Modelling based on the Birnbaum-Saunders distribution has received considerable attention in recent years. In this article, we introduce a new approach for Birnbaum-Saunders regression models, which allows us to analyze data in their original scale and to model non-constant variance. In addition, we propose four types of residuals for these models and conduct a simulation study to establish which of them has a better performance. Moreover, we develop methods of local influence by calculating the normal curvatures under different perturbation schemes. Finally, we perform a statistical analysis with real data by using the approach proposed in the article. This analysis shows the potentiality of our proposal.
The Birnbaum-Saunders (BS) distribution is receiving considerable attention. We propose a methodology for inventory logistics that allows demand data with zeros to be modeled by means of a new discrete-continuous mixture distribution, which is constructed by using a probability mass at zero and a continuous component related to the BS distribution. We obtain some properties of the new mixture distribution and conduct a simulation study to evaluate the performance of the estimators of its parameters. The methodology for stochastic inventory models considers also financial indicators. We illustrate the proposed methodology with two real-world demand data sets. It shows its potential, highlighting the convenience of using it by improving the contribution margins of a Chilean food industry.Appl. Stochastic Models Bus. Ind. 2016, 32 74-89 V. LEIVA ET AL.Based on its genesis, the BS distribution considers the duration of a counting period (daily or weekly), which may be switched without collecting extra data, among other properties. It permits the BS distribution to have theoretical arguments for modeling demand data (see details in [30]). Rojas et al. [5] carried out an empirical study in which the BS distribution shows to be a good model to describe the demand for different food products.Despite the wide use of the BS distribution, it is well defined only for positive values. This makes that data sets that contain zero values, such as demand data, cannot be modeled with this distribution. Thus, in the presence of zero values, we should adapt the BS distribution to allow these values to be captured in the modeling. A way for deriving a model suitable to data on the interval [0, ∞) is using a mixture distribution of two components: a BS distribution (continuous component) and a degenerate distribution at a zero value (discrete component). It is well known that the mixture models are powerful and popular tools to generate flexible distributions with good properties [31,32].Santos-Neto et al.[33] proposed a reparameterized BS (RBS) distribution, which has several interesting properties (see also [25,34]). For example, one of the two parameters of the RBS distribution is its mean and the other one a precision parameter. This allows us to make different statistical analyses mimicking the case of the normal distribution, often used to model demand data, but now in an asymmetric framework, which is closer to reality of this kind of data. Then, we use the RBS distribution and a degenerate distribution at zero to construct the demand semi-continuous mixture model. We name this new class of models as the zero-adjusted RBS (ZARBS) distribution, because they are in the line of zero-adjusted models ([35-38]).The main objectives of this paper are as follows: (i) to propose the new ZARBS distribution and (ii) to introduce a methodology for inventory models based on this distribution including financial indicators. We derive several features of the ZARBS distribution and estimate its parameters. We use this distribution because it a...
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