Problem with TransformedDistributionCalculate probability functionWhen are `If`, `Piecewise`, `Switch`, and `Which` interchangeable and when are they not?Calculate PDF and CDF of a product of independent exponentially distributed random variablesConditional probabilityFullSimplify on TransformedDistributionNProbability not reliability analysis?TransformedDistribution using $k$ iid random variables, but $k$ not fixedConvolve discrete random variables efficientlyProbability distribution defined by partitioning an intervalDistribution of Function of Random Sum of Random Variables
copy and scale one figure (wheel)
Lowest total scrabble score
Yosemite Fire Rings - What to Expect?
Creepy dinosaur pc game identification
What is the evidence for the "tyranny of the majority problem" in a direct democracy context?
The probability of Bus A arriving before Bus B
What is this called? Old film camera viewer?
Is this toilet slogan correct usage of the English language?
Does a 'pending' US visa application constitute a denial?
Why should universal income be universal?
Loading commands from file
Are the IPv6 address space and IPv4 address space completely disjoint?
Multiplicative persistence
How to indicate a cut out for a product window
How can I block email signup overlays or javascript popups in Safari?
Is it improper etiquette to ask your opponent what his/her rating is before the game?
Why is it that I can sometimes guess the next note?
Sklearn 'Seed' Not Working Properly In a Section of Code
How do you respond to a colleague from another team when they're wrongly expecting that you'll help them?
How should I respond when I lied about my education and the company finds out through background check?
Store Credit Card Information in Password Manager?
Is the U.S. Code copyrighted by the Government?
How much character growth crosses the line into breaking the character
If infinitesimal transformations commute why dont the generators of the Lorentz group commute?
Problem with TransformedDistribution
Calculate probability functionWhen are `If`, `Piecewise`, `Switch`, and `Which` interchangeable and when are they not?Calculate PDF and CDF of a product of independent exponentially distributed random variablesConditional probabilityFullSimplify on TransformedDistributionNProbability not reliability analysis?TransformedDistribution using $k$ iid random variables, but $k$ not fixedConvolve discrete random variables efficientlyProbability distribution defined by partitioning an intervalDistribution of Function of Random Sum of Random Variables
$begingroup$
I am trying to use Mathematica to obtain the probability distribution of $frac12(A + B)$ where $A$ and $B$ are independent random variables each distributed according to the uniform distribution, with lower and upper bounds of $L$ and $H$ respectively.
I suspect the distribution is triangular with lower and upper bounds of $L$ and $H$ respectively and mode equal to $frac12(A + B)$. However, I am having difficulty using TransformedDistribution to show that.
My code is:
[ScriptCapitalD] = TransformedDistribution[1/2 (A + B), B [Distributed] UniformDistribution[L, H], A [Distributed] UniformDistribution[L, H]]
probability-or-statistics
asked 1 hour ago
user120911user120911
71328
$endgroup$
|
show 3 more comments
$begingroup$
I am trying to use Mathematica to obtain the probability distribution of $frac12(A + B)$ where $A$ and $B$ are independent random variables each distributed according to the uniform distribution, with lower and upper bounds of $L$ and $H$ respectively.
I suspect the distribution is triangular with lower and upper bounds of $L$ and $H$ respectively and mode equal to $frac12(A + B)$. However, I am having difficulty using TransformedDistribution to show that.
My code is:
[ScriptCapitalD] = TransformedDistribution[1/2 (A + B), B [Distributed] UniformDistribution[L, H], A [Distributed] UniformDistribution[L, H]]
probability-or-statistics
asked 1 hour ago
user120911user120911
71328
$endgroup$
$begingroup$
That was a typo. But I am still not getting what I expect.
$endgroup$
– user120911
1 hour ago
$begingroup$
Did you tryPDF[[ScriptCapitalD], y]?
$endgroup$
– JimB
1 hour ago
$begingroup$
PDF[[ScriptCapitalD], y] produces one expression with a denominator that looks correct, but the triangular distribution is split at the mode. Mathematica is not showing that. At least not in a way that is easy to see.
$endgroup$
– user120911
1 hour ago
$begingroup$
Are you awareTriangularDistribution[]is built-in?
$endgroup$
– J. M. is slightly pensive♦
1 hour ago
1
$begingroup$
Why not check the PDFs?Simplify[PDF[TransformedDistribution[(a + b)/2, a, b [Distributed] UniformDistribution[l, h, l, h]], t] == PDF[TriangularDistribution[l, h], t], l < t < h]
$endgroup$
– J. M. is slightly pensive♦
41 mins ago
|
show 3 more comments
$begingroup$
I am trying to use Mathematica to obtain the probability distribution of $frac12(A + B)$ where $A$ and $B$ are independent random variables each distributed according to the uniform distribution, with lower and upper bounds of $L$ and $H$ respectively.
I suspect the distribution is triangular with lower and upper bounds of $L$ and $H$ respectively and mode equal to $frac12(A + B)$. However, I am having difficulty using TransformedDistribution to show that.
My code is:
[ScriptCapitalD] = TransformedDistribution[1/2 (A + B), B [Distributed] UniformDistribution[L, H], A [Distributed] UniformDistribution[L, H]]
probability-or-statistics
asked 1 hour ago
user120911user120911
71328
$endgroup$
I am trying to use Mathematica to obtain the probability distribution of $frac12(A + B)$ where $A$ and $B$ are independent random variables each distributed according to the uniform distribution, with lower and upper bounds of $L$ and $H$ respectively.
I suspect the distribution is triangular with lower and upper bounds of $L$ and $H$ respectively and mode equal to $frac12(A + B)$. However, I am having difficulty using TransformedDistribution to show that.
My code is:
[ScriptCapitalD] = TransformedDistribution[1/2 (A + B), B [Distributed] UniformDistribution[L, H], A [Distributed] UniformDistribution[L, H]]
probability-or-statistics
probability-or-statistics
asked 1 hour ago
user120911user120911
71328
asked 1 hour ago
user120911user120911
71328
edited 1 hour ago
user120911
asked 1 hour ago
user120911user120911
71328
asked 1 hour ago
user120911user120911
71328
asked 1 hour ago
user120911user120911
71328
71328
$begingroup$
That was a typo. But I am still not getting what I expect.
$endgroup$
– user120911
1 hour ago
$begingroup$
Did you tryPDF[[ScriptCapitalD], y]?
$endgroup$
– JimB
1 hour ago
$begingroup$
PDF[[ScriptCapitalD], y] produces one expression with a denominator that looks correct, but the triangular distribution is split at the mode. Mathematica is not showing that. At least not in a way that is easy to see.
$endgroup$
– user120911
1 hour ago
$begingroup$
Are you awareTriangularDistribution[]is built-in?
$endgroup$
– J. M. is slightly pensive♦
1 hour ago
1
$begingroup$
Why not check the PDFs?Simplify[PDF[TransformedDistribution[(a + b)/2, a, b [Distributed] UniformDistribution[l, h, l, h]], t] == PDF[TriangularDistribution[l, h], t], l < t < h]
$endgroup$
– J. M. is slightly pensive♦
41 mins ago
|
show 3 more comments
$begingroup$
That was a typo. But I am still not getting what I expect.
$endgroup$
– user120911
1 hour ago
$begingroup$
Did you tryPDF[[ScriptCapitalD], y]?
$endgroup$
– JimB
1 hour ago
$begingroup$
PDF[[ScriptCapitalD], y] produces one expression with a denominator that looks correct, but the triangular distribution is split at the mode. Mathematica is not showing that. At least not in a way that is easy to see.
$endgroup$
– user120911
1 hour ago
$begingroup$
Are you awareTriangularDistribution[]is built-in?
$endgroup$
– J. M. is slightly pensive♦
1 hour ago
1
$begingroup$
Why not check the PDFs?Simplify[PDF[TransformedDistribution[(a + b)/2, a, b [Distributed] UniformDistribution[l, h, l, h]], t] == PDF[TriangularDistribution[l, h], t], l < t < h]
$endgroup$
– J. M. is slightly pensive♦
41 mins ago
$begingroup$
That was a typo. But I am still not getting what I expect.
$endgroup$
– user120911
1 hour ago
$begingroup$
That was a typo. But I am still not getting what I expect.
$endgroup$
– user120911
1 hour ago
$begingroup$
Did you try
PDF[[ScriptCapitalD], y]?$endgroup$
– JimB
1 hour ago
$begingroup$
Did you try
PDF[[ScriptCapitalD], y]?$endgroup$
– JimB
1 hour ago
$begingroup$
PDF[[ScriptCapitalD], y] produces one expression with a denominator that looks correct, but the triangular distribution is split at the mode. Mathematica is not showing that. At least not in a way that is easy to see.
$endgroup$
– user120911
1 hour ago
$begingroup$
PDF[[ScriptCapitalD], y] produces one expression with a denominator that looks correct, but the triangular distribution is split at the mode. Mathematica is not showing that. At least not in a way that is easy to see.
$endgroup$
– user120911
1 hour ago
$begingroup$
Are you aware
TriangularDistribution[] is built-in?$endgroup$
– J. M. is slightly pensive♦
1 hour ago
$begingroup$
Are you aware
TriangularDistribution[] is built-in?$endgroup$
– J. M. is slightly pensive♦
1 hour ago
1
1
$begingroup$
Why not check the PDFs?
Simplify[PDF[TransformedDistribution[(a + b)/2, a, b [Distributed] UniformDistribution[l, h, l, h]], t] == PDF[TriangularDistribution[l, h], t], l < t < h]$endgroup$
– J. M. is slightly pensive♦
41 mins ago
$begingroup$
Why not check the PDFs?
Simplify[PDF[TransformedDistribution[(a + b)/2, a, b [Distributed] UniformDistribution[l, h, l, h]], t] == PDF[TriangularDistribution[l, h], t], l < t < h]$endgroup$
– J. M. is slightly pensive♦
41 mins ago
|
show 3 more comments
2 Answers
2
active
oldest
votes
$begingroup$
You get what you expect if you do it it in two steps
[ScriptCapitalD] =
TransformedDistribution[x/2,
x [Distributed] TransformedDistribution[(A + B),
B [Distributed] UniformDistribution[L, H],
A [Distributed] UniformDistribution[L, H]]]
(* TriangularDistribution[L, H] *)
answered 33 mins ago
Bob HanlonBob Hanlon
60.9k33597
$endgroup$
$begingroup$
That is very nice!
$endgroup$
– user120911
20 mins ago
add a comment |
$begingroup$
PDF[[ScriptCapitalD]][z]
(((-30 + z)Sign[-30 + z])/2 - (-20 + z)
Sign[-20 + z] + ((-10 + z)*Sign[-10 + z])/2)/100
For plotting, assign values to L and H:
L = 10; H = 30;
Plot[Evaluate@PDF[[ScriptCapitalD]][x], x, 10, 30]
pdF[l_, h_] := Module[L = l, H = h, Evaluate[PDF[[ScriptCapitalD]]]]
Plot[Evaluate @ Flatten@Table[pdF[l, h][x], l, 0, 5, h, 10, 15], x, 0, 15,
PlotRange -> All,
PlotLegends -> (Flatten @ Table[ToString@l, h, l, 0, 5, h, 10, 15])]
answered 1 hour ago
kglrkglr
189k10206424
$endgroup$
$begingroup$
That confirms my intution, but can you get Mathematica to output the PDF for the triangular distribution? That is what I am having trouble doing.
$endgroup$
– user120911
1 hour ago
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "387"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f193838%2fproblem-with-transformeddistribution%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You get what you expect if you do it it in two steps
[ScriptCapitalD] =
TransformedDistribution[x/2,
x [Distributed] TransformedDistribution[(A + B),
B [Distributed] UniformDistribution[L, H],
A [Distributed] UniformDistribution[L, H]]]
(* TriangularDistribution[L, H] *)
answered 33 mins ago
Bob HanlonBob Hanlon
60.9k33597
$endgroup$
$begingroup$
That is very nice!
$endgroup$
– user120911
20 mins ago
add a comment |
$begingroup$
You get what you expect if you do it it in two steps
[ScriptCapitalD] =
TransformedDistribution[x/2,
x [Distributed] TransformedDistribution[(A + B),
B [Distributed] UniformDistribution[L, H],
A [Distributed] UniformDistribution[L, H]]]
(* TriangularDistribution[L, H] *)
answered 33 mins ago
Bob HanlonBob Hanlon
60.9k33597
$endgroup$
$begingroup$
That is very nice!
$endgroup$
– user120911
20 mins ago
add a comment |
$begingroup$
You get what you expect if you do it it in two steps
[ScriptCapitalD] =
TransformedDistribution[x/2,
x [Distributed] TransformedDistribution[(A + B),
B [Distributed] UniformDistribution[L, H],
A [Distributed] UniformDistribution[L, H]]]
(* TriangularDistribution[L, H] *)
answered 33 mins ago
Bob HanlonBob Hanlon
60.9k33597
$endgroup$
You get what you expect if you do it it in two steps
[ScriptCapitalD] =
TransformedDistribution[x/2,
x [Distributed] TransformedDistribution[(A + B),
B [Distributed] UniformDistribution[L, H],
A [Distributed] UniformDistribution[L, H]]]
(* TriangularDistribution[L, H] *)
answered 33 mins ago
Bob HanlonBob Hanlon
60.9k33597
answered 33 mins ago
Bob HanlonBob Hanlon
60.9k33597
answered 33 mins ago
Bob HanlonBob Hanlon
60.9k33597
answered 33 mins ago
Bob HanlonBob Hanlon
60.9k33597
60.9k33597
$begingroup$
That is very nice!
$endgroup$
– user120911
20 mins ago
add a comment |
$begingroup$
That is very nice!
$endgroup$
– user120911
20 mins ago
$begingroup$
That is very nice!
$endgroup$
– user120911
20 mins ago
$begingroup$
That is very nice!
$endgroup$
– user120911
20 mins ago
add a comment |
$begingroup$
PDF[[ScriptCapitalD]][z]
(((-30 + z)Sign[-30 + z])/2 - (-20 + z)
Sign[-20 + z] + ((-10 + z)*Sign[-10 + z])/2)/100
For plotting, assign values to L and H:
L = 10; H = 30;
Plot[Evaluate@PDF[[ScriptCapitalD]][x], x, 10, 30]
pdF[l_, h_] := Module[L = l, H = h, Evaluate[PDF[[ScriptCapitalD]]]]
Plot[Evaluate @ Flatten@Table[pdF[l, h][x], l, 0, 5, h, 10, 15], x, 0, 15,
PlotRange -> All,
PlotLegends -> (Flatten @ Table[ToString@l, h, l, 0, 5, h, 10, 15])]
answered 1 hour ago
kglrkglr
189k10206424
$endgroup$
$begingroup$
That confirms my intution, but can you get Mathematica to output the PDF for the triangular distribution? That is what I am having trouble doing.
$endgroup$
– user120911
1 hour ago
add a comment |
$begingroup$
PDF[[ScriptCapitalD]][z]
(((-30 + z)Sign[-30 + z])/2 - (-20 + z)
Sign[-20 + z] + ((-10 + z)*Sign[-10 + z])/2)/100
For plotting, assign values to L and H:
L = 10; H = 30;
Plot[Evaluate@PDF[[ScriptCapitalD]][x], x, 10, 30]
pdF[l_, h_] := Module[L = l, H = h, Evaluate[PDF[[ScriptCapitalD]]]]
Plot[Evaluate @ Flatten@Table[pdF[l, h][x], l, 0, 5, h, 10, 15], x, 0, 15,
PlotRange -> All,
PlotLegends -> (Flatten @ Table[ToString@l, h, l, 0, 5, h, 10, 15])]
answered 1 hour ago
kglrkglr
189k10206424
$endgroup$
$begingroup$
That confirms my intution, but can you get Mathematica to output the PDF for the triangular distribution? That is what I am having trouble doing.
$endgroup$
– user120911
1 hour ago
add a comment |
$begingroup$
PDF[[ScriptCapitalD]][z]
(((-30 + z)Sign[-30 + z])/2 - (-20 + z)
Sign[-20 + z] + ((-10 + z)*Sign[-10 + z])/2)/100
For plotting, assign values to L and H:
L = 10; H = 30;
Plot[Evaluate@PDF[[ScriptCapitalD]][x], x, 10, 30]
pdF[l_, h_] := Module[L = l, H = h, Evaluate[PDF[[ScriptCapitalD]]]]
Plot[Evaluate @ Flatten@Table[pdF[l, h][x], l, 0, 5, h, 10, 15], x, 0, 15,
PlotRange -> All,
PlotLegends -> (Flatten @ Table[ToString@l, h, l, 0, 5, h, 10, 15])]
answered 1 hour ago
kglrkglr
189k10206424
$endgroup$
PDF[[ScriptCapitalD]][z]
(((-30 + z)Sign[-30 + z])/2 - (-20 + z)
Sign[-20 + z] + ((-10 + z)*Sign[-10 + z])/2)/100
For plotting, assign values to L and H:
L = 10; H = 30;
Plot[Evaluate@PDF[[ScriptCapitalD]][x], x, 10, 30]
pdF[l_, h_] := Module[L = l, H = h, Evaluate[PDF[[ScriptCapitalD]]]]
Plot[Evaluate @ Flatten@Table[pdF[l, h][x], l, 0, 5, h, 10, 15], x, 0, 15,
PlotRange -> All,
PlotLegends -> (Flatten @ Table[ToString@l, h, l, 0, 5, h, 10, 15])]
answered 1 hour ago
kglrkglr
189k10206424
answered 1 hour ago
kglrkglr
189k10206424
answered 1 hour ago
kglrkglr
189k10206424
answered 1 hour ago
kglrkglr
189k10206424
189k10206424
$begingroup$
That confirms my intution, but can you get Mathematica to output the PDF for the triangular distribution? That is what I am having trouble doing.
$endgroup$
– user120911
1 hour ago
add a comment |
$begingroup$
That confirms my intution, but can you get Mathematica to output the PDF for the triangular distribution? That is what I am having trouble doing.
$endgroup$
– user120911
1 hour ago
$begingroup$
That confirms my intution, but can you get Mathematica to output the PDF for the triangular distribution? That is what I am having trouble doing.
$endgroup$
– user120911
1 hour ago
$begingroup$
That confirms my intution, but can you get Mathematica to output the PDF for the triangular distribution? That is what I am having trouble doing.
$endgroup$
– user120911
1 hour ago
add a comment |
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f193838%2fproblem-with-transformeddistribution%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
That was a typo. But I am still not getting what I expect.
$endgroup$
– user120911
1 hour ago
$begingroup$
Did you try
PDF[[ScriptCapitalD], y]?$endgroup$
– JimB
1 hour ago
$begingroup$
PDF[[ScriptCapitalD], y] produces one expression with a denominator that looks correct, but the triangular distribution is split at the mode. Mathematica is not showing that. At least not in a way that is easy to see.
$endgroup$
– user120911
1 hour ago
$begingroup$
Are you aware
TriangularDistribution[]is built-in?$endgroup$
– J. M. is slightly pensive♦
1 hour ago
1
$begingroup$
Why not check the PDFs?
Simplify[PDF[TransformedDistribution[(a + b)/2, a, b [Distributed] UniformDistribution[l, h, l, h]], t] == PDF[TriangularDistribution[l, h], t], l < t < h]$endgroup$
– J. M. is slightly pensive♦
41 mins ago