fitPP.fun {NHPoisson} | R Documentation |

This function fits by maximum likelihood a NHPP where the intensity *λ(t)*
is formulated as a function of covariates. It also calculates and plots
approximate confidence intervals for *λ(t)*.

fitPP.fun(covariates = NULL, beta, posE = NULL, inddat = NULL, POTob = NULL, namcovariates = NULL, n = NULL, tind = "TRUE", tim = NULL, modCI = "TRUE", CIty = "Delta", clevel = 0.95, tit = '', modSim = "FALSE", dplot = TRUE, xlegend = "topleft")

`covariates` |
Matrix of the covariates to be included in the linear predictor of the PP intensity (each column is a covariate). |

`beta` |
Numeric vector of the initial values for the estimation of
the |

`posE` |
Optional (see Details section). Numeric vector of the position of the PP occurrence points. |

`inddat` |
Optional (see Details section). Index vector equal to 1 for the observations used in the estimation process By default, all the observations are considered. |

`POTob` |
Optional (see Details section). List with elements T and thres
that defines the PP resulting from a POT approach;
see |

`namcovariates` |
Optional. Vector of the names of the variables in covariates. |

`n` |
Optional. Number of observations in the observation period; it is only neccessary if POTob, inddat and covariates are NULL. |

`tind` |
Logical flag. If it is TRUE, an independent term is fitted in the linear predictor. |

`tim` |
Optional. Time vector of the observation period. By default, a vector 1,...n is considered. |

`modCI` |
Logical flag. If it is TRUE, confidence intervals
for |

`CIty` |
Label indicating the method to calculate the approximate
confidence intervals for |

`clevel` |
Confidence level of the confidence intervals. |

`tit` |
Character string. A title for the plot. |

`modSim` |
Logical flag. If it is FALSE, information on the estimation process is shown on the screen. For simulation process, the option TRUE should be prefered. |

`dplot` |
Logical flag. If it is TRUE, the fitted intensity is plotted. |

`xlegend` |
Label indicating the position where the legend on the graph will be located. |

A Poisson process (PP) is usually specified by a vector containing the occurrence
points of the process *(t_i)_{i=1}^k*, (argument posE).
Since PP are often used in the framework of POT models, `fitPP.fun`

also
provides the possibility of
using as input the series of the observed values in a POT model
*(x_i)_{i=1}^n* and the threshold used to define the extreme events
(argument POTob).

In the case of PP defined by a POT approach,
the observations of the extreme events which are
not defined as the occurrence point are not considered in the estimation. This is done
through the argument inddat, see `POTevents.fun`

. If the input is provided via argument POTob, index inddat
is calculated automatically. See Coles (2001) for more details on the POT approach.

The estimation of the *β* covariance matrix is based on the
asymptotic distribution of the MLE *\hat β*, and calculated as the inverse of the hessian.
Confidence intervals for *λ(t)* can be calculated using two approaches,
the delta method or a transformation of the confidence interval for the
linear predictor *ν(t)=\textbf{X(t)} β*.
The interval for *ν(t)* is also based on the asymptotic properties of the
MLE *\hat ν(t)*. See Casella (2002) for more details on ML theory and delta method.

A list with elements

`llik ` |
Value of the loglikelihood function. |

`npar ` |
Number of estimated parameters. |

`beta ` |
Vector of the MLE |

`inddat ` |
Input argument. |

`VARbeta ` |
Covariance matrix of the |

`lambdafit ` |
Vector of the fitted intensity |

`LIlambda ` |
Vector of lower extremes of the CI |

`LUlambda ` |
Vector of upper extremes of the CI. |

`posE ` |
Input argument. |

`namcovariates ` |
Input argument. |

`tit ` |
Input argument. |

`tind ` |
Input argument. |

A homogeneous Poisson process (HPP) can be fitted as a particular case, using an intensity defined by only an independent term and no covariates.

Coles, S. (2001). *An introduction to statistical modelling of extreme
values.* Springer.

Casella, G. and Berger, R.L., (2002). *Statistical inference.* Brooks/Cole.

`POTevents.fun`

, `globalval.fun`

,
`VARbeta.fun`

, `CItran.fun`

, `CIdelta.fun`

#model fitted using as input posE and inddat and no confidence intervals data(BarTxTn) covB<-cbind(cos(2*pi*BarTxTn$dia/365), sin(2*pi*BarTxTn$dia/365), BarTxTn$TTx,BarTxTn$Txm31,BarTxTn$Txm31**2) BarEv<-POTevents.fun(T=BarTxTn$Tx,thres=318, date=cbind(BarTxTn$ano,BarTxTn$mes,BarTxTn$dia)) mod1B<-fitPP.fun(tind='TRUE',covariates=covB, posE=BarEv$Px, inddat=BarEv$inddat, tit='BAR Tx; cos, sin, TTx, Txm31, Txm31**2', beta=c(-100,1,10,0,0,0)) #model fitted using as input a list from POTevents.fun and with confidence intervals tiempoB<-BarTxTn$ano+rep(c(0:152)/153,55) mod2B<-fitPP.fun(tind='TRUE',covariates=covB, POTob=list(T=BarTxTn$Tx, thres=318), tim=tiempoB, tit='BAR Tx; cos, sin, TTx, Txm31, Txm31**2', beta=c(-100,1,10,0,0,0),CIty='Transf',modCI=TRUE, modSim=TRUE)

[Package *NHPoisson* version 1.0 Index]