{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T16:37:27Z","timestamp":1769186247249,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T00:00:00Z","timestamp":1639094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSP-2021\/363"],"award-info":[{"award-number":["RSP-2021\/363"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The inverted Topp\u2013Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp\u2013Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp\u2013Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress\u2013strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress\u2013strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.<\/jats:p>","DOI":"10.3390\/e23121662","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T08:17:58Z","timestamp":1639124278000},"page":"1662","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Reliability Analysis of the New Exponential Inverted Topp\u2013Leone Distribution with Applications"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8234-9545","authenticated-orcid":false,"given":"Ahmed Sayed M.","family":"Metwally","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4442-8458","authenticated-orcid":false,"given":"Amal S.","family":"Hassan","sequence":"additional","affiliation":[{"name":"Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-1275","authenticated-orcid":false,"given":"Ehab M.","family":"Almetwally","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6073-1978","authenticated-orcid":false,"given":"B M Golam","family":"Kibria","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Florida International University (FIU), 11200 SW 8th St, Miami, FL 33199, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6821-4406","authenticated-orcid":false,"given":"Hisham M.","family":"Almongy","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, El-Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1316345","DOI":"10.1155\/2020\/1316345","article-title":"A new lifetime exponential-X family of distributions with applications to reliability data","volume":"2020","author":"Huo","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_2","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_3","first-page":"37","article-title":"Inverted Kumumaraswamy distribution: Properties and estimation","volume":"33","year":"2017","journal-title":"Pak. J. Stat."},{"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","doi-asserted-by":"crossref","first-page":"587","DOI":"10.18187\/pjsor.v15i3.2378","article-title":"Weibull inverse Lomax distribution","volume":"15","author":"Hassan","year":"2019","journal-title":"Pak. J. Stat. Oper. Res."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"1370","DOI":"10.35378\/gujs.452885","article-title":"Parameter estimation of inverse exponentiated Lomax with right censored data","volume":"32","author":"Hassan","year":"2019","journal-title":"Gazi Univ. J. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5","DOI":"10.18576\/msl\/100102","article-title":"Extended odd Weibull inverse Rayleigh distribution with application on carbon fibres","volume":"10","author":"Almetwally","year":"2021","journal-title":"Math. Sci. Lett."},{"key":"ref_9","first-page":"99","article-title":"Parameter estimation of an extended inverse power Lomax distribution with Type I right censored data","volume":"28","author":"Hassan","year":"2021","journal-title":"Commun. Stat. Appl. Methods"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"319","DOI":"10.18576\/jsap\/090212","article-title":"Statistical properties and estimation of inverted Topp\u2013Leone distribution","volume":"9","author":"Hassan","year":"2020","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_11","first-page":"991","article-title":"Power inverted Topp\u2013Leone distribution in acceptance sampling plans","volume":"67","author":"Abushal","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_12","first-page":"337","article-title":"Kumaraswamy inverted Topp\u2013Leone distribution with applications to COVID-19 data","volume":"68","author":"Hassan","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"353","DOI":"10.32604\/iasc.2021.017586","article-title":"Parameter estimation of alpha power inverted Topp\u2013Leone distribution with applications","volume":"29","author":"Ibrahim","year":"2021","journal-title":"Intell. Autom. Soft Comput."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Almetwally, E.M., Alharbi, R., Alnagar, D., and Hafez, E.H. (2021). A new inverted Topp\u2013Leone distribution: Applications to the COVID-19 mortality rate in two different countries. Axioms, 10.","DOI":"10.3390\/axioms10010025"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Almetwally, E.M. (2021). The odd Weibull inverse Topp\u2013Leone distribution with applications to COVID-19 data. Ann. Data Sci., 1\u201320.","DOI":"10.1007\/s40745-021-00329-w"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Bantan, R.A., Jamal, F., Chesneau, C., and Elgarhy, M. (2020). Type II power Topp\u2013Leone generated family of distributions with statistical inference and applications. Symmetry, 12.","DOI":"10.3390\/sym12010075"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4227346","DOI":"10.1155\/2021\/4227346","article-title":"Stressstrength reliability for exponentiated invertedWeibull distribution with application on breaking of jute fiber and carbon fibers","volume":"2021","author":"Almetwally","year":"2021","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9770","DOI":"10.3934\/math.2021568","article-title":"Inference of fuzzy reliability model for inverse Rayleigh distribution","volume":"6","author":"Sabry","year":"2021","journal-title":"AIMS Math."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Yousef, M.M., and Almetwally, E.M. (2021). Multi stress-strength reliability based on progressive first failure for Kumaraswamy model: Bayesian and non-Bayesian estimation. Symmetry, 13.","DOI":"10.3390\/sym13112120"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1007\/s40995-020-01033-9","article-title":"Stress\u2013strength reliability for the generalized inverted exponential distribution using MRSS","volume":"45","author":"Hassan","year":"2021","journal-title":"Iran. J. Sci. Technol. Trans. A Sci."},{"key":"ref_21","first-page":"21","article-title":"Marshall-Olkin generalized Pareto distribution: Bayesian and non Bayesian estimation","volume":"16","author":"Almetwally","year":"2020","journal-title":"Pak. J. Stat. Oper. Res."},{"key":"ref_22","first-page":"327","article-title":"Marshall-Olkin alpha power inverse Weibull distribution: Non Bayesian and Bayesian Estimations","volume":"10","author":"Basheer","year":"2020","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_23","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"},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"124251","DOI":"10.1016\/j.physa.2020.124251","article-title":"Progressive type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution","volume":"553","author":"Almetwally","year":"2020","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"El-Sherpieny, E.S.A., Almetwally, E.M., and Muhammed, H.Z. (2021). Bayesian and non-Bayesian estimation for the parameter of bivariate generalized Rayleigh distribution based on Clayton Copula under progressive type-II censoring with random removal. Sankhya A, 1\u201338.","DOI":"10.1007\/s13171-021-00254-3"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Almongy, H.M., Alshenawy, F.Y., Almetwally, E.M., and Abdo, D.A. (2021). Applying transformer insulation using Weibull extended distribution based on progressive censoring scheme. Axioms, 10.","DOI":"10.3390\/axioms10020100"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Haj Ahmad, H., Salah, M.M., Eliwa, M.S., Ali Alhussain, Z., Almetwally, E.M., and Ahmed, E.A. (2021). Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power Lindley distribution. J. Appl. Stat., 1\u201321.","DOI":"10.1080\/02664763.2021.1931819"},{"key":"ref_29","first-page":"2859","article-title":"Bayesian analysis in partially accelerated life tests for weighted Lomax distribution","volume":"68","author":"Bantan","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_30","first-page":"3795","article-title":"Entropy Bayesian analysis for the generalized inverse exponential distribution based on URRSS","volume":"69","author":"Hassan","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3889","DOI":"10.3934\/math.2021231","article-title":"Dynamic cumulative residual R\u00e9nyi entropy for Lomax distribution: Bayesian and non-Bayesian methods","volume":"6","author":"Hassan","year":"2021","journal-title":"AIM Math."},{"key":"ref_32","first-page":"96","article-title":"Entropy Bayesian estimation for Lomax distribution based on record","volume":"19","author":"Hassan","year":"2021","journal-title":"Thail. Stat."},{"key":"ref_33","first-page":"130","article-title":"Acquisition of resistance in guinea pies infected with different doses of virulent tubercle bacilli","volume":"72","author":"Bjerkedal","year":"1960","journal-title":"Am. J. Hyg."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Nelson, W. (1982). Applied Life Data Analysis, John Wiley & Sons.","DOI":"10.1002\/0471725234"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/12\/1662\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:44:42Z","timestamp":1760168682000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/12\/1662"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,10]]},"references-count":34,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["e23121662"],"URL":"https:\/\/doi.org\/10.3390\/e23121662","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,10]]}}}