1,721,080 research outputs found
Probability and Statistics Questions and Tests : a critical analysis
No full textIn probability and statistics courses, a popular method for the evaluation of the students is to assess them using multiple choice tests. The use of these tests allows to evaluate certain types of skills such as fast response, short-term memory, mental clarity and ability to compete. In our opinion, the verification through testing can certainly be useful for the analysis of certain aspects, and to speed up the process of assessment, but we should be aware of the limitations of such a standardized procedure and then exclude that the assessments of pupils, classes and schools can be reduced to processing of test results. To prove this thesis, this article argues in detail the main test limits, presents some recent models which have been proposed in the literature and suggests some alternative valuation methods.
Quesiti e test di Probabilità e Statistica: un'analisi critica
Nei corsi di Probabilità e Statistica, un metodo molto diffuso per la valutazione degli studenti consiste nel sottoporli a quiz a risposta multipla. L'uso di questi test permette di valutare alcuni tipi di abilità come la rapidità di risposta, la memoria a breve termine, la lucidità mentale e l'attitudine a gareggiare. A nostro parere, la verifica attraverso i test può essere sicuramente utile per l'analisi di alcuni aspetti e per velocizzare il percorso di valutazione ma si deve essere consapevoli dei limiti di una tale procedura standardizzata e quindi escludere che le valutazioni di alunni, classi e scuole possano essere ridotte a elaborazioni di risultati di test. A dimostrazione di questa tesi, questo articolo argomenta in dettaglio i limiti principali dei test, presenta alcuni recenti modelli proposti in letteratura e propone alcuni metodi di valutazione alternativi.
Parole Chiave: item responce theory, valutazione, test, probabilit
Dealing with randomness and vagueness in business and management sciences: the fuzzy-probabilistic approach as a tool for the study of statistical relationships between imprecise variables
Full text linkIn practical applications relating to business and management sciences, there are many variables that, for their own nature, are better described by a pair of ordered values (i.e. financial data). By summarizing this measurement with a single value, there is a loss of information; thus, in these situations, data are better described by interval values rather than by single values. Interval arithmetic studies and analyzes this type of imprecision; however, if the intervals has no sharp boundaries, fuzzy set theory is the most suitable instrument. Moreover, fuzzy regression models are able to overcome some typical limitation of classical regression because they do not need the same strong assumptions. In this paper, we present a review of the main methods introduced in the literature on this topic and introduce some recent developments regarding the concept of randomness in fuzzy regression
Aggregate Bound Choices about Random and Nonrandom Goods Studied via a Nonlinear Analysis
Full text linkIn this paper, bound choices are made after summarizing a finite number of alternatives.
This means that each choice is always the barycenter of masses distributed over a finite set of
alternatives. More than two marginal goods at a time are not handled. This is because a quadratic
metric is used. In our models, two marginal goods give rise to a joint good, so aggregate bound
choices are shown. The variability of choice for two marginal goods that are the components of a
multiple good is studied. The weak axiom of revealed preference is checked and mean quadratic
differences connected with multiple goods are proposed. In this paper, many differences from vast
majority of current research about choices and preferences appear. First of all, conditions of certainty
are viewed to be as an extreme simplification. In fact, in almost all circumstances, and at all times, we
all find ourselves in a state of uncertainty. Secondly, the two notions, probability and utility, on which
the correct criterion of decision-making depends, are treated inside linear spaces over R having a
different dimension in accordance with the pure subjectivistic point of vie
Tensors Associated with Mean Quadratic Differences Explaining the Riskiness of Portfolios of Financial Assets
Full text linkBound choices such as portfolio choices are studied in an aggregate fashion using an
extension of the notion of barycenter of masses. This paper answers the question of whether such an
extension is a natural fashion of studying bound choices or not. Given n risky assets, the question of
why it is appropriate to treat only two risky assets at a time inside the budget set of the decision-maker
is handled in this paper. Two risky assets are two goods. They are two marginal goods. The question
of why they always give rise to a joint good inside the budget set of the decision-maker is addressed
by this research work. A single risky asset is viewed as a double one using four nonparametric joint
distributions of probability. The variability of a joint distribution of probability always depends on
the state of information and knowledge associated with a given decision-maker. For this reason, two
variability tensors are defined to identify the riskiness of the same risky asset. A multilinear version
of the Sharpe ratio is shown. It is based on tensors. After computing the expected return on an n-risky
asset portfolio, its riskiness is obtained using mean quadratic differences developed through tensor
Finite geometric spaces, Steiner systems and cooperative games
No full textSome relations between finite geometric spaces and cooperative games are considered. The games associated to Steiner systems, in particular projective and affine planes, are considered. The properties of winning and blocking coalitions are investigated
Jensen’s Inequality Connected with a Double Random Good
No full textIn this paper, we define a multiple random good of order 2 denoted by
X12 whose possible values are of a monetary nature. A two-risky asset portfolio is a multiple random good of order 2. It is firstly possible to establish
its expected return by using a linear and quadratic metric. We secondly establish the expected return on X12 denoted by P(X12) by using a multilinear
and quadratic metric. An extension of the notion of mathematical expectation of X12 is carried out by using the notion of α-norm of an antisymmetric
tensor of order 2. An extension of the notion of variance of X12 denoted by
Var(X12) is shown by using the notion of α-norm of an antisymmetric tensor of order 2 based on changes of origin. An extension of the notion of
expected utility connected with X12 is considered. An extension of Jensen’s
inequality is shown as well. We focus on how the decision-maker maximizes
the expected utility connected with multiple random goods of order 2 being
chosen by her under conditions of uncertainty and riskines
The consumer's demand functions defined to study contingent consumption plans. Summarized probability distributions: a mathematical application to contingent consumption choices
Full text linkGiven two probability distributions expressing returns on two single risky assets of a
portfolio, we innovatively defne two consumer’s demand functions connected with two
contingent consumption plans. This thing is possible whenever we coherently summarize
every probability distribution being chosen by the consumer. Since prevision choices are
consumption choices being made by the consumer inside of a metric space, we show that
prevision choices can be studied by means of the standard economic model of consumer
behavior. Such a model implies that we consider all coherent previsions of a joint distri-
bution. They are decomposed inside of a metric space. Such a space coincides with the
consumer’s consumption space. In this paper, we do not consider a joint distribution only.
It follows that we innovatively defne a stand-alone and double risky asset. Diferent sum-
mary measures of it characterizing consumption choices being made by the consumer can
then be studied inside of a linear space over R. We show that it is possible to obtain difer-
ent summary measures of probability distributions by using two diferent quadratic metrics.
In this paper, our results are based on a particular approach to the origin of the variability
of probability distributions. We realize that it is not standardized, but it always depends on
the state of information and knowledge of the consumer
Combining unsupervised and supervised learning techniques for enhancing the performance of functional data classifiers
Full text linkThis paper offers a supervised classification strategy that combines functional data analysis with unsupervised and supervised classification methods. Specifically, a two-steps classification technique for high-dimensional time series treated as functional data is suggested. The first stage is based on extracting additional knowledge from the data using unsupervised classification employing suitable metrics. The second phase applies functional supervised classification of the new patterns learned via appropriate basis representations. The experiments on ECG data and comparison with the classical approaches show the effectiveness of the proposed technique and exciting refinement in terms of accuracy. A simulation study with six scenarios is also offered to demonstrate the efficacy of the suggested strategy. The results reveal that this line of investigation is compelling and worthy of further development
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