2022
DOI: 10.3390/e24111654
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Tsallis Entropy for Loss Models and Survival Models Involving Truncated and Censored Random Variables

Abstract: The aim of this paper consists in developing an entropy-based approach to risk assessment for actuarial models involving truncated and censored random variables by using the Tsallis entropy measure. The effect of some partial insurance models, such as inflation, truncation and censoring from above and truncation and censoring from below upon the entropy of losses is investigated in this framework. Analytic expressions for the per-payment and per-loss entropies are obtained, and the relationship between these e… Show more

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Cited by 4 publications
(3 citation statements)
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“…Among the applications of other entropies (Rényi entropy, Varma entropy, Kaniadakis entropy, relative entropy, weighted entropy, etc. ), we can list the following: Markov chains (see [16][17][18]), model selection (see [19,20]), combinatorics (see [21,22]), finance (see [23][24][25]), Lie symmetries (see [26,27]), and machine learning (see [28,29]).…”
Section: Introductionmentioning
confidence: 99%
“…Among the applications of other entropies (Rényi entropy, Varma entropy, Kaniadakis entropy, relative entropy, weighted entropy, etc. ), we can list the following: Markov chains (see [16][17][18]), model selection (see [19,20]), combinatorics (see [21,22]), finance (see [23][24][25]), Lie symmetries (see [26,27]), and machine learning (see [28,29]).…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, the concept of entropy has been intensively studied and multiple generalizations have appeared, i.e., Tsallis entropy, Varma entropy, Rényi entropy, Kaniadakis entropy, fractional entropy, fractal entropy, natural time entropy, etc., with applications in many areas such as earthquakes [1][2][3][4][5][6], stock exchanges [7,8], plasma [9][10][11], signal processing [12], Markov chains [13][14][15], astrophysics [16,17], model selection [18,19], finance [20][21][22][23] and Lie symmetries [24,25].…”
Section: Introductionmentioning
confidence: 99%
“…Indeed, distances and entropies are related to inferential statistics, including both estimation and hypothesis testing problems [ 1 , 2 , 3 , 4 , 5 , 6 ], model selection criteria [ 7 , 8 , 9 ] and probabilistic and statistical modelling with applications in multivariate analysis, actuarial science, portfolio optimization, survival analysis, reliability theory, change-point problems, etc. [ 10 , 11 , 12 , 13 , 14 , 15 ]. Thus, the significance of entropy and divergence measures that emerges in these and many more scientific fields is a topic of great interest to scientists, researchers, medical experts, engineers, industrial managers, computer experts, data analysts, etc.…”
mentioning
confidence: 99%