{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T06:25:09Z","timestamp":1769149509735,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T00:00:00Z","timestamp":1652486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Council for Scientific and Technological Development (CNPq)","award":["305305\/2019-0"],"award-info":[{"award-number":["305305\/2019-0"]}]},{"name":"National Council for Scientific and Technological Development (CNPq)","award":["1200525"],"award-info":[{"award-number":["1200525"]}]},{"name":"Comiss\u00e3o de Aperfei\u00e7oamento de Pessoal do N\u00edvel Superior (CAPES)","award":["305305\/2019-0"],"award-info":[{"award-number":["305305\/2019-0"]}]},{"name":"Comiss\u00e3o de Aperfei\u00e7oamento de Pessoal do N\u00edvel Superior (CAPES)","award":["1200525"],"award-info":[{"award-number":["1200525"]}]},{"name":"FONDECYT","award":["305305\/2019-0"],"award-info":[{"award-number":["305305\/2019-0"]}]},{"name":"FONDECYT","award":["1200525"],"award-info":[{"award-number":["1200525"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the signal of a digital image sensor. Wavelets are employed to extract information from a wide range of types of data, including audio signals and images often related to sensors, as unstructured data. Specifically, the cumulative wavelet integral function is defined to build the perturbation on a probability with the help of this function. We show that an arbitrary distribution function additively perturbed is still a distribution function, which can be seen as a privatized distribution, with the privatization mechanism being a wavelet function. Thus, we offer a mathematical method for choosing a suitable probability distribution for data by starting from some guessed initial distribution. Examples of the proposed method are discussed. Computational experiments were carried out using a database-sensor and two related algorithms. Several knowledge areas can benefit from the new approach proposed in this investigation. The areas of artificial intelligence, machine learning, and deep learning constantly need techniques for data fitting, whose areas are closely related to sensors. Therefore, we believe that the proposed privatization mechanism is an important contribution to increasing the spectrum of existing techniques.<\/jats:p>","DOI":"10.3390\/s22103743","type":"journal-article","created":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T09:48:22Z","timestamp":1652608102000},"page":"3743","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A New Wavelet-Based Privatization Mechanism for Probability Distributions"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6843-0635","authenticated-orcid":false,"given":"H\u00e9lio M.","family":"de Oliveira","sequence":"first","affiliation":[{"name":"Department of Statistics, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9884-9090","authenticated-orcid":false,"given":"Raydonal","family":"Ospina","sequence":"additional","affiliation":[{"name":"Department of Statistics, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4755-3270","authenticated-orcid":false,"given":"V\u00edctor","family":"Leiva","sequence":"additional","affiliation":[{"name":"School of Industrial Engineering, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Valpara\u00edso 2362807, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8797-681X","authenticated-orcid":false,"given":"Carlos","family":"Martin-Barreiro","sequence":"additional","affiliation":[{"name":"Faculty of Natural Sciences and Mathematics, Escuela Superior Polit\u00e9cnica del Litoral ESPOL, Guayaquil 090902, Ecuador"},{"name":"Faculty of Engineering, Universidad Esp\u00edritu Santo, Samborond\u00f3n 0901952, Ecuador"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1522-9292","authenticated-orcid":false,"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universit\u00e9 de Caen Basse-Normandie, F-14032 Caen, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nor, A.K.M., Pedapati, S.R., Muhammad, M., and Leiva, V. 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