{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:27:36Z","timestamp":1771673256549,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T00:00:00Z","timestamp":1712793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Semillero UA-2024"},{"name":"IOAP of University of Seville, Spain"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper presents the Slash-Exponential-Fr\u00e9chet distribution, which is an expanded version of the Fr\u00e9chet distribution. Through its stochastic representation, probability distribution function, moments and other relevant features are obtained. Evidence supports that the updated model displays a lighter right tail than the Fr\u00e9chet model and is more flexible as for skewness and kurtosis. Results on maximum likelihood estimators are given. Our proposition\u2019s applicability is demonstrated through a simulation study and the evaluation of two real-world datasets.<\/jats:p>","DOI":"10.3390\/axioms13040253","type":"journal-article","created":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T07:09:28Z","timestamp":1712819368000},"page":"253","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Extension of the Fr\u00e9chet Distribution and Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8092-9666","authenticated-orcid":false,"given":"Yolanda M.","family":"G\u00f3mez","sequence":"first","affiliation":[{"name":"Departamento de Estad\u00edstica, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n 4081112, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9064-2597","authenticated-orcid":false,"given":"Inmaculada","family":"Barranco-Chamorro","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Facultad de Matem\u00e1ticas, Universidad de Sevilla, 41012 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-5247-8308","authenticated-orcid":false,"given":"Jaime S.","family":"Castillo","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica y Ciencias de Datos, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3726-5507","authenticated-orcid":false,"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica y Ciencias de Datos, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,11]]},"reference":[{"key":"ref_1","first-page":"93","article-title":"Sur la loi de probabilit\u00e9 de l\u2019\u00e9cart maximum","volume":"6","year":"1927","journal-title":"Ann. Soc. Polon. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1017\/S0305004100015681","article-title":"Limiting forms of the frequency distribution of the largest and smallest member of a sample","volume":"24","author":"Fisher","year":"1928","journal-title":"Proc. Camb. Philos. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gumbel, E.J. (1958). Statistics of Extremes, Columbia University Press.","DOI":"10.7312\/gumb92958"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Embrechts, P., Kl\u00fcppelberg, C., and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer.","DOI":"10.1007\/978-3-642-33483-2"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Resnick, S.I. (1987). Extreme Values, Regular Variation and Point Processes, Springer.","DOI":"10.1007\/978-0-387-75953-1"},{"key":"ref_6","unstructured":"Haan, L., and Ferreira, A. (2007). Extreme Value Theory: An Introduction, Springer."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kotz, S., and Nadarajah, S. (2000). Extreme Value Distributions: Theory and Applications, Imperial College Press.","DOI":"10.1142\/9781860944024"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1080\/03610929808832134","article-title":"Modeling failure time data by Lehman alternatives","volume":"27","author":"Gupta","year":"1998","journal-title":"Commun. Stat. Methods"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values, Springer.","DOI":"10.1007\/978-1-4471-3675-0"},{"key":"ref_10","first-page":"549","article-title":"The Fr\u00e9chet distribution: Estimation and application\u2014An overview","volume":"23","author":"Ramos","year":"2020","journal-title":"J. Stat. Manag. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0951-8320(89)90056-2","article-title":"Confidence limits for reliability and tolerance limits in the inverse Weibull distribution","volume":"24","author":"Calabria","year":"1989","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1080\/0094965031000099140","article-title":"Conditional confidence interval estimation for the inverse Weibull distribution based on censored generalized order statistics","volume":"73","author":"Maswadah","year":"2003","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_13","first-page":"389","article-title":"Order statistics from inverse Weibull distribution and characterizations","volume":"61","author":"Salman","year":"2003","journal-title":"Metron"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2945","DOI":"10.1080\/03610926.2013.802351","article-title":"Analysis of Fr\u00e9chet distribution using reference priors","volume":"44","author":"Abbas","year":"2015","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_15","first-page":"38","article-title":"Slash Exponential Distribution: Theory and Applications","volume":"8","author":"Punathumparambath","year":"2020","journal-title":"Bull. Math. Stat. Res."},{"key":"ref_16","unstructured":"Abramowitz, M., and Stegun, I.A. (1968). National Bureau of Standards Applied Mathematics Series 55, United State Department of Commerce."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1111\/1467-842X.00072","article-title":"Generalized Exponential Distributions","volume":"41","author":"Gupta","year":"1999","journal-title":"Aust. New Zealand J. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1080\/00949650108812098","article-title":"Generalized Exponential Distribution: Different Methods of Estimations","volume":"69","author":"Gupta","year":"2001","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1080\/03610926.2015.1032426","article-title":"Slashed generalized exponential distribution","volume":"46","author":"Astorga","year":"2017","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Castillo, J.S., Rojas, M.A., and Reyes, J. (2023). A More Flexible Extension of the Fr\u00e9chet Distribution Based on the Incomplete Gamma Function and Applications. Symmetry, 15.","DOI":"10.20944\/preprints202307.2159.v1"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.1467-9574.1972.tb00191.x","article-title":"Understanding some long-tailed symmetrical distributions","volume":"26","author":"Rogers","year":"1972","journal-title":"Stat. Neerl."},{"key":"ref_22","unstructured":"Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H., and Tukey, J.W. (1972). Robust Estimates of Location: Survey and Advances, Princeton University Press."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1016\/j.spl.2006.11.006","article-title":"A new Family of Slash-Distributions with Elliptical Contours","volume":"77","author":"Quintana","year":"2007","journal-title":"Stat. Probab. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1016\/j.jspi.2008.07.007","article-title":"A generalization of the multivariate slash distribution","volume":"139","author":"Arslan","year":"2009","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1080\/03610926.2019.1568484","article-title":"Generalized modified slash distribution with applications","volume":"49","author":"Reyes","year":"2020","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.spl.2015.12.013","article-title":"Slash distributions of the sum of independent logistic random variables","volume":"110","year":"2016","journal-title":"Stat. Probab. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"371","DOI":"10.3390\/stats2030026","article-title":"On Generalized Slash Distributions: Representation by Hypergeometric Functions","volume":"2","year":"2019","journal-title":"Stats"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1007\/s00362-013-0546-6","article-title":"An extension of the generalized half-normal distribution","volume":"55","author":"Olmos","year":"2014","journal-title":"Stat. Pap."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Barranco-Chamorro, I., Iriarte, Y.A., G\u00f3mez, Y.M., Astorga, J.M., and G\u00f3mez, H.W. (2021). A generalized Rayleigh family of distributions based on the modified slash model. Symmetry, 13.","DOI":"10.3390\/sym13071226"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Barrios, L., G\u00f3mez, Y.M., Venegas, O., Barranco-Chamorro, I., and G\u00f3mez, H.W. (2022). The Slashed Power Half-Normal Distribution with Applications. Mathematics, 10.","DOI":"10.3390\/math10091528"},{"key":"ref_31","first-page":"283","article-title":"Statistical properties and applications of the Lindley slash distribution","volume":"20","author":"Gui","year":"2012","journal-title":"J. Appl. Stat. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Castillo, J.S., Barranco-Chamorro, I., Venegas, O., and G\u00f3mez, H.W. (2023). Slash-Weighted Lindley Distribution: Properties, Inference, and Applications. Mathematics, 11.","DOI":"10.3390\/math11183980"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Lehman, L.E. (1999). Elements of Large-Sample Theory, Springer.","DOI":"10.1007\/b98855"},{"key":"ref_34","unstructured":"Jones, D. (1979). Elementary Information Theory, Clarendon Press."},{"key":"ref_35","unstructured":"Awad, A.M. (1991, January 2\u20134). The Shannon entropy of generalized gamma and related distributions. Proceedings of the First Jordamian Mathematics Conference, Amman, Jordan."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1017\/S0269964800005064","article-title":"The reversed hazard rate function","volume":"12","author":"Block","year":"1998","journal-title":"Probab. Eng. Inf. Sci."},{"key":"ref_37","unstructured":"Johnson, R.A. (1988). Handbook of Statistics, North-Holland Press."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1090\/S0025-5718-1985-0777276-4","article-title":"The generalized integro-exponential function","volume":"44","author":"Milgram","year":"1985","journal-title":"Math. Comput."},{"key":"ref_39","unstructured":"R Core Team (2023). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. Available online: https:\/\/www.R-project.org\/."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Rohatgi, V.K., and Saleh, A.K. (2001). An Introduction to Probability and Statistics, John Wiley& Sons. [3rd ed.].","DOI":"10.1002\/9781118165676"},{"key":"ref_41","unstructured":"Lehman, L.E., and Casella, G. (1998). Theory of Point Estimation, Springer. [2nd ed.]."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Wang, W., Cui, Z., Chen, R., Wang, Y., and Zhao, X. (2023). Regression analysis of clustered panel count data with additive mean models. Stat. Pap.","DOI":"10.1007\/s00362-023-01511-3"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"108136","DOI":"10.1016\/j.ress.2021.108136","article-title":"Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints","volume":"218 Pt A","author":"Luo","year":"2022","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Automat. Contr."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Stat."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Iriarte, Y.A., Varela, H., G\u00f3mez, H.J., and G\u00f3mez, H.W. (2020). A Gamma-Type Distribution with Applications. Symmetry, 12.","DOI":"10.3390\/sym12050870"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Lee, E.T., and Wang, J. (2003). Statistical Methods for Survival Data Analysis, John Wiley & Sons.","DOI":"10.1002\/0471458546"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1080\/00401706.1963.10490105","article-title":"Theoretical explanation of observed decreasing failure rate","volume":"5","author":"Proschan","year":"1963","journal-title":"Technometrics"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/4\/253\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:26:17Z","timestamp":1760106377000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/4\/253"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,11]]},"references-count":48,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["axioms13040253"],"URL":"https:\/\/doi.org\/10.3390\/axioms13040253","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,11]]}}}