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## Combining Expected Utility and Weighted Gini-Simpson Index into a Non-Expected Utility Device

### Citations

10891 |
A mathematical theory of communication
- Shannon
- 1948
(Show Context)
Citation Context ...stinguish among decisions under risk, meaning circumstances or outcomes with known probabilities,sas opposed to situations on uncertainty where probabilities are not known (e.g. [3]). Shannon entropy =-=[4]-=- measures the uncertainty of a random variable, and, for example, an entropy-based risk measure concerning financialsasset pricing is claimed to be more precise than other models [5]. A recent review ... |

6297 | Prospect theory: an analysis of decision under risk
- Kahneman, Tversky
- 1979
(Show Context)
Citation Context ...tuations, what was illustrated for example by the Ellsberg paradox published in 1961.sOther paradoxes were mentioned later such as those referred to by Kahneman and Tversky concerning prospectstheory =-=[17]-=- where the carriers of value are changes in wealth or welfare rather than final states. Machina [18]shighlighted that the independence axiom of EUT tends to be systematically violated in practice and ... |

1169 |
Information Theory and Statistical Mechanics
- Jaynes
- 1963
(Show Context)
Citation Context ...ithms for Obtaining the Maximum PointsIt must be noted that we are certain that the maximum point exists as it is implied by Weierstrass theorem. Thesproblem we are dealing has an old root, as Jaynes =-=[53]-=- in 1957 had already noticed, saying that the negative terms2 ip−∑shas many of the qualitative properties of Shannon’s entropy but has the inherent difficulty arising fromsthe fact that using Lagrange... |

883 | Subjective probability and expected utility without additivity
- Schmeidler
- 1989
(Show Context)
Citation Context ...Uswe begin ordering the set such as we are now dealing with the lottery in the form of an act described as a lottery where the outcomes or utilities are real numbers ordered in a decreasing way (e.g. =-=[54]-=-): ( ) ( )1 nu u≥ ≥ ; as it is for sure that ( )1usand ( )2usimply strictly positives* 1psands* 2psthe problem begins with the evaluation of *3p . Does ( )3usverifies the condition ( ) ( ) ( ) ( ) ( ... |

454 |
Developments in Non-expected Utility Theory: The Hunt for A Descriptive Theory of Choice under Risk
- Starmer
- 2000
(Show Context)
Citation Context ... outcome which has a low probability will, by virtue of its rarity,shave a higher utility value than the same outcome would have if it had a high probability.sA substantial review was made by Starmer =-=[28]-=- under the name of non-expected utility theory, the case ofssubjective probabilities being framed within the conventional strategy approach focused on theories with decision weights, in particular the... |

441 |
The Utility Analysis of Choices Involving Risk
- Friedman, Savage
- 1948
(Show Context)
Citation Context ...ed by attaching a numerical value toseach—designated its utility; also, choosing among alternatives involving risk entails that it is selected that onesfor which the expected utility is highest (e.g. =-=[1]-=-). As Weirich [2] points out, such an utterance inherits from thestheory of rationality a collection of problems concerning evaluation of acts with respect to information. It issuseful to distinguish ... |

410 | A definition of subjective probability.
- Anscombe, Aumann
- 1963
(Show Context)
Citation Context ...actically as a synonym for proportion of successes in trails governed by large numbers laws as discussed in Ramsey [16]—outlined subsequently as inter-ssubjective probabilities by Anscombe and Aumann =-=[46]-=-—or even as subjective probability measuring the degreesof belief of an agent, we can provide the result ( )2 22 2uD I U H= =susing the formulas for generalized useful information of degree 2α =sprevi... |

349 |
Truth and probability
- Ramsey
- 1926
(Show Context)
Citation Context ...omes that are considered certain compared to outcomes whichsare merely probable (e.g. [15] for a review).sSubjective expected utility, having a first cornerstone in the works of de Finetti and Ramsey =-=[16]-=- both published in 1931, followed by a further substantial development with Savage in 1954, was regarded by most decision analysts to be the preferred normative model for how individuals should make d... |

280 |
Expected Utility Analysis without The Independence Axiom
- Machina
- 1982
(Show Context)
Citation Context ...s were mentioned later such as those referred to by Kahneman and Tversky concerning prospectstheory [17] where the carriers of value are changes in wealth or welfare rather than final states. Machina =-=[18]-=-shighlighted that the independence axiom of EUT tends to be systematically violated in practice and concludedsthat the main concepts, results and tools of expected utility analysis may be derived from... |

227 |
Dynamic Consistency and Non-expected Utility Models of Choice Under Uncertainty
- Machina
- 1989
(Show Context)
Citation Context ... Frosini [21] presented recently a discussion revisiting Borchsparadox linked to a general criterion of choice between prospects.sHere we will be focused in lotteries, a concept we shall retain (e.g. =-=[22]-=-): a lottery is defined as a list or finitescollection of simple consequences or outcomes ( )1, , nX x x= swith associated, usually unknown, probabilities stated as [ ]Pr i iX x p= =sfor 1, ,i n= sc... |

227 |
Investigating Generalizations of Expected Utility Theory Using Experimental Data
- Hey, Orme
- 1994
(Show Context)
Citation Context ...ironmental quality of water undersJ. P. Casquilhos188suncertainty is outlined in [30].sThere are many other approaches to surpass the limitations of independence axiom, and, for example, Hey andsOrme =-=[31]-=- compared traditional expected utility and non-expected utility methods with a total of 11 types ofspreference functionals, evaluating the trade-off of explaining observed differences of the data rela... |

213 | Choice under uncertainty: Problems solved and unsolved
- Machina
- 1987
(Show Context)
Citation Context ...dispersion of the utilities around their mean values and alsosbecause, in general, people overweight positive outcomes that are considered certain compared to outcomes whichsare merely probable (e.g. =-=[15]-=- for a review).sSubjective expected utility, having a first cornerstone in the works of de Finetti and Ramsey [16] both published in 1931, followed by a further substantial development with Savage in ... |

142 | Quantification method of classification processes. concept of structural α-entropy
- Havrda, Charvat
- 1967
(Show Context)
Citation Context ...= , hence retrieving weighted Shannon entropy. In 1978, Sharma et al. [43]sdiscussed a non-additive information measure generalizing the structural α -entropy previously studied bysHavrda and Charvat =-=[44]-=-; they named their mathematical device “generalized useful information of degree α ”,srelative to the utility information scheme stated above and denoted as:s( ) ( ) ( )1 11 1 2 1 with 1.n i i iiI U u... |

89 |
Mean-Variance versus Direct Utility Maximization
- Kroll, Levy, et al.
- 1984
(Show Context)
Citation Context ...; this remarkable work outlinedsthe scope of generalized expected utility analysis or non-expected utility frameworks. Other methods were pro-sposed and used such as mean-variance analysis (e.g. [19] =-=[20]-=-); based on this type of method and using meansabsolute deviation instead of standard deviation, Frosini [21] presented recently a discussion revisiting Borchsparadox linked to a general criterion of ... |

47 |
Theory of Decision Under Uncertainty.
- Gilboa
- 2009
(Show Context)
Citation Context ...ce between utilities and numbers, involving complete ordering and the algebra of combining. Nevertheless, based on their theorem one is restricted tossituations in which probabilities are given (e.g. =-=[13]-=-).sSince that time there were innumerable contributions on the theme. For instance, Alchian [14] outlines the issue stating that if, in a given context, it is possible to assign numerical values for d... |

36 | Nonlinear decision weights in choice under uncertainty.
- Wu, Gonzalez
- 1999
(Show Context)
Citation Context ...ransforms the individual probabilities of each consequence into weights, and, in general, it is assumed thats( ).πsis a continuous non-decreasing function with ( )0 0π =sand ( )1 1π =s(e.g. [13] [28] =-=[29]-=-); decisionsweights are also named capacities if additionally they satisfy monotonicity with respect to set inclusion. An example of a decision weight procedure concerning assessing preferences for en... |

18 |
On the Utility Theoretic Foundation of MeanVariance Analysis
- Baron
- 1977
(Show Context)
Citation Context ...tions; this remarkable work outlinedsthe scope of generalized expected utility analysis or non-expected utility frameworks. Other methods were pro-sposed and used such as mean-variance analysis (e.g. =-=[19]-=- [20]); based on this type of method and using meansabsolute deviation instead of standard deviation, Frosini [21] presented recently a discussion revisiting Borchsparadox linked to a general criterio... |

17 |
The meaning of utility measurement.”
- Alchian
- 1953
(Show Context)
Citation Context ...rtheless, based on their theorem one is restricted tossituations in which probabilities are given (e.g. [13]).sSince that time there were innumerable contributions on the theme. For instance, Alchian =-=[14]-=- outlines the issue stating that if, in a given context, it is possible to assign numerical values for different entities competing,sJ. P. Casquilhos187sthen a selection process of rational choices is... |

16 |
A quantitative-qualitative measure of information in cybernetic systems,”
- Belis, Guiasu
- 1968
(Show Context)
Citation Context ... paper.s2.2. Generalized Useful Information Measures and Weighted Gini-Simpson IndexsThe quantitative-qualitative measure of information generalizing Shannon entropy characterized by Belis andsGuiasu =-=[33]-=- is additive and may be associated with a utility information scheme, anchored in a finite samplesspace, establishing that an elementary event iεsoccurring with (objective) probability ipsentails a po... |

11 |
Evaluating public risk preferences in forest land-use choices using multi-attribute utility theory,
- Ananda, Herath
- 2006
(Show Context)
Citation Context ...on. It issuseful to distinguish among decisions under risk, meaning circumstances or outcomes with known probabilities,sas opposed to situations on uncertainty where probabilities are not known (e.g. =-=[3]-=-). Shannon entropy [4] measures the uncertainty of a random variable, and, for example, an entropy-based risk measure concerning financialsasset pricing is claimed to be more precise than other models... |

10 |
Nonlinear Utility and the Probability Score.
- Winkler, Murphy
- 1970
(Show Context)
Citation Context ...robability score—generat-sing utility functions that are nonlinear in the probabilities—is not an innovative method and we can identify ansexample concerning meteorology forecasts dating back to 1970 =-=[8]-=-. Those approaches were later merged understhe name of “non-expected utility” methods in the 1980s and consist of different conceptual types, the one wesshall be dealing with framing into the category... |

10 | Why environmental and resource economists should care about non-expected utility models. Resource and Energy
- Shaw, Woodward
(Show Context)
Citation Context ... meaning in EUT, andsan example of a concave utility function used to assess optimal expected utility of wealth under the scope of insurance business can be acknowledged in [25].sAs Shaw and Woodward =-=[26]-=- say, focusing on the issue of natural resources management, the problem insclassical utility theory is that the optimization of the models may have to accommodate preferences that are nonlinear in th... |

9 |
A measure of risk and a decision-making model based on expected utility and entropy
- Yang, Qiu
- 2005
(Show Context)
Citation Context ...ion weights or non-additive probabilities, also named capacities. A decision-making model based on expected utility and entropy (EU-E) introducing a risk tradeoff factor was discussed by Yang and Qiu =-=[9]-=-, where Shannon entropy measures the objectivesuncertainty of the corresponding set of states, or its variability; recently, the authors reframed their model into asnormalized expected utility-entropy... |

7 |
1738/1954) Exposition of a New Theory on the Measurement of Risk
- Bernoulli
(Show Context)
Citation Context ...rsburg paradox using logarithms of thesvalues at stake, thereby making the numerical series associated with the calculation of the mean value convergent (there referred to as “moral hope”). Bernoulli =-=[11]-=- explicitly stated that the determination of the value of ansitem should not be based on its price but rather on the utility that it produces, being the marginal utility of money inversely proportiona... |

7 |
Utility, subjective probability, their interaction, and variance preferences
- Edwards
- 1962
(Show Context)
Citation Context ... optimization of the models may have to accommodate preferences that are nonlinear in the probabilities. There are many approaches with this perspective, known at least since Edwards ins1955 and 1962 =-=[27]-=- discussed in parallel the theory of Kurt Lewin utility and the theory of subjective probabilitysof Francis Irwin, introducing the concept of decision weights instead of probabilities; the Lewin utili... |

5 |
Weighted Entropy
- Guiasu
- 1971
(Show Context)
Citation Context ...standard formula ( ) 1 log n i i iiI U u p p== −∑sand is usuallysreferred to as weighted (Shannon) entropy. This mathematical device was further discussed and studied analyti-scally by Guiasu in 1971 =-=[34]-=-, considered as a measure of uncertainty or information supplied by a probabilisticsexperiment depending both on the probabilities of events and on corresponding qualitative positive weights. Thesfunc... |

5 |
Ecomosaico: Indices para o Diagnóstico de Proporções de Composição. (tese de doutoramento). Instituto Superior de Agronomia, Universidade Técnica de Lisboa,
- CASQUILHO
- 1999
(Show Context)
Citation Context ... index as a relevantsmeasure in the context of ecological diversity assessment (e. g. [47] [48]).sThe formulation and analytical study of weighted Gini-Simpson index was first introduced by Casquilho =-=[49]-=-swithin a set of indices built as mathematical devices applied to discuss compositional scenarios of landscapesJ. P. Casquilhos189smosaics (or ecomosaics), using either ecological or economic weights—... |

4 |
Complex number valuation of habitats and information index of the landscape mosaic.
- CASQUILHO
- 2009
(Show Context)
Citation Context ...economic applications we have examples such as: estimating optimal diversification in allocationsproblems [50] and other developments concerning ecomosaics composition assessment with forest habitats =-=[51]-=-s[52]. In [49] [51] it is shown that weighted Gini-Simpson index can be interpreted as a sum of variances of interdependent Bernoulli variables thus becoming a measure of the variability of the system... |

3 |
Relative Concave Utility for Risk and Ambiguity
- Baillon, Driesen, et al.
- 2012
(Show Context)
Citation Context ... convexitysentails risk prone behavior by an individual agent. The Arrow-Pratt measure (e.g. [23]) is commonly used to assess the issues of risk-avert or risk-prone behavior. Recently, Baillon et al. =-=[24]-=- presented a general and simplestechnique for comparing the concavity of different utility functions isolating its empirical meaning in EUT, andsan example of a concave utility function used to assess... |

3 | Preferences for Environmental Quality under Uncertainty
- Roberts, Boyer, et al.
- 2008
(Show Context)
Citation Context ...icity with respect to set inclusion. An example of a decision weight procedure concerning assessing preferences for environmental quality of water undersJ. P. Casquilhos188suncertainty is outlined in =-=[30]-=-.sThere are many other approaches to surpass the limitations of independence axiom, and, for example, Hey andsOrme [31] compared traditional expected utility and non-expected utility methods with a to... |

3 |
Valuing life: Experimental evidence using sensitivity to rare events,
- Chanel, Chichilnisky
- 2013
(Show Context)
Citation Context ...ta relative to thesmodels versus loosing predictive power. Recently, a reasoning of decision-making with catastrophic risks motivated the incorporation of a new axiom named sensitivity to rare events =-=[32]-=-. But simple decision weight utilitysmodeling is the conceptual type of non-expected utility methods that is relevant in this paper.s2.2. Generalized Useful Information Measures and Weighted Gini-Simp... |

3 |
State-Value Weighted Entropy as a Measure of Investment Risk
- Nawrocki, Harding
- 1986
(Show Context)
Citation Context ... weights. Thesfunctional ( )I Uswas also named useful information (e.g. [35]). At least since the eighties of last centurysweighted entropy was used in economic studies concerning investment and risk =-=[36]-=- and that scope of approachsused in financial risk assessment and security quantification proceeds until nowadays (e.g. [37]-[40]). Also, newstheoretical developments concerning weighted entropy mathe... |

3 |
On Measures of “Useful” Information
- Sharma, Mitter, et al.
- 1978
(Show Context)
Citation Context ...le it is easy to prove the result of the limit ( )1lim H I Uβ β→ = , thus allowing for the extension by continuity to the case 1β = , hence retrieving weighted Shannon entropy. In 1978, Sharma et al. =-=[43]-=-sdiscussed a non-additive information measure generalizing the structural α -entropy previously studied bysHavrda and Charvat [44]; they named their mathematical device “generalized useful information... |

3 | The weighted gini-simpson index: revitalizing an old index of biodiversity
- Guiasu, Guiasu
- 2012
(Show Context)
Citation Context ... the entropy of degree 2β =sof Emptoz (see [42]). Guiasu and Guiasu proceeded with several developments of the WGS index as a relevantsmeasure in the context of ecological diversity assessment (e. g. =-=[47]-=- [48]).sThe formulation and analytical study of weighted Gini-Simpson index was first introduced by Casquilho [49]swithin a set of indices built as mathematical devices applied to discuss compositiona... |

2 |
Utility Maximization Generalized
- Weirich
(Show Context)
Citation Context ... numerical value toseach—designated its utility; also, choosing among alternatives involving risk entails that it is selected that onesfor which the expected utility is highest (e.g. [1]). As Weirich =-=[2]-=- points out, such an utterance inherits from thestheory of rationality a collection of problems concerning evaluation of acts with respect to information. It issuseful to distinguish among decisions u... |

2 |
Entropy-Based Financial Asset Pricing
- Ormos, Zibriczky
(Show Context)
Citation Context .... Shannon entropy [4] measures the uncertainty of a random variable, and, for example, an entropy-based risk measure concerning financialsasset pricing is claimed to be more precise than other models =-=[5]-=-. A recent review of applications of entropy insfinance, mainly focused in portfolio selection and asset pricing, but also in decision theory, can be acknowl-sedged in [6].sThis work is an analogous d... |

2 |
Useful Information and Questionnaires
- BOUCHON
- 1976
(Show Context)
Citation Context ...n supplied by a probabilisticsexperiment depending both on the probabilities of events and on corresponding qualitative positive weights. Thesfunctional ( )I Uswas also named useful information (e.g. =-=[35]-=-). At least since the eighties of last centurysweighted entropy was used in economic studies concerning investment and risk [36] and that scope of approachsused in financial risk assessment and securi... |

2 |
Conditional and Weighted Measures of Ecological Diversity
- Guiasu, Guiasu
- 2003
(Show Context)
Citation Context ...its semanticscontent either as an environmental factor or a value of “information consciousness” in aggregating financial accounts.sWeighted Gini-Simpson (WGS) index was outlined by Guiasu and Guiasu =-=[45]-=- in the scope of conditionalsand weighted measures of ecological diversity denoted as ( )1 1 n u i i iiD u p p== −∑swhere the positive weightssiusreflect additional information concerning the importan... |

2 | Landscape mosaic composition and mean contributive value index.
- CASQUILHO
- 2010
(Show Context)
Citation Context ...here is another point that deserves an explanation: it was claimed in [7] that index uKscould be nameds“mean contributive value” because of the rationale that is exposed in a more detailed version in =-=[55]-=-, concerningsKant valuation moral philosophy. What about the maximand functional uZ ? The similitude is so compellingsthat we have no option but to claim it should be considered as a formulation of “m... |

1 |
Applications of Entropy in Finance: A
- Zhou, Cai, et al.
- 2013
(Show Context)
Citation Context ...re precise than other models [5]. A recent review of applications of entropy insfinance, mainly focused in portfolio selection and asset pricing, but also in decision theory, can be acknowl-sedged in =-=[6]-=-.sThis work is an analogous development of another paper recently published, where it was discussed an expected utility and weighted entropy framework, with acronym EU-WE [7]. We shall prove that the ... |

1 |
Discussion of an Expected Utility and Weighted Entropy Framework
- Casquilho
- 2014
(Show Context)
Citation Context ... can be acknowl-sedged in [6].sThis work is an analogous development of another paper recently published, where it was discussed an expected utility and weighted entropy framework, with acronym EU-WE =-=[7]-=-. We shall prove that the claimedsanalogy has here a proper sense, as either weighted Shannon entropy or weighted Gini-Simpson index may besconsidered two cases of generalized useful information measu... |

1 |
Normalized Expected Utility-Entropy Measure of Risk
- Yang, Qiu
- 2014
(Show Context)
Citation Context ...ntropy measures the objectivesuncertainty of the corresponding set of states, or its variability; recently, the authors reframed their model into asnormalized expected utility-entropy measure of risk =-=[10]-=-, allowing for comparing acts or choices where the num-sber of states are quite apart.sFirst, we shall present a synthetic review of the theoretical background anchored in two scientific fields: expec... |

1 | A General Criterion of Choice, with Discussion of Borch Paradox
- Frosini
- 2014
(Show Context)
Citation Context ...ameworks. Other methods were pro-sposed and used such as mean-variance analysis (e.g. [19] [20]); based on this type of method and using meansabsolute deviation instead of standard deviation, Frosini =-=[21]-=- presented recently a discussion revisiting Borchsparadox linked to a general criterion of choice between prospects.sHere we will be focused in lotteries, a concept we shall retain (e.g. [22]): a lott... |

1 | Optimal Expected Utility of Wealth for Two Dependent Classes of Insurance Business
- Gosio, Lari, et al.
- 2014
(Show Context)
Citation Context ...ons isolating its empirical meaning in EUT, andsan example of a concave utility function used to assess optimal expected utility of wealth under the scope of insurance business can be acknowledged in =-=[25]-=-.sAs Shaw and Woodward [26] say, focusing on the issue of natural resources management, the problem insclassical utility theory is that the optimization of the models may have to accommodate preferenc... |

1 |
Uncertainty Theory-Based Multiple Objective Mean-Entropy
- Bhattacharyya, Chatterjee, et al.
- 2013
(Show Context)
Citation Context ...eighted entropy was used in economic studies concerning investment and risk [36] and that scope of approachsused in financial risk assessment and security quantification proceeds until nowadays (e.g. =-=[37]-=--[40]). Also, newstheoretical developments concerning weighted entropy mathematical properties are available (e.g. [41]).sIn 1976, Emptoz—quoted in Aggarwal and Picard [42]—introduced the entropy of d... |

1 | Asset Pricing and Entropy - Ormos, Zibriczky - 2013 |

1 | The Role of Weighted Entropy in Security Quantification - Patsakis, Mermigas, et al. - 2013 |

1 |
Application of Information Theoretic Divergence Measures—Forecasting Profit Maximization in Share Market
- Nager, Singh
- 2013
(Show Context)
Citation Context ...ed entropy was used in economic studies concerning investment and risk [36] and that scope of approachsused in financial risk assessment and security quantification proceeds until nowadays (e.g. [37]-=-=[40]-=-). Also, newstheoretical developments concerning weighted entropy mathematical properties are available (e.g. [41]).sIn 1976, Emptoz—quoted in Aggarwal and Picard [42]—introduced the entropy of degree... |

1 |
Simple Inequalities for Weighted Entropies. http://arxiv.org/pdf/1409.4102.pdf
- Suhov, Sekeh
- 2014
(Show Context)
Citation Context ...ancial risk assessment and security quantification proceeds until nowadays (e.g. [37]-[40]). Also, newstheoretical developments concerning weighted entropy mathematical properties are available (e.g. =-=[41]-=-).sIn 1976, Emptoz—quoted in Aggarwal and Picard [42]—introduced the entropy of degree βsof an experiment outlined with the same premises of the information scheme referred to above and defined as:s( ... |

1 |
Functional Equations and Information Measures with Preference
- Aggarwal, Picard
- 1978
(Show Context)
Citation Context ...oceeds until nowadays (e.g. [37]-[40]). Also, newstheoretical developments concerning weighted entropy mathematical properties are available (e.g. [41]).sIn 1976, Emptoz—quoted in Aggarwal and Picard =-=[42]-=-—introduced the entropy of degree βsof an experiment outlined with the same premises of the information scheme referred to above and defined as:s( ) ( )1 11 1 1 2 with 1.n i i iiH u p pβ ββ β− −== − −... |

1 |
Weighted Gini-Simpson Quadratic Index of Biodiversity for Interdependent Species
- Guiasu, Guiasu
- 2014
(Show Context)
Citation Context ...entropy of degree 2β =sof Emptoz (see [42]). Guiasu and Guiasu proceeded with several developments of the WGS index as a relevantsmeasure in the context of ecological diversity assessment (e. g. [47] =-=[48]-=-).sThe formulation and analytical study of weighted Gini-Simpson index was first introduced by Casquilho [49]swithin a set of indices built as mathematical devices applied to discuss compositional sce... |

1 |
Optimal Diversification in Allocation Problems
- Purcaru
- 2009
(Show Context)
Citation Context ...ndex is used in several domains, besides ecological and phylogenetic assessments—sfocusing in economic applications we have examples such as: estimating optimal diversification in allocationsproblems =-=[50]-=- and other developments concerning ecomosaics composition assessment with forest habitats [51]s[52]. In [49] [51] it is shown that weighted Gini-Simpson index can be interpreted as a sum of variances ... |

1 | Ecomosaic Composition and Expected Utility Indices
- Casquilho
- 2011
(Show Context)
Citation Context ...mic applications we have examples such as: estimating optimal diversification in allocationsproblems [50] and other developments concerning ecomosaics composition assessment with forest habitats [51]s=-=[52]-=-. In [49] [51] it is shown that weighted Gini-Simpson index can be interpreted as a sum of variances of interdependent Bernoulli variables thus becoming a measure of the variability of the system and ... |

1 |
Diversified Portfolios with Different Entropy Measures
- Yu, Lee, et al.
- 2014
(Show Context)
Citation Context ... to be used to form and rebalance portfolios concerning optimal criteria, and some state that the portfolio values of the models incorporating entropies are highersthan their correspondent benchmarks =-=[56]-=-. Also, we discussed the similarity between this EU-WGS device andsan EU-WE framework recently published denoted index uKs(which is a particular case of a one-parameter family of models outlined and d... |

1 |
Ecomosaico Florestal: Composição, Índices de Informação e Abdução
- Casquilho
- 2012
(Show Context)
Citation Context ...iscussed the similarity between this EU-WGS device andsan EU-WE framework recently published denoted index uKs(which is a particular case of a one-parameter family of models outlined and discussed in =-=[57]-=-), pointing out the main analogies and differences between the two related issues which can be , in any case, referred to as mean contributive values of compositional mixtures. Last, insthis paper, we... |