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Author:
Christophe Chesneau
christophe.chesneau@gmail.com
Christophe Chesneau
Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France
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In this article, we use the idea of “negation” to construct new unit distributions, i.e., continuous distributions with support equal to the unit interval [0, 1]. A notable feature of these distributions is that they have opposite shape properties to the unit distributions from which they are derived; “opposite” in the sense that, from a graphical point of view, a certain horizontal symmetry is operated. We then examine the main properties of these negation-type distributions, including distributional functions, moments, and entropy measures. Finally, concrete examples are described, namely the negation-type power distribution, the negation-type [0, 1]-truncated exponential distribution, the negation-type truncated [0, 1]-sine distribution, the negation-type [0, 1]-truncated Lomax distribution, the negation-type Kumaraswamy distribution, and the negation-type beta distribution. Some of their properties are studied, also with the help of graphics that highlight their original modeling behavior. After the analysis, it appears that the negation-type Kumaraswamy distribution stands out from the others by combining simplicity with a high degree of flexibility, in a sense completing the famous Kumaraswamy distribution. Overall, our results enrich the panel of unit distributions available in the literature with an innovative approach.
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Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary
Honorary Editors in Chief:
- János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
- † Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
- Sándor SZABÓ, University of Pécs, Pécs, Hungary
Deputy Editors in Chief:
- Erhard AICHINGER, JKU Linz, Linz, Austria
- Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
- Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary
Editorial Board
- Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
- István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
- Károly BEZDEK, University of Calgary, Calgary, Canada
- György DÓSA, University of Pannonia, Veszprém, Hungary
- Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
- Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia
- Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
- Gábor NYUL, University of Debrecen, Debrecen, Hungary
- Margit PAP, University of Pécs, Pécs, Hungary
- István PINK, University of Debrecen, Debrecen, Hungary
- Mihály PITUK, University of Pannonia, Veszprém, Hungary
- Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
- Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
- Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
- Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
- Zsolt TUZA, University of Pannonia, Veszprém, Hungary
Advisory Board
- Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
- Gabriella BÖHM
- György GÁT, University of Debrecen, Debrecen, Hungary
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Department of Mathematics
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