Centre of Statistics and its Applications

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Organizational Unit

Publications

Skewness into the product of two normally distributed variables and the risk consequences

Publication . Oliveira, Amilcar; Oliveira, Teresa A.; Seijas-Macias, J. Antonio

The analysis of skewness is an essential tool for decision-making since it can be used as an indicator on risk assessment. It is well known that negative skewed distributions lead to negative outcomes, while a positive skewness usually leads to good scenarios and consequently minimizes risks. In this work the impact of skewness on risk analysis will be explored, considering data obtained from the product of two normally distributed variables. In fact, modelling this product using a normal distribution is not a correct approach once skewness in many cases is different from zero. By ignoring this, the researcher will obtain a model understating the risk of highly skewed variables and moreover, for too skewed variables most of common tests in parametric inference cannot be used. In practice, the behaviour of the skewness considering the product of two normal variables is explored as a function of the distributions parameters: mean, variance and inverse of the coefficient variation. Using a measurement error model, the consequences of skewness presence on risk analysis are evaluated by considering several simulations and visualization tools using R software.

2016-02Journal article

Open access

The uniform distribution product: an approach to the (Q,r) inventory model using R

Publication . Oliveira, Amilcar; Oliveira, Teresa A.; Seijas-Macias, J. Antonio

In this work the probability density function (PDF) for the product of two uniformly distributed random variables is explored under the implementation of a new procedure in R language. Based on the Rohatgi theorem for the theoretical form of the product, different possibilities for the range of values of the limits of both distributions are considered. As an application, the management of a (Q,r) inventory model with the presence of lead-time and uniform demand forecasts is considered. Solution to this model looks up to minimize the total costs through the variables Q (reorder quantity) and r (the reorder point), and not always exists an analytical solution of the problem. We show a graphical procedure for the simulation results and a more exactly analytical solution. Implementation in R is straightforward.

2017-01-05Journal article

Restricted access

An overview of the systemic risk measures

Publication . Basílio, Jorge; Oliveira, Amilcar; Mahmoudvand, Rahim

Systemic risk is a specific type of risk that refers to the risk of an complex system to be affect or even collapse due to individual action taken by the agents that compounds that complex system. The goals of this work is based on an axiomatic approach establish a critic description of the most relevant methods used in the determination of systemic risk and identify advantages and disadvantages associated to those methods.

2020-11-24Conference object

Restricted access

Statistics and big data: different perspectives

Publication . Oliveira, Teresa A. ; Nunes, Sandra; Oliveira, Amilcar

Big Data has become the new slang in the world of information collection and analysis. The researches we conduct and the data we collect continue to grow, due to rapidly expansion of technology. Disciplines such as Computer Science, Engineering, and Statistics play a key role in the analysis of big data, each with its specificity but all equally important, an opinion that is not shared by all, being the Statistic considered the weakest link. This work attempts to show that Statistics have a distinct and essential role in this new world of Big Data, showing that Statistics and Big Data denote a crucial union. We will start with a brief introduction to Big Data and the several existing definitions.

2020-11-24Conference object

Restricted access

Product of two normal variables: an historical review

Publication . Seijas-Macias, J. Antonio; Oliveira, Amilcar; Oliveira, Teresa A.

This paper presents a study of the evolution the study of the product of two normally distributed variables. From first approaches in the middle of the 20th Century until the most recent ones from this decade. Nowadays, existence of an unique formula for the product was not proved. Partial results using di erent approaches: Bessel Functions, Numerical Integration, Pearson Type Function.

2020-11-24Conference object

Restricted access