# TranM: Estimation of the transition matrix of a Markov chain In IndTestPP: Tests of Independence and Analysis of Dependence Between Point Processes in Time

## Description

It estimates the transition matrix of a Makov chain to model the dependence between the discrete marks of a marked point process. The estimator is the MLE based on count data.

## Usage

 `1` ```TranM(marcas = NULL, d = NULL, vecpro = NULL) ```

## Arguments

 `marcas` Integer vector. It contains the discrete marks of the marked point process. The order of the marks in the vector must correspond to the points in the process sorted over time. `d` Integer. Number of states of the Markov chain, that is the number of different marks of the marked point process. `vecpro` A list with d elements. Element "i" of the list must be a vector including the occurrence times of the points in the marked point process with marks equal to "i".

## Details

The input of this function must be a marked point process. It can be defined by the sequence of marks of all the points in the process (arguments `marcas` and `d`), or alternatively by a vector of `d` point processes (argument `vecpro`). If `marcas` or `d` are NULL, `vecpro` must be provided. If they are not NULL, they are used to define the marked Poisson process.

## Value

 `prob` The estimated transition matrix of probabilities.

`DepNHPPMarked`
 ```1 2 3``` ```TranM(marcas = c(1,3,3,2,1,2,1,1), d = 3) TranM(vecpro=list(n1=c(2,7,9,23), n2=c(4,5,21), n3=c(2,8,9,12,16))) ```