Statistical Inferences on Odd Fréchet Power Function Distribution

  • Muhammad Ahsan ul Haq College of Statistical & Actuarial Sciences, University of the Punjab, Pakistan; Quality Enhancement Cell, National College of Arts, Pakistan
  • Mohammed Albassam Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia
  • Muhammad Aslam Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia
  • Sharqa Hashmi Lahore College for Women University, Lahore Pakistan
Keywords: OFr-G family, power function distribution, entropy, estimation methods, data analysis

Abstract

This article introduces a new unit distribution namely odd Fréchet power (OFrPF) distribution. Numerous properties of the proposed model including reliability analysis, moments, and Rényi Entropy for the proposed distribution. The parameters of the OFrPF distribution are obtained using different approaches such as maximum likelihood, least squares, weighted least squares, percentile, Cramer-von Mises, Anderson-Darling. Furthermore, a simulation was performed to study the performance of the suggested model. We also perform a simulation study to analyze the performances of estimation methods derived. The applications are used to show the practicality of OFrPF distribution using two real data sets. OFrPF distribution performed better than other competitive models.

Downloads

Download data is not yet available.

Author Biographies

Muhammad Ahsan ul Haq, College of Statistical & Actuarial Sciences, University of the Punjab, Pakistan; Quality Enhancement Cell, National College of Arts, Pakistan

Muhammad Ahsan ul Haq received his MPhil degree in Statistics from the College of Statistical and Actuarial Sciences, University of the Punjab, Lahore, Pakistan. Also, he is a PhD Research Scholar at University of the Punjab, Pakistan. He is doing PhD Under the supervision of Dr. Ahmed Zogo Memon and Dr. Sohail Chand. His research interests include Mathematical and Applied Statistics, Distribution Theory, reliability analysis, and mixture distributions.

Mohammed Albassam, Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia

Mohammed Albassam received his B.Sc. degree from Mathematics department at King Abdulaziz University in 1990, M.Sc. and Ph.D. degrees from School of Mathematics and Statistics at University of Sheffield, UK, in 1995 and 2000. He is currently working as an Associate Professor at Statistics department in King Abdulaziz University. He has published many articles in International journals. His fields of interest are Statistical inference, Distributions theory, Neutrosophic Statistics and Time series Analysis.

Muhammad Aslam, Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia

Muhammad Aslam did his M.Sc in Statistics (2004) from GC University Lahore with Chief Minister of the Punjab merit scholarship, M. Phil in Statistics (2006) from GC University Lahore with the Governor of the Punjab merit scholarship, and Ph.D. in Statistics (2010) from National College of Business Administration & Economics Lahore under the kind supervision of Prof. Dr. Munir Ahmad. He worked as a lecturer of Statistics in Edge College System International from 2003–2006. He also worked as a Research Assistant in the Department of Statistics, GC University Lahore from 2006 to 2008. Then he joined the Forman Christian College University as a lecturer in August 2009. He was a part of visiting faculty member, Department of Statistics, GC University Lahore from 2009 to 2014. He worked as Assistant Professor in the same University from June 2010 to April 2012. He worked in the same department as Associate Professor from June 2012 to October 2014. He worked as Associate Professor of Statistics in the Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia from October 2014 to March 2017. He taught summer courses as Visiting Faculty of Statistics at Beijing Jiaotong University, China in 2016. Currently, he is working as a Full Professor of Statistics in the department of Statistics, King Abdul-Aziz University Jeddah, and Saudi Arabia. He has published more than 437 research papers in national and international well-reputed journals including, for example, IEEE Access, Journal of Applied Statistics, European Journal of Operation Research, Information Sciences, Journal of Process Control, Journal of the Operational Research Society, Applied Mathematical Modeling, International Journal of Fuzzy Systems, Complexity, ACS Ogema, Symmetry, International Journal of Advanced Manufacturer Technology, Communications in Statistics, Journal of Testing and Evaluation and Pakistan Journal of Statistics etc. His papers have been cited more than 4400 times with h-index 33 and i-10 index 114 (Google Scholar). His papers have been cited more than 2700 times with h-index 25 (Web of Science Citations). He is the author of three books published by VDM, Germany, Springer and Wiley, respectively. He has published 10 chapters in well-reputed books. He is also HEC approved PhD supervisor since 2011. He supervised 5 PhD theses, more than 25 M.Phil theses and 3 M.Sc. theses. Dr. Muhammad Aslam is currently supervising 2 Master theses in Statistics. He is a reviewer of more than 70 well-reputed international journals. He has reviewed more than 160 research papers for various well-reputed international journals. He received meritorious services award in research from National College of Business Administration & Economics Lahore in 2011. He received Research Productivity Award for the year 2012 by Pakistan Council for Science and Technology. His name Listed at 2nd Position among Statistician in the Directory of Productivity Scientists of Pakistan 2013. His name Listed at 1st Position among Statistician in the Directory of Productivity Scientists of Pakistan 2014. He got 371 positions in the list of top 2210 profiles of Scientist of Saudi Institutions 2016. He Received King Abdulaziz University Excellence Awards in Scientific Research for the paper entitled “Aslam, M., Azam, M., Khan, N. and Jun, C.-H. (2015). A New Mixed Control Chart to Monitor the Process, International Journal of Production Research, 53 (15), 4684–4693. He Received King Abdulaziz University citation award for the paper entitled “Azam, M., Aslam, M. and Jun, C.-H. (2015). Designing of a hybrid exponentially weighted moving average control chart using repetitive sampling, International Journal of Advanced Manufacturing Technology, 77:1927–1933 in 2018. Prof. Muhammad Aslam is listed in, top 2% of scientists of the world in the list released by Stanford University, USA. He is at rank 35/93 among the King Abdulaziz University Scientist.

Prof. Muhammad Aslam introduced the area of Neutrosophic Statistical Quality Control (NSQC) the first time. He is the founder of neutrosophic inferential statistics (NIS) and NSQC. His contribution is the development of neutrosophic statistics theory for the inspection, inference, and process control. He originally developed the theory in these areas under the Neutrosophic Statistics. He extended the Classical Statistics theory to Neutrosophic Statistics originally in 2018.

He is the member of the editorial board of Electronic Journal of Applied Statistical Analysis, Neutrosophic Sets and Systems, Pakistan Journal of Commence and Social sciences and International Journal of Neutrosophic Science. He is also a member of the Islamic Countries Society of Statistical Sciences. He is appointed as an external examiner for 2016/2017–2018/2019 triennium at The University of Dodoma, Tanzania. His areas of interest include Industrial Statistics, neutrosophic inferential statistics, neutrosophic statistics, neutrosophic quality control, neutrosophic applied statistics, and classical applied Statistics.

Sharqa Hashmi, Lahore College for Women University, Lahore Pakistan

Sharqa Hashmi completed her PhD from University of the Punjab, Pakistan. She did her research work under the supervisor is Prof. Dr. Ahmed Zogo Memon. She got first position (Gold Medal) in the M.Sc (Statistics) in 1996 from University of the Punjab, Pakistan. She received her B.Sc. in Statistics from the same University. Her research interests include mathematical statistics, probability distributions, and distribution theory. She worked as a lecturer in department of statistics, Lahore College for Women University (LCWU), Lahore, Pakistan from 1999 to 2011. She has been working an Assistant Professor of Statistics in same university since 2011. She also won foreign PhD Scholarship under faculty development program of LCWU, in 2007 and got admission in UK and Australia but unable to join due to some family issues.

She conducted a five day workshop as resource person titled “Data Visualization and Optimization of Generalized Models through Mathematica” from 24th

Feb, 2020 to 28th Feb., 2020 at LCWU, Lahore, Pakistan. She also conducted a two day workshop as resource person titled “Statistical tools in Pharmacy” from 20–21 Feb, 2020. She worked as Technical Advisor in six days workshop titled “TIDYVERSE FOR DATA SCIENCE” from 15th July, 2019 to 20th July, 2019 at Bureau of Statistics, Lahore. Also worked as Co-instructor in six days workshop titled “TIDYVERSE FOR DATA SCIENCE” from 29th July, 2019 to 3rd August, 2019 at Bureau of Statistics, Lahore and many online workshops during COVID.19.

Published
2021-04-07
Section
Articles