Description Usage Arguments Details Value References See Also Examples

This function generates a vector of two (or three) independent homogeneous or nonhomogeneous processes conditionally on the first one, by simulating the second (and the third) process using a parametric model (Poisson processes or Neyman-Scott cluster processes).

It also calculates the set of close points and the mean distance in the generated vector, for each point *t_{x_i}*
in the first process.

`DistSimfix`

allows to fix a seed in the generation process.

1 2 3 4 5 6 7 | ```
DistSim(posx, NumProcess=2, type = "Poisson", lambdaMarg = NULL,
lambdaParent = NULL, lambdaNumP=NULL, dist = "normal", sigmaC = 1,
minC = -1, maxC = 1, PA = FALSE,info=FALSE,...)
DistSimfix(posx, NumProcess=2, type = "Poisson", lambdaMarg = NULL,
lambdaParent = NULL,lambdaNumP=NULL, dist = "normal", sigmaC = 1,
minC = -1, maxC = 1, PA = FALSE,info=FALSE,fixed.seed=1,...)
``` |

`posx` |
Numeric vector. Position of the occurrence points in the first process. |

`NumProcess` |
Optional. Integer equal to 2 or 3, the number of processes in the vector. |

`type` |
Optional. Label "Poisson" or "PoissonCluster". Type of point processes to be generated. Up to now, only two types are available: Poisson processes ("Poisson") and Neyman-Scott cluster processes ("PoissonCluster"). |

`lambdaMarg` |
Two-column matrix. Only used when |

`lambdaParent` |
Numeric vector. Only used when |

`lambdaNumP` |
Numeric vector (length |

`dist` |
Optional. Label "normal" or "uniform". Only used when |

`sigmaC` |
Optional. Numeric vector. Only used when |

`minC` |
Optional. Numeric vector. Only used when |

`maxC` |
Optional. Numeric vector. Only used when |

`PA` |
Optional. Logical flag. If it is TRUE, the close point relation is broadened by including the previous and the following points to the overlapping intervals. |

`info` |
Optional. Logical flag. If it is TRUE, information about the generated points is shown on the screen and dotcharts and bivariate charts of the occurrence points of the three processes are displayed. |

`fixed.seed` |
Optional. Only available in |

`...` |
Further arguments to be passes to the functions |

This function is mainly used in the application of a parametric bootstrap approach to generate a pair of independent
processes with the same marginal distributions than the observed ones. To that aim, the first process is fixed and the others are generated using a parametric model.
These processes are used for example to build a test to assess the independecne
between two or three processes, see `TestIndNH`

.

Two types of processes (Poisson, "Poisson", and Neyman-Scott cluster
processes,"PoissonCluster") can be generated. Generation of nonhomogeneous Poisson processes is done using the inversion algorithm, see
`simNHPc`

. For generation of Neyman-Scott processes, see `IndNHNeyScot`

.

The function also calculates the set of close points and the mean distance
for each point *t_{x_i}* in the first process, in the new generated vector of processes.

The lenght of the period where the processes are generated is determined by the length of
the argument `lambdaParent`

or the number of rows of `lambdaMarg`

. Homogenous processes are generated if the intensity vectors in `lambdaParent`

or in
`lambdaMarg`

are constant (that is if all the values in the vector are equal).

If a seed must be fixed in the generation process, function `DistSimfix`

has to be used.
The functions `DistSim`

and `DistSimfix`

are similar, the difference is that the first one uses a
random seed to generate the processes, while the second one uses a seed set by the argument `fixed.seed`

.

`DistTri` |
Vector of the mean distances of each point |

Abaurrea, J. Asin, J. and Cebrian, A.C. (2015). A Bootstrap Test of Independence Between Three Temporal Nonhomogeneous Poisson Processes
and its Application to Heat Wave Modeling. *Environmental and Ecological Statistics*, 22(1), 127-144.

`TestIndNH`

, `DistObs`

, `IndNHNeyScot`

,
`simNHPc`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
#Calculation of the distances in a vector of three independent Poisson processes
#conditionally to the first one
set.seed(123)
lambdax<-runif(200, 0.01,0.15)
posaux<-simNHPc(lambda=lambdax, fixed.seed=123)$posNH
set.seed(124)
lambday<-runif(200, 0.005,0.1)
set.seed(125)
lambdaz<-runif(200, 0.005,0.2)
DistSimfix(posx=posaux, type = "Poisson", lambdaMarg = cbind(lambday,lambdaz),
fixed.seed=123, info=TRUE)
#DistSim(posx=posaux, type = "Poisson", lambdaMarg = cbind(lambday,lambdaz))
``` |

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