{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T07:26:58Z","timestamp":1763105218455},"reference-count":35,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:p>Beta distributions have been applied in a variety of fields in part due to its similarity to the normal distribution while allowing for a larger flexibility of skewness and kurtosis coverage when compared to the normal distribution. In spite of these advantages, the two-sided power (TSP) distribution was presented as an alternative to the beta distribution to address some of its short-comings, such as not possessing a cumulative density function (cdf) in a closed form and a difficulty with the interpretation of its parameters. The introduction of the biparabolic distribution and its generalization in this paper may be thought of in the same vein. Similar to the TSP distribution, the generalized biparabolic (GBP) distribution also possesses a closed form cdf, but contrary to the TSP distribution its density function is smooth at the mode. We shall demonstrate, using a moment ratio diagram comparison, that the GBP distribution provides for a larger flexibility in skewness and kurtosis coverage than the beta distribution when restricted to the unimodal domain. A detailed mean-variance comparison of GBP, beta and TSP distributions is presented in a Project Evaluation and Review Technique (PERT) context. Finally, we shall fit a GBP distribution to an example of financial European stock data and demonstrate a favorable fit of the GBP distribution compared to other distributions that have traditionally been used in that field, including the beta distribution.<\/jats:p>","DOI":"10.1142\/s0218488509005930","type":"journal-article","created":{"date-parts":[[2009,6,5]],"date-time":"2009-06-05T09:34:12Z","timestamp":1244194452000},"page":"377-396","source":"Crossref","is-referenced-by-count":6,"title":["THE GENERALIZED BIPARABOLIC DISTRIBUTION"],"prefix":"10.1142","volume":"17","author":[{"given":"CATALINA BEATRIZ GARC\u00cdA","family":"GARC\u00cdA","sequence":"first","affiliation":[{"name":"Departamento de M\u00e9todos Cuantitativos para la Econom\u00eda y la Empresa, University of Granada, Campus Universitario de La Cartuja, Granada, 18071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JOS\u00c9 GARC\u00cdA","family":"P\u00c9REZ","sequence":"additional","affiliation":[{"name":"Departamento de Econom\u00eda Aplicada, University of Almer\u00eda, La Ca\u00f1ada de San Urbano, s\/n, Almer\u00eda, 04071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SALVADOR CRUZ","family":"RAMBAUD","sequence":"additional","affiliation":[{"name":"Departamento de Direcci\u00f3n y Gesti\u00f3n de Empresas, University of Almer\u00eda, La Ca\u00f1ada de San Urbano, s\/n, Almer\u00eda, 04071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000105"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1080\/10429247.2005.11415285"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1287\/opre.7.5.646"},{"key":"rf4","first-page":"17","volume":"15","author":"Yao A. 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