# Non-randomized Probability Integral Transformation

### Description

Functions to produce the non-randomized probability integral transform (PIT) to check the adequacy of the distributional assumption of the GLARMA model.

### Usage

1 2 | ```
glarmaPredProb(object)
glarmaPIT(object, bins = 10)
``` |

### Arguments

`object` |
An object of class |

`bins` |
Numeric; the number of bins used in the PIT. |

### Details

These functions are used for the assessment of predictive distributions in discrete data. They obtain the predictive probabilities and the probability integral transformation for a fitted GLARMA model.

### Value

`glarmaPredProb`

returns a list with values:

`upper` |
the predictive cumulative probabilities used as the upper bound for computing the non-randomized PIT. |

`lower` |
the predictive cumulative probabilities used as the lower bound for computing the non-randomized PIT. |

`glarmaPIT`

returns a list with values:

`upper` |
the predictive cumulative probabilities used as the upper bound for computing the non-randomized PIT. |

`lower` |
the predictive cumulative probabilities used as the lower bound for computing the non-randomized PIT. |

`conditionalPIT` |
the conditional probability integral transformation given the observed counts. |

`PIT` |
the probability integral transformation. |

### Author(s)

"David J. Scott" <d.scott@auckland.ac.nz> and "Cenanning Li" <cli113@aucklanduni.ac.nz>

### References

Czado, Claudia and Gneiting, Tilmann and Held, Leonhard (2009)
Predictive model assessment for count data. *Biometrics*,
**65**, 1254–1261.

Jung, Robert.C and Tremayne, A.R (2011) Useful models for time series
of counts or simply wrong ones? *Advances in Statistical
Analysis*, **95**, 59–91.

### Examples

1 2 3 4 5 6 7 8 9 | ```
### Example from Davis, Dunsmuir Wang (1999)
## MA(1,2,5), Pearson Residuals, Fisher Scoring
data(Polio)
y <- Polio[, 2]
X <- as.matrix(Polio[, 3:8])
glarmamod <- glarma(y, X, thetaLags = c(1,2,5), type = "Poi", method = "FS",
residuals = "Pearson", maxit = 100, grad = 2.22e-16)
glarmaPredProb(glarmamod)
glarmaPIT(glarmamod)
``` |