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Why does the PoissonDistribution not plot around its mean for moderate large numbers?

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2

$begingroup$

I plotted the Poisson Distribution for various mean values (plot label and vertical line). The plots does not peak around the mean as the mean increase. Any advice to get the right plot, or at least the right distribution values?

Same when plotting the log of the distribution -s + n Log[s] - LogGamma[n + 1]

Table[ListPlot[Table[PDF[PoissonDistribution[s], n], n, Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]], PlotLabel -> s, GridLines -> s, None], s, 50, 60, 70, 80, 100, 150]

plotting distributions precision-and-accuracy

share|improve this question

edited Jun 11 at 13:07

user64494

4,28122 gold badges1414 silver badges2323 bronze badges

asked Jun 11 at 7:27

jssjss

15511 silver badge88 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Also try DiscretePlot, for example: Table[DiscretePlot[ PDF[PoissonDistribution[s], n], n, Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]], PlotLabel -> s, GridLines -> s, None], s, 50, 60, 70, 80, 100, 150]
  $endgroup$
  – becko
  Jun 11 at 8:41
  

  
  
  
  

add a comment
 | 

2

$begingroup$

I plotted the Poisson Distribution for various mean values (plot label and vertical line). The plots does not peak around the mean as the mean increase. Any advice to get the right plot, or at least the right distribution values?

Same when plotting the log of the distribution -s + n Log[s] - LogGamma[n + 1]

Table[ListPlot[Table[PDF[PoissonDistribution[s], n], n, Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]], PlotLabel -> s, GridLines -> s, None], s, 50, 60, 70, 80, 100, 150]

plotting distributions precision-and-accuracy

share|improve this question

edited Jun 11 at 13:07

user64494

4,28122 gold badges1414 silver badges2323 bronze badges

asked Jun 11 at 7:27

jssjss

15511 silver badge88 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Also try DiscretePlot, for example: Table[DiscretePlot[ PDF[PoissonDistribution[s], n], n, Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]], PlotLabel -> s, GridLines -> s, None], s, 50, 60, 70, 80, 100, 150]
  $endgroup$
  – becko
  Jun 11 at 8:41
  

  
  
  
  

add a comment
 | 

$begingroup$

I plotted the Poisson Distribution for various mean values (plot label and vertical line). The plots does not peak around the mean as the mean increase. Any advice to get the right plot, or at least the right distribution values?

Same when plotting the log of the distribution -s + n Log[s] - LogGamma[n + 1]

Table[ListPlot[Table[PDF[PoissonDistribution[s], n], n, Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]], PlotLabel -> s, GridLines -> s, None], s, 50, 60, 70, 80, 100, 150]

plotting distributions precision-and-accuracy

share|improve this question

edited Jun 11 at 13:07

user64494

4,28122 gold badges1414 silver badges2323 bronze badges

asked Jun 11 at 7:27

jssjss

15511 silver badge88 bronze badges

$endgroup$

Table[ListPlot[Table[PDF[PoissonDistribution[s], n], n, Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]], PlotLabel -> s, GridLines -> s, None], s, 50, 60, 70, 80, 100, 150]

share|improve this question

edited Jun 11 at 13:07

user64494

4,28122 gold badges1414 silver badges2323 bronze badges

asked Jun 11 at 7:27

jssjss

15511 silver badge88 bronze badges

share|improve this question

edited Jun 11 at 13:07

user64494

4,28122 gold badges1414 silver badges2323 bronze badges

asked Jun 11 at 7:27

jssjss

15511 silver badge88 bronze badges

edited Jun 11 at 13:07

user64494

4,28122 gold badges1414 silver badges2323 bronze badges

edited Jun 11 at 13:07

user64494

4,28122 gold badges1414 silver badges2323 bronze badges

asked Jun 11 at 7:27

jssjss

15511 silver badge88 bronze badges

asked Jun 11 at 7:27

jssjss

15511 silver badge88 bronze badges

1 Answer
1

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oldest

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8

$begingroup$

Because of the way you are generating the lists. What you are plotting is just a list of "y" values without the corresponding "x", that with ListPlot are plotted by Mathematica from 1 to n (with n the number of elements). If you start the list from a "x" value larger than one, Mathematica still plots from 1 to n.

Try with the following code where I explicitly add the "x" values to the lists: this should fix the problem.

Table[ListPlot[
 Table[n, PDF[PoissonDistribution[s], n], n, 
 Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]]
 , PlotLabel -> s, GridLines -> s, None]
 , s, 50, 60, 70, 80, 100, 150]

share|improve this answer

answered Jun 11 at 7:44

FraccaloFraccalo

3,33266 silver badges1919 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Well I see, I miss the x coordinate. Thank you. That is the answer!
  $endgroup$
  – jss
  Jun 11 at 7:50
  
  

  
  
  
  

add a comment
 | 

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8

$begingroup$

Because of the way you are generating the lists. What you are plotting is just a list of "y" values without the corresponding "x", that with ListPlot are plotted by Mathematica from 1 to n (with n the number of elements). If you start the list from a "x" value larger than one, Mathematica still plots from 1 to n.

Try with the following code where I explicitly add the "x" values to the lists: this should fix the problem.

Table[ListPlot[
 Table[n, PDF[PoissonDistribution[s], n], n, 
 Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]]
 , PlotLabel -> s, GridLines -> s, None]
 , s, 50, 60, 70, 80, 100, 150]

share|improve this answer

answered Jun 11 at 7:44

FraccaloFraccalo

3,33266 silver badges1919 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Well I see, I miss the x coordinate. Thank you. That is the answer!
  $endgroup$
  – jss
  Jun 11 at 7:50
  
  

  
  
  
  

add a comment
 | 

8

$begingroup$

Because of the way you are generating the lists. What you are plotting is just a list of "y" values without the corresponding "x", that with ListPlot are plotted by Mathematica from 1 to n (with n the number of elements). If you start the list from a "x" value larger than one, Mathematica still plots from 1 to n.

Try with the following code where I explicitly add the "x" values to the lists: this should fix the problem.

Table[ListPlot[
 Table[n, PDF[PoissonDistribution[s], n], n, 
 Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]]
 , PlotLabel -> s, GridLines -> s, None]
 , s, 50, 60, 70, 80, 100, 150]

share|improve this answer

answered Jun 11 at 7:44

FraccaloFraccalo

3,33266 silver badges1919 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Well I see, I miss the x coordinate. Thank you. That is the answer!
  $endgroup$
  – jss
  Jun 11 at 7:50
  
  

  
  
  
  

add a comment
 | 

$begingroup$

Because of the way you are generating the lists. What you are plotting is just a list of "y" values without the corresponding "x", that with ListPlot are plotted by Mathematica from 1 to n (with n the number of elements). If you start the list from a "x" value larger than one, Mathematica still plots from 1 to n.

Try with the following code where I explicitly add the "x" values to the lists: this should fix the problem.

Table[ListPlot[
 Table[n, PDF[PoissonDistribution[s], n], n, 
 Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]]
 , PlotLabel -> s, GridLines -> s, None]
 , s, 50, 60, 70, 80, 100, 150]

share|improve this answer

answered Jun 11 at 7:44

FraccaloFraccalo

3,33266 silver badges1919 bronze badges

$endgroup$

Table[ListPlot[
 Table[n, PDF[PoissonDistribution[s], n], n, 
 Round[Max[s - 8 Sqrt[s], 0]], Round[s + 8 Sqrt[s]]]
 , PlotLabel -> s, GridLines -> s, None]
 , s, 50, 60, 70, 80, 100, 150]

share|improve this answer

answered Jun 11 at 7:44

FraccaloFraccalo

3,33266 silver badges1919 bronze badges

answered Jun 11 at 7:44

FraccaloFraccalo

3,33266 silver badges1919 bronze badges

answered Jun 11 at 7:44

FraccaloFraccalo

3,33266 silver badges1919 bronze badges