{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T07:40:41Z","timestamp":1781163641174,"version":"3.54.1"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T00:00:00Z","timestamp":1614297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame\u00b4r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.<\/jats:p>","DOI":"10.3390\/axioms10010025","type":"journal-article","created":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T04:36:24Z","timestamp":1614314184000},"page":"25","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":65,"title":["A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-1275","authenticated-orcid":false,"given":"Ehab","family":"Almetwally","sequence":"first","affiliation":[{"name":"Faculty of Business Administration, Delta University of Science and Technology, El-Mansoura 11152, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6698-4933","authenticated-orcid":false,"given":"Randa","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Tabuk, Tabuk 71491, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0196-2490","authenticated-orcid":false,"given":"Dalia","family":"Alnagar","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Tabuk, Tabuk 71491, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2527-5938","authenticated-orcid":false,"given":"Eslam","family":"Hafez","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Helwan University, Helwan 11795, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,26]]},"reference":[{"key":"ref_1","first-page":"26","article-title":"On a fractional beta- distribution","volume":"26","author":"Anake","year":"2015","journal-title":"Int. J. Math. Comput."},{"key":"ref_2","first-page":"37","article-title":"Inverted Kumaraswamy Distribution: Properties and Estimation","volume":"33","year":"2017","journal-title":"Pak. J. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6308","DOI":"10.1080\/03610918.2016.1202274","article-title":"The inverse power Lindley distribution","volume":"46","author":"Barco","year":"2017","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s40745-018-0183-y","article-title":"On the inverse power Lomax distribution","volume":"6","author":"Hassan","year":"2019","journal-title":"Ann. Data Sci."},{"key":"ref_5","first-page":"17","article-title":"On the inverted Topp Leone distribution","volume":"20","author":"Muhammed","year":"2019","journal-title":"Int. J. Reliab. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42519-020-00116-5","article-title":"The inverted modified Lindley distribution","volume":"14","author":"Chesneau","year":"2020","journal-title":"J. Stat. Theory Pract."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.jksus.2018.05.021","article-title":"The Marshall-Olkin extended inverted Kumaraswamy distribution: Theory and applications","volume":"32","author":"Usman","year":"2020","journal-title":"J. King Saud Univ.-Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"265","DOI":"10.35378\/gujs.537832","article-title":"Theoretical Analysis of the Weibull Alpha Power Inverted Exponential Distribution: Properties and Applications","volume":"33","author":"Eferhonore","year":"2020","journal-title":"Gazi Univ. J. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s40745-020-00289-7","article-title":"Monitoring Novel Corona Virus (COVID-19) Infections in India by Cluster Analysis","volume":"7","author":"Kumar","year":"2020","journal-title":"Ann. Data Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40745-020-00314-9","article-title":"Outbreak Prediction of COVID-19 for Dense and Populated Countries Using Machine Learning","volume":"8","author":"Khakharia","year":"2020","journal-title":"Ann. Data Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, Y.z.J. (2020). A call for caution in extrapolating chest CT sensitivity for COVID-19 derived from hospital data to patients among general population. Quant. Imaging Med. Surg., 10.","DOI":"10.21037\/qims.2020.03.04"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lalmuanawma, S., Hussain, J., and Chhakchhuak, L. (2020). Applications of machine learning and artificial intelligence for Covid-19 (SARS-CoV-2) pandemic: A review. Chaos Solitons Fractals, 139.","DOI":"10.1016\/j.chaos.2020.110059"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bullock, J., Pham, K.H., Lam, C.S.N., and Luengo-Oroz, M. (2020). Mapping the landscape of artificial intelligence applications against COVID-19. arXiv.","DOI":"10.1613\/jair.1.12162"},{"key":"ref_14","unstructured":"Hassan, A.S., Elgarhy, M., and Ragab, R. (2020). Statistical Properties and Estimation of Inverted Topp-Leone Distribution. J. Stat. Appl. Probab., forthcoming."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8778","DOI":"10.1080\/03610926.2016.1193199","article-title":"The exponentiated reduced Kies distribution: Properties and applications","volume":"46","author":"Kumar","year":"2017","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_16","first-page":"332","article-title":"Moments and estimation of reduced Kies distribution based on progressive type-II right censored order statistics","volume":"48","author":"Dey","year":"2019","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Al-Babtain, A.A., Shakhatreh, M.K., Nassar, M., and Afify, A.Z. (2020). A New Modified Kies Family: Properties, Estimation Under Complete and type-II Censored Samples, and Engineering Applications. Mathematics, 8.","DOI":"10.3390\/math8081345"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Muhammed, H.Z., and Almetwally, E.M. (2020). Bayesian and Non-Bayesian Estimation for the Bivariate Inverse Weibull Distribution Under Progressive Type-II Censoring. Ann. Data Sci.","DOI":"10.1007\/s40745-020-00316-7"},{"key":"ref_19","first-page":"1","article-title":"On a bivariate Fr\u00e9chet distribution","volume":"9","author":"Almetwally","year":"2020","journal-title":"J. Stat Appl Probab."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"El-Morshedy, M., Alhussain, Z.A., Atta, D., Almetwally, E.M., and Eliwa, M.S. (2020). Bivariate Burr X generator of distributions: Properties and estimation methods with applications to complete and type-II censored samples. Mathematics., 8.","DOI":"10.3390\/math8020264"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1007\/s40745-020-00293-x","article-title":"Copula Approach for Developing a Biomarker Panel for Prediction of Dengue Hemorrhagic Fever","volume":"7","author":"Kim","year":"2020","journal-title":"Ann. Data Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s40745-020-00261-5","article-title":"Maximum Product Spacing Estimation of Weibull Distribution Under Adaptive Type-II Progressive Censoring Schemes","volume":"7","author":"Almetwally","year":"2020","journal-title":"Ann. Data Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1007\/s40745-020-00310-z","article-title":"Bayesian Estimation of Transmuted Pareto Distribution for Complete and Censored Data","volume":"7","author":"Aslam","year":"2020","journal-title":"Ann. Data Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1111\/j.2517-6161.1983.tb01268.x","article-title":"Estimating parameters in continuous univariate distributions with a shifted origin","volume":"45","author":"Cheng","year":"1983","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_25","first-page":"219","article-title":"Maximum product spacings method for the estimation of parameters of generalized inverted exponential distribution under Progressive Type II Censoring","volume":"19","author":"Singh","year":"2016","journal-title":"J. Stat. Manag. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"407","DOI":"10.6339\/JDS.201904_17(2).0010","article-title":"Maximum product spacing and Bayesian method for parameter estimation for generalized power Weibull distribution under censoring scheme","volume":"17","author":"Almetwally","year":"2019","journal-title":"J. Data Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1007\/s11009-018-9676-6","article-title":"Estimation of Inverse Lindley Distribution Using Product of Spacings Function for Hybrid Censored Data","volume":"21","author":"Basu","year":"2019","journal-title":"Methodol. Comput. Appl. Probab."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"802","DOI":"10.6339\/JDS.201910_17(4).0010","article-title":"Adaptive type-II progressive censoring schemes based on maximum product spacing with application of generalized Rayleigh distribution","volume":"17","author":"Almetwally","year":"2019","journal-title":"J. Data Sci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"El-Sherpieny, E.S.A., Almetwally, E.M., and Muhammed, H.Z. (2020). Progressive Type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution. Phys. A Stat. Mech. Its Appl., 553.","DOI":"10.1016\/j.physa.2020.124251"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Alshenawy, R., Al-Alwan, A., Almetwally, E.M., Afify, A.Z., and Almongy, H.M. (2020). Progressive Type-II Censoring Schemes of Extended Odd Weibull Exponential Distribution with Applications in Medicine and Engineering. Mathematics, 8.","DOI":"10.3390\/math8101679"},{"key":"ref_31","first-page":"2973","article-title":"Product Spacing of Stress\u2013Strength under Progressive Hybrid Censored for Exponentiated-Gumbel Distribution","volume":"66","author":"Alshenawy","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1016\/j.csda.2005.09.011","article-title":"Fitting the generalized Pareto distribution to data using maximum goodness of fit estimators","volume":"51","author":"Luceno","year":"2006","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1093\/biomet\/84.3.641","article-title":"A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families","volume":"84","author":"Marshall","year":"1997","journal-title":"Biometrika"},{"key":"ref_34","first-page":"90","article-title":"Transmuted Inverse Rayleigh distribution: A generalization of the Inverse Rayleigh distribution","volume":"4","author":"Ahmad","year":"2014","journal-title":"Math. Theory Model."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/1\/25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:29:05Z","timestamp":1760160545000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/1\/25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,26]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["axioms10010025"],"URL":"https:\/\/doi.org\/10.3390\/axioms10010025","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,26]]}}}