Academic literature on the topic 'Inverse stochastic dominance'

The inverse stochastic dominance of degree r is a stochastic order of interest in several branches of economics. We discuss it in depth, the central point being the characterization in terms of the weak r-majorization of the vectors of expected order statistics. The weak r-majorization (a notion introduced in the paper) is a natural extension of the classical (reverse) weak majorization of Hardy, Littlewood and Pòlya. This work also shows the equivalence between the continuous majorization (of higher order) and the discrete r-majorization. In particular, our results make it clear that the cases r = 1, 2 differ substantially from those with r ≥ 3, a fact observed earlier by Muliere and Scarsini (1989), among other authors. Motivated by this fact, we introduce new stochastic orderings, as well as new social inequality indices to compare the distribution of the wealth in two populations, which could be considered as natural extensions of the first two dominance rules and the S-Gini indices, respectively.

The inverse stochastic dominance of degree r is a stochastic order of interest in several branches of economics. We discuss it in depth, the central point being the characterization in terms of the weak r-majorization of the vectors of expected order statistics. The weak r-majorization (a notion introduced in the paper) is a natural extension of the classical (reverse) weak majorization of Hardy, Littlewood and Pòlya. This work also shows the equivalence between the continuous majorization (of higher order) and the discrete r-majorization. In particular, our results make it clear that the cases r = 1, 2 differ substantially from those with r ≥ 3, a fact observed earlier by Muliere and Scarsini (1989), among other authors. Motivated by this fact, we introduce new stochastic orderings, as well as new social inequality indices to compare the distribution of the wealth in two populations, which could be considered as natural extensions of the first two dominance rules and the S-Gini indices, respectively.

Humans are notoriously bad at understanding probabilities, exhibiting a host of biases and distortions that are context dependent. This has serious consequences on how we assess risks and make decisions. Several theories have been developed to replace the normative rational expectation theory at the foundation of economics. These approaches essentially assume that (subjective) probabilities weight multiplicatively the utilities of the alternatives offered to the decision maker, although evidence suggest that probability weights and utilities are often not separable in the mind of the decision maker. In this context, we introduce a simple and efficient framework on how to describe the inherently probabilistic human decision-making process, based on a representation of the deliberation activity leading to a choice through stochastic processes, the simplest of which is a random walk. Our model leads naturally to the hypothesis that probabilities and utilities are entangled dual characteristics of the real human decision making process. It predicts the famous fourfold pattern of risk preferences. Through the analysis of choice probabilities, it is possible to identify two previously postulated features of prospect theory: the inverse S-shaped subjective probability as a function of the objective probability and risk-seeking behavior in the loss domain. It also predicts observed violations of stochastic dominance, while it does not when the dominance is “evident”. Extending the model to account for human finite deliberation time and the effect of time pressure on choice, it provides other sound predictions: inverse relation between choice probability and response time, preference reversal with time pressure, and an inverse double-S-shaped probability weighting function. Our theory, which offers many more predictions for future tests, has strong implications for psychology, economics and artificial intelligence.

The pension landscape is changing due to the market situation, and technological change has enabled financial innovations. Pension savers usually seek financial advice to make a personalised decision in selecting the right pension fund for them. As such, decision rules based on the assumed risk profile of the decision maker could be generated by making use of stochastic dominance (SD). In the paper, the second-pillar pension funds operating in Lithuania and Slovakia are analysed according to SD rules. The importance of the distributional assumption is explored while comparing the results of empirical, student-t, Hyperbolic and Normal Inverse Gaussian distributions to generate SD-based rules that could be integrated into an advisory solution. Moreover, due to the differences in SD results under different distributional assumptions, a new SD ratio is proposed that condenses the dominance-based relations for all considered dominance orders and probability distributions. The empirical results indicate that this new SD ratio efficiently characterises not only the preference of each fund individually but also of a group of funds with the same attributes, thus enabling multi-risk and multi-country comparisons.

The sequential sampling of populations with unequal probabilities and with replacement in a closed population is a recurrent problem in ecology and evolution. Examples range from biodiversity sampling, epidemiology to the estimation of signal repertoire in animal communication. Many of these questions can be reformulated as urn problems, often as special cases of the coupon collector problem, most simply expressed as the number of coupons that must be collected to have a complete set. We aimed to apply the coupon collector model in a comprehensive manner to one example—hosts (balls) being searched (draws) and parasitized (ball colour change) by parasitic wasps—to evaluate the influence of differences in sampling probabilities between items on collection speed. Based on the model of a complete multinomial process over time, we define the distribution, distribution function, expectation and variance of the number of hosts parasitized after a given time, as well as the inverse problem, estimating the sampling effort. We develop the relationship between the risk distribution on the set of hosts and the speed of parasitization and propose a more elegant proof of the weak stochastic dominance among speeds of parasitization, using the concept of Schur convexity and the ‘Robin Hood transfer’ numerical operation. Numerical examples are provided and a conjecture about strong dominance—an ordering characteristic of random variables—is proposed. The speed at which new items are discovered is a function of the entire shape of the sampling probability distribution. The sole comparison of values of variances is not sufficient to compare speeds associated with different distributions, as generally assumed in ecological studies.

Electron emission from the boundary is ubiquitous in a capacitively coupled plasma (CCP) and precipitates nonnegligible influence on the discharge properties. Here, we present Particle-in-Cell/Monte Carlo Collision simulation of an Ohmic-dominant heating mode of the capacitively coupled plasma, where the stochastic heating vanishes and only Ohmic heating sustains the discharge due to sheath inversion by boundary electron emission. The inverted CCP features negative sheath potential without Bohm presheath, hence excluding plasma heating due to sheath edge oscillation. The particle and energy transport of the proposed heating mode is analyzed. The influence of boundary electron emission flux, source voltage, and neutral pressure on the transition between classic and Ohmic-dominant CCP heating modes is shown with designated simulation scans. A modified inverse sheath–plasma coupling due to excessive ionization is discovered. In the end, key indicators of the proposed heating mode in plasma diagnostics are provided for future experimental verifications.

Questa tesi si focalizza sui problemi di misura della dissomiglianza tra distribuzioni di variabili economiche rilevanti e sulle implicazioni in termini di disuguaglianza di opportunità. I criteri di uguaglianza di opportunità hanno ricevuto una crescente attenzione in letteratura cosi come tra i policymakers, poiché definiscono i principi etici su cui si fondano le politiche distributive e redistributive di una varietà di risultati economici tra i differenti gruppi sociali. Si dimostra in questa tesi che le metodologie di valutazione basate su dei criteri di uguaglianza di opportunità appoggiano sempre su dei confronti del grado di dissomiglianza tra distribuzioni condizionate. Si derivano quindi dei criteri empirici che implementano questi confronti. Nel primo capitolo si propone una caratterizzazione assiomatica dell’ordinamento parziale di dissomiglianza per distribuzioni discrete di gruppi sociali tra classi di risultati economici. Si dimostra che: quando le classi non sono ordinate i confronti di dissomiglianza sono rappresentati dall’ordinamento di maggiorizzazione di matrici, e sono implementati verificando l’inclusione degli zonotopi associati a queste matrici; quando le classi sono ordinate, il criterio di dissomiglianza richiede un numero finito di confronti di maggiorizzazione alla Lorenz tra le proporzioni dei diversi gruppi, calcolate a differenti livelli di aggregazione della popolazione totale distribuita tra le classi di realizzazioni. Nel secondo capitolo si dimostra la rilevanza degli ordinamenti di dissomiglianza nello studio della segregazione a livello individuale. In questo capitolo è caratterizzata una famiglia di indicatori di segregazione e si propone uno studio approfondito di uno di essi, l’indice di Gini Exposure, anche utilizzando dei dati italiani. L’ultimo capitolo presenta invece un criterio innovativo di valutazione del grado di uguaglianza di opportunità garantito da una società prima e dopo l’introduzione di una certa policy. Questo confronto dinamico si basa su un principio semplice: l’uguaglianza di opportunità è verificata quando, all’interno di una data classe di preferenze, non c’è accordo nello stabilire quale sia il gruppo più svantaggiato tra tutti i confronti a coppie. Le variazioni nel grado di (mancanza di) consenso sull’esistenza e sulla dimensione di un vantaggio economico dovute al cambio di regime di policy sono utilizzate per caratterizzare il criterio dinamico di uguaglianza di opportunità. Sono inoltre discusse le restrizioni più appropriate per questo modello, cosi come una serie di procedure di aggregazione delle valutazioni. Si dimostra inoltre che il criterio dinamico di uguaglianza di opportunità è identificato nella classe di preferenze dipendenti dai ranghi, ed è quindi testabile ricorrendo all’ordinamento di dominanza stocastica inversa. Sono inoltre discussi dei risultati innovativi riguardanti l’inferenza di quest’ultimo ordinamento. Due applicazioni con dati francesi dimostrano la maggior incidenza, in termini di uguaglianza di opportunità, di politiche di istruzione che influenzano la carriera scolastica degli studenti sin dal suo inizio.
This thesis focuses on the measurement of dissimilarity in the distribution of relevant economic attributes and inequality of opportunity. Equality of opportunity has gained popularity for defining the relevant equalitarian objective for the distribution of a broad range of social and economic outcomes among social groups. I show that equality of opportunity concerns in policy evaluation always rely on dissimilarity comparisons between conditional distributions, and I provide empirically testable criteria to implement these comparisons. In the first chapter, I characterize axiomatically the dissimilarity partial order for discrete conditional distributions of groups across outcome classes. I prove that, when classes are permutable, dissimilarity is rationalized by matrix majorization and implemented by checking Zonotopes inclusion, while when classes are ordered the dissimilarity criterion resorts on a finite number of Lorenz majorization comparisons among groups' proportions, performed at different cumulation stages of the overall population. In the second chapter, I discuss the relevance of the dissimilarity partial order for the study of segregation at individual level. I fully characterize a well defined family of segregation indicators and I study one of them, the Gini exposure index, by using Italian data. The final chapter presents the equalization of opportunity criterion for outcome achievements. The guiding principle is that equality of opportunity is reached if there is no consensus, for a given class of preferences, in determining the disadvantaged group out of pairwise comparisons. I use the changes in (lack of) consensus on the existence and on the extent of this type of disadvantage to characterize the equalization of opportunity criterion. Meaningful restrictions and possible aggregation procedures are also discussed. I motivate that this criterion is identified within the rank dependent utility model, and I provide innovative inference results for inverse stochastic dominance to test it. Two applications on French data illustrate the equalizing impact of educational policies taking place early in students life.

Among the novel sources of nonclassical light that have recently been studied are a number of novel lasers. Conventional laser theory describes a classical stochastic field. I show that with a change in the standard operating conditions the conventional laser model produces nonclassical fields. Deviations from the classical description in standard laser theory are small by some inverse power of the threshold photon number. Operating conditions are designed to make stimulated emission dominant; thus laser cavities are good cavities that store photons and give a high threshold photon number. Low threshold photon numbers are achieved in bad cavities and most readily in a single-atom bad-cavity system. Such a system trades phase coherence for reduced intensity noise.

Energy harvesting (EH), which scavenges electric power from ambient, otherwise wasted, energy sources, has received considerable attention for the purpose of powering wireless sensor networks and low-power electronics. Among ambient energy sources, widely available vibration energy can be converted into electrical energy using piezoelectric materials that generate an electrical potential in response to applied mechanical stress. As a basis for designing a piezoelectric energy harvester, an analytical model should be developed to estimate electric power under a given vibration condition. Many analytical models under the assumption of the deterministic excitation cannot deal with random nature in vibration signals, although the randomness considerably affects variation in harvestable electrical energy. Thus, predictive capability of the analytical models is normally poor under random vibration signals. Such a poor power prediction is mainly caused by the variation of the dominant frequencies and their peak acceleration levels. This paper thus proposes the three-step framework of the stochastic piezoelectric energy harvesting analysis under non-stationary random vibrations. As a first step, the statistical time-frequency analysis using the Wigner-Ville spectrum was used to estimate a time-varying power spectral density (PSD) of an input random excitation. The second step is to employ an existing electromechanical model as a linear operator for calculating the output voltage response. The final step is to estimate a time-varying PSD of the output voltage response from the linear relationship. Then, the expected electric power was estimated from the autocorrelation function that is inverse Fourier transform of the time-varying PSD of the output voltage response. Therefore, the proposed framework can be used to predict the expected electric power under non-stationary random vibrations in a stochastic manner.