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- Skewness into the product of two normally distributed variables and the risk consequencesPublication . Oliveira, Amilcar; Oliveira, Teresa A.; Seijas-Macias, J. AntonioThe 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.
- The uniform distribution product: an approach to the (Q,r) inventory model using RPublication . Oliveira, Amilcar; Oliveira, Teresa A.; Seijas-Macias, J. AntonioIn 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.