## Morokoff & Caflisch (1995) Function 1

### Description:

*Dimensions: d*

The exact value of the integral with this function as an integrand is 1 (Gerstner & Griebel, 1998). The variance and variation are easily obtained, because the function is formed from the products of one-dimensional functions.

Kucherenko et al. (2011) classify it as a Type B function, meaning that it has dominant low-order terms and a small effective dimension.

### Input Domain:

The function is integrated over x_{i}∈ [0, 1], for all i = 1, …, d.

### Code:

### References:

Gerstner, T., & Griebel, M. (1998). Numerical integration using sparse grids. *Numerical algorithms, 18*(3-4), 209-232.

Kucherenko, S., Feil, B., Shah, N., & Mauntz, W. (2011). The identification of model effective dimensions using global sensitivity analysis. *Reliability Engineering & System Safety, 96*(4), 440-449.

Levitan, Y. L., Markovich, N. I., Rozin, S. G., & Sobol, I. Y. M. (1988). Short communications on quasirandom sequences for numerical computations. *USSR Computational Mathematics and Mathematical Physics, 28*(3), 88-92.

Morokoff, W. J., & Caflisch, R. E. (1995). Quasi-monte carlo integration. *Journal of computational physics, 122*(2), 218-230.

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

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