Some Study of kurtosis: A new measure of peakedness for distribution”, Advances and applications in Statisticsvol.2(2)(2002),pp, 131-137

DeCarlo, L. T. (1997). “On the meaning and use of kurtosis”, Psychlogical Methods, 2, 292-307.

Groeneveld, R. A. and Meeden, G. L. (1984). “Measuring skewness and Kurtosis”, the Statistician, 33, 391-399.

Haq, M., Khurshid, A. and Ahmed, S. A. (1991). “Peakedness in Distributions with no moments”, Journal of Indian Society of Statistics and Operations Research, 12, 5-14.

Hopkins, K. D. and Weeks, D. L. (1990). “Tests for normality and Measures of skewness and kurtosis: Their place in research reporting”, Educational and Psychological Measurement, 50, 717-729.

Sahai, H. and Khurshid, A. (2002). Pocket dictionary of statistics. McGraw- Hill: New York.

Schmid, F. and Trede, M. (2003). “Simple Tests for peakedness, fat tails and leptokurtosis based on quantiles”, Computational Statistics and Data Analysis, 43, 1-12.

Wu, D. W. (2002). “Some study of kurtosis: A new measure of Peakedness for distribution”, Advances and Application in Statistics, 2, 131-137.

Chissom, Brad. S. (1970), “Interpretation of The

Balanda, K.P. And MacGillivay, H.L. (1987). Kurtosis: A Critical Review. Journal of the American Statistician 42, 119-119, May.

Wu, D.W. (1999) “Estimation of Multimodal Densities,” Proceedings of the Mathematical Modeling Symposium, 221-229.

DOI: http://dx.doi.org/10.22555/pjets.v1i1.135


  • There are currently no refbacks.

Chief Editor

Prof. Dr. Ejaz Ahmed 
College of Computer Science & Information Systems


Prof Dr. S. M. Aqil Burney

Associate Editors

Prof. Dr. Tariq Rahim Soomro
Dr. Muhammad Mansoor Aalam

Publication Coordinator
Konpal Darakshan

Editorial Advisory Board (Internal)

Dr. Syed Irfan Hyder
Dr. Mohammad Irshad Khan
Dr. Shahid Amjad
Dr. Abdul Rauf Farooqui
Dr. Syed Iftikhar Ali
Dr. Tajuddin Islamuddin
Dr. Muhammad Danish Khan
Dr. Imran Majid
Dr. Fatima Riaz
Dr. Zeeshan Shahid
Ms. Seema Ansari

Editorial Advisory Board (International)

Prof. Dr. Mazliham Mohd Su'ud, President, Universiti Kuala Lumpur, Malaysia
Prof. Dr. Ghassan Al-Qaimari, President, Emirates College of Technology, Abu Dhabi, UAE
Prof. Dr. Patrice Boursier, Universite de La Rochelle, La Rochelle, France
Prof. Dr. Mudassir Uddin, Professor, University of Karachi, Pakistan
Dr. Nadeem Doudpota, Associate Professor, Al-Baha University, KSA
Dr. Haithem Abdelrazaq Almefleh, Associate Professor, Yarmouk University, Yarmouk, Jordan
Dr. Saiful Islam Ansari, Assistant Professor, University of Tabuk, Saudi Arabia

Member Editorial Review Board (International – Academia)

Dr. Asadaullah Shah, Professor, International Islamic University, MalaysiaDr. Hasan Wahba, President American College of Dubai, United Arab Emirates (UAE)
Dr. Tahseen Jilani, Assistant Professor, University of Manchester, UKDr. Atif Memon, Associate Professor, The University of Maryland, USA
Dr. Syed Waliullah Shah, University Sains, MalaysiaDr. Inayatullah Shah, International Islamic University, (Kuantam), Malaysia
Dr. Salahttin Kuru, Kemeburgaz University, TurkeyDr. Soon Min, INTI International University, Malaysia
Dr. Shahrulniza Musa, Professor, Malaysian France Institute, Universiti Kuala Lumpur, Bandar Baru Bangi, MalaysiaDr. R. Praveen Sam, Professor, Department of Computer Science and Engineering, G. Pulla Reddy Engineering College, KURNOOL, India
Dr. Manzoor Ahmed Hashmani, Associate Professor, University Technology Petronas, MalaysiaDr. Alveera Mehdi, Professor, Aligarh Muslim University, Aligarh, India

Dr. Sajjad Waheed, Professor, Department of Information and Communication Technology, Mawlana Bhashani Science and Technology University, Tangail 1902, Bangladesh

Dr. Kushairy Bin Abdul Kadir, Associate Professor, British Malaysian Institute, Universiti Kuala Lumpur, Gombak, Malaysia
Dr. Mohammad Hameed Ahmed AlTaei, Assistant Professor, Applied Sciences College, Sohar, OmanDr. Eiad Yafi, Associate Professor, Malaysian Institute of Information Technology Universiti, Malaysia
Dr. Muhammad Azam Sheikh, Assistant Professor, Chalmers University, SwedenDr. Safeeullah Soomro, Postdoc Dean College of Computer Studies, AMA Int. University, Bahrian
Dr. Aymen Adil Belghith, Assistant Professor, University of Sfax, Sfax,TunisiaDr. Radwan Alsadiq Alqirmazi, Assistant Professor, University of Sfax, Sfax,Tunisia
Dr. Mohammad Arif Amin, Assistant Professor, Higher College of Technology, Abu Dhabi Men’s College, Abu Dhabi, United Arab Emirates (UAE)Dr. Ismat Aldmour, Assistant Professor, Al-Baha University, Kingdom of Saudi Arabia (KSA)
Dr. AbdulRahman Ahmed Mohammed Al-Sewari, Senior Lecturer, Universiti Malaysia Pahang, Pahang, MalaysiaDr. Mohammed A. Afifi, Director, Associate of Science in Computer Science, Al Dar University College, Dubai, United Arab Emirates (UAE)
Dr. Youssef Ahmed Masmoudi, Assistant Professor, Saudi Electronic University, Jeddah male Campus, Kingdom of Saudi Arabia (KSA)Dr. Zulfiqar Memon, Assistant Professor, Ajman University of Science & Technology, Ajman, United Arab Emirates (UAE)
Dr. Abdul Basit Samsuddin Banga, Assistant Professor, Saudi Electronic University, Jeddah male Campus, Kingdom of S. Arabia (KSA)Dr. Mohamad Ismail Sulaiman, Senior Lecturer, British Malaysian Institute, Universiti Kuala Lumpur, Gombak, Malaysia
Dr. Syed Faiz Ahmed, Senior Lecturer, British Malaysian Institute, Universiti Kuala Lumpur, Gombak, Malaysia

Dr. Jawad Ali Shah, Senior Lecturer, British Malaysian Institute, Universiti Kuala Lumpur, Gombak, Malaysia

Dr. Sarfraz Nawaz Brohi, Lecturer, Taylor’s Unversity, Lakeside Campus, Malaysia

Dr. Fahad Sikander, Assistant Professor, Saudi Electronic University, Kingdom of Saudi Arabia (KSA)

Member Editorial Review Board (International – Non Academia)

Dr. Abdul Razaque Memon, Director Solution Marketing at Huawei Technology, AustraliaDr. Syed Abbas, Project Director, NetSys Technical Services, Business Bay, Duabi, United Arab Emirates (UAE)
Dr. Muntasser Khater, Educational Senior Consultant, CAN DU e-Business, Dubai, United Arab Emirates (UAE) 

Member Editorial Review Board (National – Academia)

Dr. Madad Ali Shah, Professor and Vice Chancellor, BBS University of Technology & Skill Development, KhairpurDr. B. S. Chaudhry, Professor, Mehran University of Engineering & Technology (MUET), Jamshoro
Dr. Mir Ghulam Hyder Talpur, Professor, University of Sindh, JamshoroDr. Imdad Ismaili, Professor, University of Sindh, Jamshoro
Dr. Syed Asif Ali, Professor, Sindh Maderessah Tul Islam University, KarachiDr. Mukhtiar Ali Unar, Professor, Mehran University of Engineering & Technology (MUET), Jamshoro
Dr. Syed Amir Iqbal, Associate Professor, NED University, KarachiDr. Syed Haider Shah, Associate Professor, Univeristy of Balochistan, Quetta
Dr. Talal Shrafat Rehmani, NUST, KarachiLt. Cdr. Dr. Asif Mansoor, NUST, Karachi
Dr. Faisal Maqbool Zahid, Associate Professor, University of Faisalabad 

Member Editorial Review Board (National – Non Academia)

Dr. Amir Khan, Ministry of Defense, Govt. of Pakistan, KarachiDr. Bahrawar Jan, Pakistan Bureau of Statistics, Islamabad