How to plot a Histogram and compare with a particular probability density function PDFMathematica envelope...
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How to plot a Histogram and compare with a particular probability density function PDF
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I would like to know how to plot a make a comparison between a histogram and a set of random data, I have the following probability density function (PDF) which is given for this problem. I can generate the histogram but I do not know how to add the PDF function and make the plot both together.
I have seen some question and problem using RandomVariate function but it does not work. This is the code.
Clear["Global`*"]; Remove["Global`*"];
L = 10; Ns = 10^4;
x = Table[RandomReal[L], {x, 0,Ns}];
y = Table[RandomReal[L], {y, 0, Ns}];
z = Table[RandomReal[L], {z, 0, Ns}];
sf = Abs[Sin[x^2 + y^2] + Cos[x y z]];
Histogram[sf, {0.25}, "Probability"]
The (PDF) is f = k^2/(k^2 + 1)^(5/2)
The goal is to obtain a similar plot like this, 
, where the line represent in this case f.
plotting graphics probability-or-statistics pdf-format
asked 2 days ago
irondonioirondonio
1257 bronze badges
$endgroup$
add a comment |
$begingroup$
I would like to know how to plot a make a comparison between a histogram and a set of random data, I have the following probability density function (PDF) which is given for this problem. I can generate the histogram but I do not know how to add the PDF function and make the plot both together.
I have seen some question and problem using RandomVariate function but it does not work. This is the code.
Clear["Global`*"]; Remove["Global`*"];
L = 10; Ns = 10^4;
x = Table[RandomReal[L], {x, 0,Ns}];
y = Table[RandomReal[L], {y, 0, Ns}];
z = Table[RandomReal[L], {z, 0, Ns}];
sf = Abs[Sin[x^2 + y^2] + Cos[x y z]];
Histogram[sf, {0.25}, "Probability"]
The (PDF) is f = k^2/(k^2 + 1)^(5/2)
The goal is to obtain a similar plot like this, , where the line represent in this case f.
plotting graphics probability-or-statistics pdf-format
asked 2 days ago
irondonioirondonio
1257 bronze badges
$endgroup$
$begingroup$
There are a number of problems with your formulation. First, you do not needx = Table[RandomReal[L], {x, 0,Ns}];the x on the RHS is superfluous, and likely to cause problems. All you need is:x = RandomReal[10, 10^4];Second, your random data sf is constrained to lie between 0 and 2 (i.e. is bounded). Your pdf is not bounded (or if it is, it is not stated). Third, even if your density was unbounded, it does not integrate to unity, so is not well-defined. All that leaves aside the fact that the density does not fit the data.
$endgroup$
– wolfies
2 days ago
add a comment |
$begingroup$
I would like to know how to plot a make a comparison between a histogram and a set of random data, I have the following probability density function (PDF) which is given for this problem. I can generate the histogram but I do not know how to add the PDF function and make the plot both together.
I have seen some question and problem using RandomVariate function but it does not work. This is the code.
Clear["Global`*"]; Remove["Global`*"];
L = 10; Ns = 10^4;
x = Table[RandomReal[L], {x, 0,Ns}];
y = Table[RandomReal[L], {y, 0, Ns}];
z = Table[RandomReal[L], {z, 0, Ns}];
sf = Abs[Sin[x^2 + y^2] + Cos[x y z]];
Histogram[sf, {0.25}, "Probability"]
The (PDF) is f = k^2/(k^2 + 1)^(5/2)
The goal is to obtain a similar plot like this, , where the line represent in this case f.
plotting graphics probability-or-statistics pdf-format
asked 2 days ago
irondonioirondonio
1257 bronze badges
$endgroup$
I would like to know how to plot a make a comparison between a histogram and a set of random data, I have the following probability density function (PDF) which is given for this problem. I can generate the histogram but I do not know how to add the PDF function and make the plot both together.
I have seen some question and problem using RandomVariate function but it does not work. This is the code.
Clear["Global`*"]; Remove["Global`*"];
L = 10; Ns = 10^4;
x = Table[RandomReal[L], {x, 0,Ns}];
y = Table[RandomReal[L], {y, 0, Ns}];
z = Table[RandomReal[L], {z, 0, Ns}];
sf = Abs[Sin[x^2 + y^2] + Cos[x y z]];
Histogram[sf, {0.25}, "Probability"]
The (PDF) is f = k^2/(k^2 + 1)^(5/2)
The goal is to obtain a similar plot like this, , where the line represent in this case f.
plotting graphics probability-or-statistics pdf-format
plotting graphics probability-or-statistics pdf-format
asked 2 days ago
irondonioirondonio
1257 bronze badges
asked 2 days ago
irondonioirondonio
1257 bronze badges
asked 2 days ago
irondonioirondonio
1257 bronze badges
asked 2 days ago
irondonioirondonio
1257 bronze badges
asked 2 days ago
irondonioirondonio
1257 bronze badges
1257 bronze badges
$begingroup$
There are a number of problems with your formulation. First, you do not needx = Table[RandomReal[L], {x, 0,Ns}];the x on the RHS is superfluous, and likely to cause problems. All you need is:x = RandomReal[10, 10^4];Second, your random data sf is constrained to lie between 0 and 2 (i.e. is bounded). Your pdf is not bounded (or if it is, it is not stated). Third, even if your density was unbounded, it does not integrate to unity, so is not well-defined. All that leaves aside the fact that the density does not fit the data.
$endgroup$
– wolfies
2 days ago
add a comment |
$begingroup$
There are a number of problems with your formulation. First, you do not needx = Table[RandomReal[L], {x, 0,Ns}];the x on the RHS is superfluous, and likely to cause problems. All you need is:x = RandomReal[10, 10^4];Second, your random data sf is constrained to lie between 0 and 2 (i.e. is bounded). Your pdf is not bounded (or if it is, it is not stated). Third, even if your density was unbounded, it does not integrate to unity, so is not well-defined. All that leaves aside the fact that the density does not fit the data.
$endgroup$
– wolfies
2 days ago
$begingroup$
There are a number of problems with your formulation. First, you do not need
x = Table[RandomReal[L], {x, 0,Ns}]; the x on the RHS is superfluous, and likely to cause problems. All you need is: x = RandomReal[10, 10^4]; Second, your random data sf is constrained to lie between 0 and 2 (i.e. is bounded). Your pdf is not bounded (or if it is, it is not stated). Third, even if your density was unbounded, it does not integrate to unity, so is not well-defined. All that leaves aside the fact that the density does not fit the data.$endgroup$
– wolfies
2 days ago
$begingroup$
There are a number of problems with your formulation. First, you do not need
x = Table[RandomReal[L], {x, 0,Ns}]; the x on the RHS is superfluous, and likely to cause problems. All you need is: x = RandomReal[10, 10^4]; Second, your random data sf is constrained to lie between 0 and 2 (i.e. is bounded). Your pdf is not bounded (or if it is, it is not stated). Third, even if your density was unbounded, it does not integrate to unity, so is not well-defined. All that leaves aside the fact that the density does not fit the data.$endgroup$
– wolfies
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Use Show:
Show[
Histogram[sf, {0.25}, "Probability"],
Plot[f, {k, 0, 2}]
]
answered 2 days ago
ThemisThemis
5313 silver badges10 bronze badges
$endgroup$
$begingroup$
I think you want"PDF"rather than"Probability".
$endgroup$
– JimB
2 days ago
$begingroup$
You're right, I coppied/pasted the code from the OP.
$endgroup$
– Themis
2 days ago
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
$begingroup$
Use Show:
Show[
Histogram[sf, {0.25}, "Probability"],
Plot[f, {k, 0, 2}]
]
answered 2 days ago
ThemisThemis
5313 silver badges10 bronze badges
$endgroup$
$begingroup$
I think you want"PDF"rather than"Probability".
$endgroup$
– JimB
2 days ago
$begingroup$
You're right, I coppied/pasted the code from the OP.
$endgroup$
– Themis
2 days ago
add a comment |
$begingroup$
Use Show:
Show[
Histogram[sf, {0.25}, "Probability"],
Plot[f, {k, 0, 2}]
]
answered 2 days ago
ThemisThemis
5313 silver badges10 bronze badges
$endgroup$
$begingroup$
I think you want"PDF"rather than"Probability".
$endgroup$
– JimB
2 days ago
$begingroup$
You're right, I coppied/pasted the code from the OP.
$endgroup$
– Themis
2 days ago
add a comment |
$begingroup$
Use Show:
Show[
Histogram[sf, {0.25}, "Probability"],
Plot[f, {k, 0, 2}]
]
answered 2 days ago
ThemisThemis
5313 silver badges10 bronze badges
$endgroup$
Use Show:
Show[
Histogram[sf, {0.25}, "Probability"],
Plot[f, {k, 0, 2}]
]
answered 2 days ago
ThemisThemis
5313 silver badges10 bronze badges
answered 2 days ago
ThemisThemis
5313 silver badges10 bronze badges
answered 2 days ago
ThemisThemis
5313 silver badges10 bronze badges
answered 2 days ago
ThemisThemis
5313 silver badges10 bronze badges
5313 silver badges10 bronze badges
$begingroup$
I think you want"PDF"rather than"Probability".
$endgroup$
– JimB
2 days ago
$begingroup$
You're right, I coppied/pasted the code from the OP.
$endgroup$
– Themis
2 days ago
add a comment |
$begingroup$
I think you want"PDF"rather than"Probability".
$endgroup$
– JimB
2 days ago
$begingroup$
You're right, I coppied/pasted the code from the OP.
$endgroup$
– Themis
2 days ago
$begingroup$
I think you want
"PDF" rather than "Probability".$endgroup$
– JimB
2 days ago
$begingroup$
I think you want
"PDF" rather than "Probability".$endgroup$
– JimB
2 days ago
$begingroup$
You're right, I coppied/pasted the code from the OP.
$endgroup$
– Themis
2 days ago
$begingroup$
You're right, I coppied/pasted the code from the OP.
$endgroup$
– Themis
2 days ago
add a comment |
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$begingroup$
There are a number of problems with your formulation. First, you do not need
x = Table[RandomReal[L], {x, 0,Ns}];the x on the RHS is superfluous, and likely to cause problems. All you need is:x = RandomReal[10, 10^4];Second, your random data sf is constrained to lie between 0 and 2 (i.e. is bounded). Your pdf is not bounded (or if it is, it is not stated). Third, even if your density was unbounded, it does not integrate to unity, so is not well-defined. All that leaves aside the fact that the density does not fit the data.$endgroup$
– wolfies
2 days ago