{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:55:29Z","timestamp":1760057729188,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T00:00:00Z","timestamp":1740182400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Direcci\u00f3n de Investigaci\u00f3n-Universidad del B\u00edo-B\u00edo"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We propose a new distribution which is the sum of two independent Akash (AK) random variables with the same parameter. We refer to this distribution as the AKS distribution. We study the density and some of its properties. We derive the method of moments (MM) and the maximum likelihood (ML) estimator, along with the Fisher information. The performance of the ML estimator is evaluated through a simulation study. In addition, we present two real data applications, demonstrating in these cases the superiority of the AKS distribution compared to two other distributions.<\/jats:p>","DOI":"10.3390\/axioms14030158","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T05:36:47Z","timestamp":1740375407000},"page":"158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On a Sum of Two Akash Distributions: Inference and Applications"],"prefix":"10.3390","volume":"14","author":[{"given":"Luis","family":"Firinguetti-Limone","sequence":"first","affiliation":[{"name":"Departamento de Estad\u00edstica, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n 4081112, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5434-2853","authenticated-orcid":false,"given":"Neveka M.","family":"Olmos","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica y Ciencias de Datos, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6643-6972","authenticated-orcid":false,"given":"Osvaldo","family":"Venegas","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Matem\u00e1ticas y F\u00edsicas, Facultad de Ingenier\u00eda, Universidad Cat\u00f3lica de Temuco, Temuco 4780000, Chile"}]},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1111\/j.2517-6161.1958.tb00278.x","article-title":"Fiducial distributions and Bayes\u2019 theorem","volume":"20","author":"Lindley","year":"1958","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_2","unstructured":"Hussain, E. (2006). The Non-Linear Functions of Order Statistics and Their Properties in Selected Probability Models. [Ph.D Thesis, Department of Statistics, University of Karachi]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/j.matcom.2007.06.007","article-title":"Lindley distribution and its applications","volume":"78","author":"Ghitany","year":"2008","journal-title":"Math. Comput. Simul."},{"key":"ref_4","first-page":"13","article-title":"Generalized Lindley distribution","volume":"3","author":"Zakerzadeh","year":"2009","journal-title":"J. Math. Ext."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1080\/00949655.2010.487825","article-title":"The discrete Lindley distribution: Properties and application","volume":"81","year":"2011","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.matcom.2011.07.005","article-title":"Reliability estimation in Lindley distribution with progressively type II right censored sample","volume":"82","author":"Krishna","year":"2011","journal-title":"Math. Comput. Simulat."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.jkss.2011.06.002","article-title":"An extended Lindley distribution","volume":"41","author":"Bakouch","year":"2012","journal-title":"J. Korean Stat. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"363","DOI":"10.4236\/am.2013.42056","article-title":"A two-parameter Lindley distribution for modeling waiting and survival times data","volume":"4","author":"Shanker","year":"2013","journal-title":"Appl. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.csda.2013.02.026","article-title":"Power Lindley distribution and associated inference","volume":"64","author":"Ghitany","year":"2013","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1080\/03610926.2011.563011","article-title":"Inferences on stress-strength reliability from Lindley distributions","volume":"42","author":"Ghitany","year":"2013","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2072","DOI":"10.1080\/00949655.2014.917308","article-title":"A new class of generalized Lindley distribution with applications","volume":"85","author":"Oluyede","year":"2014","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_12","first-page":"1","article-title":"On modeling of Lifetimes data using exponential and Lindley distributions","volume":"2","author":"Shanker","year":"2015","journal-title":"Biom. Biostat. Int. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3662","DOI":"10.1080\/00949655.2014.995101","article-title":"A new generalized Lindley distribution","volume":"85","author":"Abouammoh","year":"2015","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_14","first-page":"65","article-title":"Akash Distribution and Its Applications","volume":"4","author":"Shanker","year":"2015","journal-title":"Int. J. Probab. Stat."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Shanker, R., and Shukla, K.K. (2017). On Two-Parameter Akash Distribution. Biom. Biostat. Int. J., 6.","DOI":"10.15406\/bbij.2017.06.00178"},{"key":"ref_16","first-page":"1","article-title":"Power Akash Distribution and Its Application","volume":"12","author":"Shanker","year":"2017","journal-title":"J. Appl. Quant. Methods"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"G\u00f3mez, Y.M., Firinguetti-Limone, L., Gallardo, D.I., and G\u00f3mez, H.W. (2014). An Extension of the Akash Distribution: Properties, Inference and Application. Mathematics, 12.","DOI":"10.3390\/math12010031"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yaghoubi, A. (2022). Sum of Independent Random Variable for Shanker, Akash, Ishita, Pranav, Rani and Ram Awadh Distributions. arXiv.","DOI":"10.20944\/preprints202108.0523.v1"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1080\/01621459.1980.10477530","article-title":"Bathtub and Related Failure Rate Characterizations","volume":"75","author":"Glaser","year":"1980","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_20","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_21","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1117\/12.187363","article-title":"Fracture mechanics approach to the design of glass aircraft windows: A case study, SPIE Procceding","volume":"Volume 2286","author":"Fuller","year":"1994","journal-title":"Window and Dome Technologies and Materials IV"},{"key":"ref_22","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_23","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_24","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1111\/j.2517-6161.1979.tb01072.x","article-title":"The Determination of the order of an autoregression","volume":"41","author":"Hannan","year":"1979","journal-title":"J. R. Stat. Soc. Series B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1080\/10618600.1996.10474708","article-title":"Randomized Quantile Residuals","volume":"5","author":"Dunn","year":"1996","journal-title":"J. Comput. Graph. Stat."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/158\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:40:34Z","timestamp":1760028034000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/158"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,22]]},"references-count":25,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["axioms14030158"],"URL":"https:\/\/doi.org\/10.3390\/axioms14030158","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,2,22]]}}}