Modelling snowfall as a random walk with a drift
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
edited Dec 31 '18 at 4:56
m_goldberg
84.3k872195
asked Dec 31 '18 at 2:21
Will
734
add a comment |
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
edited Dec 31 '18 at 4:56
m_goldberg
84.3k872195
asked Dec 31 '18 at 2:21
Will
734
add a comment |
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
edited Dec 31 '18 at 4:56
m_goldberg
84.3k872195
asked Dec 31 '18 at 2:21
Will
734
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
edited Dec 31 '18 at 4:56
m_goldberg
84.3k872195
asked Dec 31 '18 at 2:21
Will
734
edited Dec 31 '18 at 4:56
m_goldberg
84.3k872195
asked Dec 31 '18 at 2:21
Will
734
edited Dec 31 '18 at 4:56
m_goldberg
84.3k872195
edited Dec 31 '18 at 4:56
m_goldberg
84.3k872195
edited Dec 31 '18 at 4:56
m_goldberg
84.3k872195
84.3k872195
asked Dec 31 '18 at 2:21
Will
734
asked Dec 31 '18 at 2:21
Will
734
asked Dec 31 '18 at 2:21
Will
734
734
add a comment |
add a comment |
1 Answer
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votes
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]
answered Dec 31 '18 at 5:18
m_goldberg
84.3k872195
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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]
answered Dec 31 '18 at 5:18
m_goldberg
84.3k872195
add a comment |
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]
answered Dec 31 '18 at 5:18
m_goldberg
84.3k872195
add a comment |
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]
answered Dec 31 '18 at 5:18
m_goldberg
84.3k872195
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]
answered Dec 31 '18 at 5:18
m_goldberg
84.3k872195
answered Dec 31 '18 at 5:18
m_goldberg
84.3k872195
answered Dec 31 '18 at 5:18
m_goldberg
84.3k872195
answered Dec 31 '18 at 5:18
m_goldberg
84.3k872195
84.3k872195
add a comment |
add a comment |
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