# Gauss-Hermite integration points

### Description

Calculate Gaussian Quadrature points for the Normal distribution using the abscissas and weights for Hermite integration.

### Usage

1 | ```
gqz(numnodes=20, minweight=0.000001)
``` |

### Arguments

`numnodes` |
theoretical number of quadrature points. |

`minweight` |
locations with weights that are less than this value will be omitted. |

### Details

The conversion of the locations and weights is given in Lindsey (1992,
page 169:3) and Skrondal & Rabe-Hesketh (2004, page 165:1).
The argument numnodes is the theoretical number of quadrature points,
locations with weights that are less than the argument `minweight`

will
be omitted. The default value of `minweight=0.000001`

returns 14 masspoints
for the default `numnodes=20`

as in Aitkin, Francis & Hinde (2005).

### Value

A list with two vectors:

`location` |
locations of mass points |

`weight` |
masses |

### Author(s)

Nick Sofroniou (2005)

### References

Aitkin, M., Francis, B. and Hinde, J. (2005). Statistical Modelling in GLIM 4. Second Edition, Oxford Statistical Science Series, Oxford, UK.

Lindsey, J. K. (1992). The Analysis of Stochastic Processes using GLIM. Berlin: Springer-Verlag.

Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized latent variable modelling. Boca Raton: Chapman and Hall/CRC.

### See Also

`alldist`

, `allvc`

### Examples

1 2 3 4 5 | ```
gqz(20, minweight=1e-14)
# gives k=20 GH integration points. These are used in alldist
# and allvc as fixed mass point locations when working with
# option random.distribution='gq', and serve as EM starting points
# otherwise.
``` |

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