cadenas de markov en R

# Cadenas de Markov en R --------------------------------------------------

#Estados
estados = c(1:5)

#Inicializar la matriz

mat1 = matrix(data = 0,nrow = 5, ncol = 5)
filas = estados
columnas = estados

#Llenar la matriz
for (i in filas) {
  for (j in columnas) {
    if (j == i + 1 & i < 5) {
      mat1[i,j] = 0.5
    }
    if (j == i & 1 < i & i < 5) {
      mat1[i,j] = 0.3
    }
    if (j == i - 1 & i > 1) {
      mat1[i,j] = 0.2
    }
    if (j == i & i == 1) {
      mat1[i,j] = 0.5
    }
    if (j == i & i == 5) {
      mat1[i,j] = 0.8
    }
  }
}
print(mat1)
rowSums(mat1)


# Cadena de markov --------------------------------------------------------

library(markovchain)

cmtd = new(Class = "markovchain", states = as.character(estados), transitionMatrix = mat1) 

#Para visualizar la cadena de markov
plot(cmtd)


# Analisis transitorio
alpha = c(0,1,0,0,0) 
probs2pasos = alpha * (cmtd^2)
probs2pasos


#Matriz en tiempo continuo

estados2 = c(0:15)

#Inicializar la matriz

mat2 = matrix(data = 0,nrow = length(estados2), ncol = length(estados2))
dimnames(mat2) = list(estados2,estados2)
filas2 = estados2
columnas2 = estados2


#Llenar la matriz
for (i in filas2) {
  for (j in columnas2) {
    if (j == i + 1 & i < 15 ) {
      mat2[i+1,j+1] = 5
    }
    if (j == i - 1 & i > 0) {
      mat2[i+1,j+1] = 9*i
    }
  }
}

#Para hacer que la suma de la filas de 0, debemos llenar la diagonal

for (i in 1:16) {
  mat2[i,i]=-sum(mat2[i,])
}


#Definir la cadena de markov

cmtc = new(Class = "ctmc", states = as.character(estados2), byrow = TRUE, 
           generator = mat2)


library(expm)

#Definir el vector de condiciones iniciales
alpha2 = c(rep(0,10),1,rep(0,5))

#Analisis transitorio
probs = alpha2%*%expm(mat2*(72))
probs

Add a new chunk by clicking the Insert Chunk button on the toolbar or by pressing Ctrl+Alt+I.

When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the Preview button or press Ctrl+Shift+K to preview the HTML file).

The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike Knit, Preview does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.