# Predictive Model Assessment with a Probability Integral Transform Histogram

### Description

The function allows a probabilistic calibration check with a Probability Integral Transform (PIT) histogram.

### Usage

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### Arguments

`object` |
an object of class |

`bins` |
number of bins in the histogram. Default value is 10. |

`response` |
integer vector. Vector of observed values. |

`pred` |
numeric vector. Vector of predicted values. |

`distr` |
character giving the conditional distribution. Currently implemented are the Poisson ( |

`distrcoefs` |
numeric vector of additional coefficients specifying the conditional distribution. For |

`...` |
additional arguments passed to |

### Details

A PIT histogram is a tool for evaluating the statistical consistency between the probabilistic forecast and the observation. The predictive distributions of the observations are compared with the actual observations. If the predictive distribution is ideal the result should be a flat PIT histogram with no bin having an extraordinary high or low level. For more information about PIT histograms see the references listed below.

### Author(s)

Philipp Probst and Tobias Liboschik

### References

Christou, V. and Fokianos, K. (2013) On count time series prediction. *Journal of Statistical Computation and Simulation* (published online), http://dx.doi.org/10.1080/00949655.2013.823612.

Czado, C., Gneiting, T. and Held, L. (2009) Predictive model assessment for count data. *Biometrics* **65**, 1254–1261, http://dx.doi.org/10.1111/j.1541-0420.2009.01191.x.

Gneiting, T., Balabdaoui, F. and Raftery, A.E. (2007) Probabilistic forecasts, calibration and sharpness. *Journal of the Royal Statistical Society: Series B (Statistical Methodology)* **69**, 243–268, http://dx.doi.org/10.1111/j.1467-9868.2007.00587.x.

### See Also

`tsglm`

for fitting a GLM for time series of counts.

`marcal`

and `scoring`

for other predictive model assessment tools.

### Examples

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