## Han et al. (2009) Function

### Description:

*Dimensions: 2*

This function has one quantitative and one qualitative input variable. The plot above shows the function for all three possible values of the qualitative z-variable.

Zhou et al. (2011) and Han et al. (2009) use this function for three different scenarios, each time using a different

**b**-vector (b

_{01}, b

_{02}, b

_{03}, b

_{11}, b

_{12}, b

_{13}, b

_{21}, b

_{22}, b

_{23}). For each scenario, the elements of the

**b**-vector are drawn from Normal distributions with a standard deviation of 0.01 and the following expected values:

(1, 0, -1, 6, 4, 5, -6, -6, -6),

(1, 0, -1, 0, 6, 5, 2, -6, -6) and

(1, 0, -1, 6, 6, 6, -6, -6, -6).

The above plot is given for the first vector in the list.

### Input Domain:

The quantitative variable x is in [0, 1], and the qualitative variable z takes on one of the three possible values in {1, 2, 3}.### Code:

### References:

Han, G., Santner, T. J., Notz, W. I., & Bartel, D. L. (2009). Prediction for computer experiments having quantitative and qualitative input variables. *Technometrics, 51*(3). 51, 278-288.

Zhou, Q., Qian, P. Z., & Zhou, S. (2011). A simple approach to emulation for computer models with qualitative and quantitative factors. *Technometrics, 53*(3).

For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.

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