# Markov chain simulation of a sample path - to get empirical probabilities Classic List Threaded 3 messages Open this post in threaded view
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## Markov chain simulation of a sample path - to get empirical probabilities

 This post was updated on . The question: A computer store sells iPods. If at the end of the day they have 0 or 1 unit of stock, they order enough new units so that their total number of units on hand is 5. New merchandise arrives before the store opens the next day. Demand each day is random with the following distribution Demand     Probability      0                0.3      1                0.4      2                0.2      3                0.1 a) What is the most likely number of units in stock on Friday given that the store opened with 5 units of stock on Monday? My assignment is to write an R code that takes as input a transition matrix and an initial distribution, and then simulates data from which I can empirically calculate probabilities... I am confident that my transition matrix is correct, it is         0.0  0.0  0.1  0.2  0.4  0.3         0.0  0.0  0.1  0.2  0.4  0.3 P=    0.3  0.4  0.3  0.0  0.0  0.0         0.1  0.2  0.4  0.3  0.0  0.0         0.0  0.1  0.2  0.4  0.3  0.0         0.0  0.0  0.1  0.2  0.4  0.3 where the row1=o units of stock                row2= 1 unit of stock....                row3= 2 units of stock etc, and the columns also follow the same order (Manually I know how to do this and I have done so, but I cannot do it in R) I have the following code: > set.seed(1413974749) > mChainSimulation=function(P,pathLength, initDist) + { +   path=numeric(pathLength) +   path=6 # Because on Monday we open with 5 units of stock (which is 6th state in Markov chain) +   for(i in 6:pathLength) +   { +     path[i]=sample(6, 1 , replace=TRUE,prob=P[path[i-1],]) +   } +   return(path) + } > numStates=6 > initDist=c(1/6,1/6,1/6,1/6,1/6,1/6) > P=matrix(c(0, 0, 0.1, 0.2, 0.4, 0.3, 0, 0, 0.1, 0.2, 0.4, 0.3, 0.3, 0.4, 0.3, 0, 0, 0, 0.1, 0.2, 0.4, 0.3, 0, 0, 0, 0.1, 0.2, 0.4, 0.3, 0, 0, 0, 0.1, 0.2, 0.4, 0.3),6,6, byrow=T) > P      [,1] [,2] [,3] [,4] [,5] [,6] [1,]  0.0  0.0  0.1  0.2  0.4  0.3 [2,]  0.0  0.0  0.1  0.2  0.4  0.3 [3,]  0.3  0.4  0.3  0.0  0.0  0.0 [4,]  0.1  0.2  0.4  0.3  0.0  0.0 [5,]  0.0  0.1  0.2  0.4  0.3  0.0 [6,]  0.0  0.0  0.1  0.2  0.4  0.3 > pathLength=4 > simNum=10000 > stock0Num=0 # number of times in the simulation that it ends on 0 units of stock, i.e. in simulations it ends on 1 > stock1Num=0 # number of times in the simulation that it ends on 1 unit of stock, i.e in simulations it ends on 2 > stock2Num=0 # number of times in the simulation that it ends on 2 units of stock, i.e in simulations it ends on 3 > stock3Num=0 # number of times in the simulation that it ends on 3 units of stock, i.e in simulations it ends on 4 > stock4Num=0 # number of times in the simulation that it ends on 4 units of stock, i.e in simulations it ends on 5   > stock5Num=0 # num !!!!!!!!!!!!!!!!!!! # I get an error here in the next few lines!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! > for(i in 1:simNum) + { +   pathSimulation=mChainSimulation(P,pathLength, initDist) +   pathEnd=pathSimulation[pathLength] +   +   if(pathEnd==1) +   { +     stock0Num=stock0Num+1 +   } +   if(pathEnd==2) +   { +     stock1Num=stock1Num+1 +   } +   if(pathEnd==3) +   { +     stock2Num=stock2Num+1 +   } +   if(pathEnd==4) +   { +     stock3Num=stock3Num+1 +   } +   if(pathEnd==5) +   { +     stock4Num=stock4Num+1 +   } +   if(pathEnd==6) +   { +     stock5Num=stock5Num+1 +   } + }  Hide Traceback    Rerun with Debug  Error in sample.int(length(x), size, replace, prob) :   incorrect number of probabilities 3 sample.int(length(x), size, replace, prob) 2 sample(1:numStates, 1, prob = P[path[i - 1], 6]) 1 mChainSimulation(P, pathLength, initDist) I don't know how to fix my error and would greatly appreciate any help.