Page 63 - Contributed Paper Session (CPS) - Volume 5

CPS886 Marcelo Bourguignon
likelihood ratio test for varying precision is significant at the level of 5% (p-
value =0.0412), for the BP regression model with the structure above.

2 2

1 1

0 0

−1 −1

−2 −2
200
100 Nitrogen(pounds/acre) 300 100 200 300
Phosphate(pounds/acre)

Figure 2: Nitrogen against the residuals () and phosphate against the

residuals ().

5. Concluding remarks
In this paper, we have developed a new parameterized BP distribution in
terms of the mean and precision parameters. The variance function of the
proposed model assumes a quadratic form. Furthermore, we have proposed a
new regression model for modelling asymmetric positive real data. An
advantage of the proposed BP regression model in relation to the GA and RBS
regression models is its flexibility for working with positive real data with high
skewness, i.e., the proposed model may serve as a good alternative to the GA
and RBS regression models for modelling asymmetric positive real data.
Maximum likelihood inference is implemented for estimating the model
parameters and its good performance has been evaluated by means of Monte
Carlo simulations. Furthermore, we provide closedform expressions for the
score function and for Fisher’s information matrix. Diagnostic tools have been
obtained to detect locally influential data in the maximum likelihood estimates.
We have proposed two types of residuals for the proposed model and
conducted a simulation study to establish their empirical properties in order
to evaluate their performances. Finally, an application using a real data set was
presented and discussed.

52 | I S I W S C 2 0 1 9