Modelling snowfall as a random walk with a drift












4














I am trying to simulate a (very) simple model of snow fall/accumulation using random walks in the following way: 



sf = 

  Accumulate[RandomVariate[BernoulliDistribution[0.2], 100] *

    RandomVariate[GammaDistribution[1, 2], 100] /. {0. -> -0.4}]



ListLinePlot[sf]


I generate Bernoulli trials with a success of probability of 0.2 to simulate days that it snows. On a day that it doesn't snow instead of a simple 0 entry I am introducing a negative drift term of -0.4 to emulate the melting of the snow.



Where I am having trouble is that you can't ever have negative snowfall. I want the walker to always remain bigger than or equal to 0. However, I can't just send all negative entries to 0 as that would eliminate the data of days where it snows but the drift term is larger than the snowfall.



Thanks.






probability-or-statistics random-process







share|improve this question





























    4














    I am trying to simulate a (very) simple model of snow fall/accumulation using random walks in the following way: 



    sf = 
    
  Accumulate[RandomVariate[BernoulliDistribution[0.2], 100] *
    
    RandomVariate[GammaDistribution[1, 2], 100] /. {0. -> -0.4}]
    

    
ListLinePlot[sf]


    I generate Bernoulli trials with a success of probability of 0.2 to simulate days that it snows. On a day that it doesn't snow instead of a simple 0 entry I am introducing a negative drift term of -0.4 to emulate the melting of the snow.



    Where I am having trouble is that you can't ever have negative snowfall. I want the walker to always remain bigger than or equal to 0. However, I can't just send all negative entries to 0 as that would eliminate the data of days where it snows but the drift term is larger than the snowfall.



    Thanks.






    probability-or-statistics random-process







    share|improve this question



























      4












      4








      4


      4





      I am trying to simulate a (very) simple model of snow fall/accumulation using random walks in the following way: 



      sf = 
      
  Accumulate[RandomVariate[BernoulliDistribution[0.2], 100] *
      
    RandomVariate[GammaDistribution[1, 2], 100] /. {0. -> -0.4}]
      

      
ListLinePlot[sf]


      I generate Bernoulli trials with a success of probability of 0.2 to simulate days that it snows. On a day that it doesn't snow instead of a simple 0 entry I am introducing a negative drift term of -0.4 to emulate the melting of the snow.



      Where I am having trouble is that you can't ever have negative snowfall. I want the walker to always remain bigger than or equal to 0. However, I can't just send all negative entries to 0 as that would eliminate the data of days where it snows but the drift term is larger than the snowfall.



      Thanks.






      probability-or-statistics random-process







      share|improve this question















      I am trying to simulate a (very) simple model of snow fall/accumulation using random walks in the following way: 



      sf = 
      
  Accumulate[RandomVariate[BernoulliDistribution[0.2], 100] *
      
    RandomVariate[GammaDistribution[1, 2], 100] /. {0. -> -0.4}]
      

      
ListLinePlot[sf]


      I generate Bernoulli trials with a success of probability of 0.2 to simulate days that it snows. On a day that it doesn't snow instead of a simple 0 entry I am introducing a negative drift term of -0.4 to emulate the melting of the snow.



      Where I am having trouble is that you can't ever have negative snowfall. I want the walker to always remain bigger than or equal to 0. However, I can't just send all negative entries to 0 as that would eliminate the data of days where it snows but the drift term is larger than the snowfall.



      Thanks.






      probability-or-statistics random-process




      probability-or-statistics random-process






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 10 hours ago









      m_goldberg

      84.2k871194




      84.2k871194










      asked 12 hours ago









      Will

      484




      484






















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          9














          I don't think Accumulate is powerful enough. Rather, you should use FoldList.



          SeedRandom[2];
          
sf =
          
  FoldList[If[#2 == 0, Max[#1 - .4, 0], #1 + #2] &, 
          
    RandomVariate[BernoulliDistribution[0.2], 100] *
          
      RandomVariate[GammaDistribution[1, 2], 100]];
          
ListLinePlot[sf]


          plot






          share|improve this answer





















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            1 Answer
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            active

            oldest

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            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            9














            I don't think Accumulate is powerful enough. Rather, you should use FoldList.



            SeedRandom[2];
            
sf =
            
  FoldList[If[#2 == 0, Max[#1 - .4, 0], #1 + #2] &, 
            
    RandomVariate[BernoulliDistribution[0.2], 100] *
            
      RandomVariate[GammaDistribution[1, 2], 100]];
            
ListLinePlot[sf]


            plot






            share|improve this answer


























              9














              I don't think Accumulate is powerful enough. Rather, you should use FoldList.



              SeedRandom[2];
              
sf =
              
  FoldList[If[#2 == 0, Max[#1 - .4, 0], #1 + #2] &, 
              
    RandomVariate[BernoulliDistribution[0.2], 100] *
              
      RandomVariate[GammaDistribution[1, 2], 100]];
              
ListLinePlot[sf]


              plot






              share|improve this answer
























                9












                9








                9






                I don't think Accumulate is powerful enough. Rather, you should use FoldList.



                SeedRandom[2];
                
sf =
                
  FoldList[If[#2 == 0, Max[#1 - .4, 0], #1 + #2] &, 
                
    RandomVariate[BernoulliDistribution[0.2], 100] *
                
      RandomVariate[GammaDistribution[1, 2], 100]];
                
ListLinePlot[sf]


                plot






                share|improve this answer












                I don't think Accumulate is powerful enough. Rather, you should use FoldList.



                SeedRandom[2];
                
sf =
                
  FoldList[If[#2 == 0, Max[#1 - .4, 0], #1 + #2] &, 
                
    RandomVariate[BernoulliDistribution[0.2], 100] *
                
      RandomVariate[GammaDistribution[1, 2], 100]];
                
ListLinePlot[sf]


                plot







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 10 hours ago









                m_goldberg

                84.2k871194




                84.2k871194






























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