| Titre : | Record Statistics and Theory of Entropy |
| Auteurs : | Hadil Kalfali, Auteur ; Nour Elhouda Zouaoui, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2023 |
| Format : | 1 vol. (161 p.) / ill., couv. ill. en coul / 30 cm |
| Langues: | Français |
| Résumé : |
In recent years, attention has been paid to the study of records statistics in terms of R´enyi extropy which was used widely in reliability and information studies. In this master’s thesis, an explained representation of records statistics is expressed and some properties results are exploited in terms of continuous distributions. In addition, some characterization results are explored based on the records values, and related properties are addressed for the R´enyi of record statistics (ordinary record and k-records). Simplified expressions of the R´enyi entropy of records are derived which allows us to investigate monotonicity properties and characterizations of some probability distributions. Moreover. These results are based on applying the result obtained by Jitto Jose E. I. Abdul Sathar (2022) |
| Sommaire : |
Contents Dedication i Acknowledgment ii Abstract iii Notations and symbols iv Table of Contents vi List of figures viii List of tables ix Introduction 1 1 Record Statistics 4 1.1 Introduction . . . . . . 4 1.2 Ordinary Record Statistics . . . . . . . . 6 1.2.1 Record Probability Density Function . . . . . 7 1.3 K-Record Statistics . . . . . . . . . 12 viTable of Contents 1.3.1 K-Record Probability Density Function . . . . . . . . . . . 13 1.4 Record From Specific Continuous Distribution . . . . . . . . . . . 18 1.4.1 Uniform Distribution . . . . . . . . . . . . . . . . . . . . . 18 1.4.2 Exponenntial Distribution . . . . . . . . . . . . . . . . . . 20 1.4.3 Weibull Distribution . . . 21 1.4.4 Pareto Distribution . . . . . . . . . . . . 2 2 Entropy of K- Record Statistics 23 2.1 Background . . . . . . . . . . . . . 23 2.2 R´enyi Entropy . . . . . . . . 26 2.3 The R´enyi Entropy of k-Record Statistics . . . . . . . . . . 28 2.4 Some Results on R´enyi Entropy of k-Record statistics . 33 2.5 Monotone properties of entropy Of k-record statistic .. 35 2.6 R´enyi entropy ordering . . . . . . . .. . 38 2.6.1 The effect of location-scale transformation . . 39 Conclusion 41 Bibliography 43 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| MM/1251 | Mémoire master | bibliothèque sciences exactes | Consultable |
