Calculating probability from inverse sampling The Next CEO of Stack OverflowSampling a combination randomlyProblems sampling from a $pdf$ over $SOleft(3right)$Need an easy CDF for Inverse transform samplingGeometric explanation of Inverse Transform SamplingMultivariate Inverse Transformation SamplingDefinition of sampling distribution and its roleHelp on statistics question: sampling distribution of meansStatistics Inverse Method in RstudioSampling distribution Normal Approximation MisfitSampling from probability distribution via multiplying probabilities by a uniform random number
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Calculating probability from inverse sampling
The Next CEO of Stack OverflowSampling a combination randomlyProblems sampling from a $pdf$ over $SOleft(3right)$Need an easy CDF for Inverse transform samplingGeometric explanation of Inverse Transform SamplingMultivariate Inverse Transformation SamplingDefinition of sampling distribution and its roleHelp on statistics question: sampling distribution of meansStatistics Inverse Method in RstudioSampling distribution Normal Approximation MisfitSampling from probability distribution via multiplying probabilities by a uniform random number
$begingroup$
I have the logistic distribution
$$F(x)=frac11+e^-x$$
and by the inverse sampling method, solving $u=F(x)$ gives
$$ F^-1(u) = -log(u^-1-1).$$
I have then generated a sample of the distribution by using the uniform distribution for $n$ sample size. Given this, how do I calculate the probability $F(1)$ by my inverse transform method? I have created this distribution in R.
My thought was to somehow calculate the area under the curve? Any hints greatly appreciated.
probability statistics
asked 2 days ago
rodger_kicksrodger_kicks
8110
$endgroup$
add a comment |
$begingroup$
I have the logistic distribution
$$F(x)=frac11+e^-x$$
and by the inverse sampling method, solving $u=F(x)$ gives
$$ F^-1(u) = -log(u^-1-1).$$
I have then generated a sample of the distribution by using the uniform distribution for $n$ sample size. Given this, how do I calculate the probability $F(1)$ by my inverse transform method? I have created this distribution in R.
My thought was to somehow calculate the area under the curve? Any hints greatly appreciated.
probability statistics
asked 2 days ago
rodger_kicksrodger_kicks
8110
$endgroup$
$begingroup$
Hint: what is the definition of $F(1)$, for an arbitrary CDF $F$?
$endgroup$
– J.G.
2 days ago
add a comment |
$begingroup$
I have the logistic distribution
$$F(x)=frac11+e^-x$$
and by the inverse sampling method, solving $u=F(x)$ gives
$$ F^-1(u) = -log(u^-1-1).$$
I have then generated a sample of the distribution by using the uniform distribution for $n$ sample size. Given this, how do I calculate the probability $F(1)$ by my inverse transform method? I have created this distribution in R.
My thought was to somehow calculate the area under the curve? Any hints greatly appreciated.
probability statistics
asked 2 days ago
rodger_kicksrodger_kicks
8110
$endgroup$
I have the logistic distribution
$$F(x)=frac11+e^-x$$
and by the inverse sampling method, solving $u=F(x)$ gives
$$ F^-1(u) = -log(u^-1-1).$$
I have then generated a sample of the distribution by using the uniform distribution for $n$ sample size. Given this, how do I calculate the probability $F(1)$ by my inverse transform method? I have created this distribution in R.
My thought was to somehow calculate the area under the curve? Any hints greatly appreciated.
probability statistics
probability statistics
asked 2 days ago
rodger_kicksrodger_kicks
8110
asked 2 days ago
rodger_kicksrodger_kicks
8110
asked 2 days ago
rodger_kicksrodger_kicks
8110
asked 2 days ago
rodger_kicksrodger_kicks
8110
asked 2 days ago
rodger_kicksrodger_kicks
8110
8110
$begingroup$
Hint: what is the definition of $F(1)$, for an arbitrary CDF $F$?
$endgroup$
– J.G.
2 days ago
add a comment |
$begingroup$
Hint: what is the definition of $F(1)$, for an arbitrary CDF $F$?
$endgroup$
– J.G.
2 days ago
$begingroup$
Hint: what is the definition of $F(1)$, for an arbitrary CDF $F$?
$endgroup$
– J.G.
2 days ago
$begingroup$
Hint: what is the definition of $F(1)$, for an arbitrary CDF $F$?
$endgroup$
– J.G.
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You could do a Monte-Carlo simulation.
Let's say you have generated $x_1,dots,x_n$, $n$ realizations of a given law, then the law of large numbers tells us that
$$
fracsum_i=1^n1_x_ileq1n xrightarrow[ntoinfty] mathbbE[1_Xleq1]=mathbbPXleq1=F(1)
$$
answered 2 days ago
Antoine FalckAntoine Falck
1
New contributor
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
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1 Answer
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active
oldest
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oldest
votes
$begingroup$
You could do a Monte-Carlo simulation.
Let's say you have generated $x_1,dots,x_n$, $n$ realizations of a given law, then the law of large numbers tells us that
$$
fracsum_i=1^n1_x_ileq1n xrightarrow[ntoinfty] mathbbE[1_Xleq1]=mathbbPXleq1=F(1)
$$
answered 2 days ago
Antoine FalckAntoine Falck
1
New contributor
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
You could do a Monte-Carlo simulation.
Let's say you have generated $x_1,dots,x_n$, $n$ realizations of a given law, then the law of large numbers tells us that
$$
fracsum_i=1^n1_x_ileq1n xrightarrow[ntoinfty] mathbbE[1_Xleq1]=mathbbPXleq1=F(1)
$$
answered 2 days ago
Antoine FalckAntoine Falck
1
New contributor
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
You could do a Monte-Carlo simulation.
Let's say you have generated $x_1,dots,x_n$, $n$ realizations of a given law, then the law of large numbers tells us that
$$
fracsum_i=1^n1_x_ileq1n xrightarrow[ntoinfty] mathbbE[1_Xleq1]=mathbbPXleq1=F(1)
$$
answered 2 days ago
Antoine FalckAntoine Falck
1
New contributor
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
You could do a Monte-Carlo simulation.
Let's say you have generated $x_1,dots,x_n$, $n$ realizations of a given law, then the law of large numbers tells us that
$$
fracsum_i=1^n1_x_ileq1n xrightarrow[ntoinfty] mathbbE[1_Xleq1]=mathbbPXleq1=F(1)
$$
answered 2 days ago
Antoine FalckAntoine Falck
1
New contributor
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 days ago
Antoine FalckAntoine Falck
1
New contributor
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 days ago
Antoine FalckAntoine Falck
1
answered 2 days ago
Antoine FalckAntoine Falck
1
1
New contributor
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Antoine Falck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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$begingroup$
Hint: what is the definition of $F(1)$, for an arbitrary CDF $F$?
$endgroup$
– J.G.
2 days ago