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Why the Cauchy Distribution is so useful?
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Why the Cauchy Distribution is so useful?
What are the properties of a half Cauchy distribution?Why does the Cauchy distribution have no mean?Approximation of Cauchy distributionEntropy of Cauchy (Lorentz) Distributionconvergence of Cauchy distributionCan the Cauchy distribution work well for modelling up-vote/down-vote ratio?What is the distribution of sample means of a Cauchy distribution?How can I find the distribution of sample mean of Cauchy distribution?Difference between a Student-T vs Cauchy distributionHow to determine if a distribution is Cauchy?Is Cauchy distribution somehow an “unpredictable” distribution?
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$begingroup$
Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
distributions continuous-data cauchy
edited 9 hours ago
Matthew Anderson
1158 bronze badges
asked 10 hours ago
Maria LavrovskayaMaria Lavrovskaya
366 bronze badges
$endgroup$
add a comment |
$begingroup$
Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
distributions continuous-data cauchy
edited 9 hours ago
Matthew Anderson
1158 bronze badges
asked 10 hours ago
Maria LavrovskayaMaria Lavrovskaya
366 bronze badges
$endgroup$
add a comment |
$begingroup$
Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
distributions continuous-data cauchy
edited 9 hours ago
Matthew Anderson
1158 bronze badges
asked 10 hours ago
Maria LavrovskayaMaria Lavrovskaya
366 bronze badges
$endgroup$
Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
distributions continuous-data cauchy
distributions continuous-data cauchy
edited 9 hours ago
Matthew Anderson
1158 bronze badges
asked 10 hours ago
Maria LavrovskayaMaria Lavrovskaya
366 bronze badges
edited 9 hours ago
Matthew Anderson
1158 bronze badges
asked 10 hours ago
Maria LavrovskayaMaria Lavrovskaya
366 bronze badges
edited 9 hours ago
Matthew Anderson
1158 bronze badges
edited 9 hours ago
Matthew Anderson
1158 bronze badges
edited 9 hours ago
Matthew Anderson
1158 bronze badges
1158 bronze badges
asked 10 hours ago
Maria LavrovskayaMaria Lavrovskaya
366 bronze badges
asked 10 hours ago
Maria LavrovskayaMaria Lavrovskaya
366 bronze badges
asked 10 hours ago
Maria LavrovskayaMaria Lavrovskaya
366 bronze badges
366 bronze badges
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The standard Cauchy distribution is derived from the ratio of two independent Normal Distributions. If $X sim N(0,1)$, and $Y sim N(0,1)$, then $tfracXY sim Cauchy(0,1)$.
The Cauchy distribution is important in physics (where it’s known as the Lorentz distribution) because it’s the solution to the differential equation describing forced resonance. In spectroscopy, it is the description of the shape of spectral lines which are subject to homogeneous broadening in which all atoms interact in the same way with the frequency range contained in the line shape.
Applications:
Used in mechanical and electrical theory, physical anthropology and
measurement and calibration problems.In physics it is called a Lorentzian distribution, where it is the
distribution of the energy of an unstable state in quantum mechanics.Also used to model the points of impact of a fixed straight line of
particles emitted from a point source.
Source.
answered 10 hours ago
Matthew AndersonMatthew Anderson
1158 bronze badges
$endgroup$
$begingroup$
Thank you. The first sentence is pretty helpful. I am quite far from the physics, could you give any examples considering finance or machine learning?
$endgroup$
– Maria Lavrovskaya
10 hours ago
1
$begingroup$
It's not really used in finance or machine learning (practically); it's used in physics (99.9% of the time). I suppose that if someone wanted to model the ratio between two independent, normally distributed variables in finance, they would use the Cauchy distribution.
$endgroup$
– Matthew Anderson
10 hours ago
1
$begingroup$
A reason it could be useful in finance is that it has extremely heavy tails. It has no moments, so it doesn’t make sense to say that it has high kurtosis, but it is prone to extreme observations, both high and low.
$endgroup$
– Dave
9 hours ago
4
$begingroup$
It is used in machine learning, in particular as a prior distribution in Bayesian inference. In particular the half-Cauchy is used as a prior for certain scale variables.
$endgroup$
– Wayne
9 hours ago
2
$begingroup$
@Wayne Could you please give an example, maybe a reference?
$endgroup$
– Dave
8 hours ago
|
show 2 more comments
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The standard Cauchy distribution is derived from the ratio of two independent Normal Distributions. If $X sim N(0,1)$, and $Y sim N(0,1)$, then $tfracXY sim Cauchy(0,1)$.
The Cauchy distribution is important in physics (where it’s known as the Lorentz distribution) because it’s the solution to the differential equation describing forced resonance. In spectroscopy, it is the description of the shape of spectral lines which are subject to homogeneous broadening in which all atoms interact in the same way with the frequency range contained in the line shape.
Applications:
Used in mechanical and electrical theory, physical anthropology and
measurement and calibration problems.In physics it is called a Lorentzian distribution, where it is the
distribution of the energy of an unstable state in quantum mechanics.Also used to model the points of impact of a fixed straight line of
particles emitted from a point source.
Source.
answered 10 hours ago
Matthew AndersonMatthew Anderson
1158 bronze badges
$endgroup$
$begingroup$
Thank you. The first sentence is pretty helpful. I am quite far from the physics, could you give any examples considering finance or machine learning?
$endgroup$
– Maria Lavrovskaya
10 hours ago
1
$begingroup$
It's not really used in finance or machine learning (practically); it's used in physics (99.9% of the time). I suppose that if someone wanted to model the ratio between two independent, normally distributed variables in finance, they would use the Cauchy distribution.
$endgroup$
– Matthew Anderson
10 hours ago
1
$begingroup$
A reason it could be useful in finance is that it has extremely heavy tails. It has no moments, so it doesn’t make sense to say that it has high kurtosis, but it is prone to extreme observations, both high and low.
$endgroup$
– Dave
9 hours ago
4
$begingroup$
It is used in machine learning, in particular as a prior distribution in Bayesian inference. In particular the half-Cauchy is used as a prior for certain scale variables.
$endgroup$
– Wayne
9 hours ago
2
$begingroup$
@Wayne Could you please give an example, maybe a reference?
$endgroup$
– Dave
8 hours ago
|
show 2 more comments
$begingroup$
The standard Cauchy distribution is derived from the ratio of two independent Normal Distributions. If $X sim N(0,1)$, and $Y sim N(0,1)$, then $tfracXY sim Cauchy(0,1)$.
The Cauchy distribution is important in physics (where it’s known as the Lorentz distribution) because it’s the solution to the differential equation describing forced resonance. In spectroscopy, it is the description of the shape of spectral lines which are subject to homogeneous broadening in which all atoms interact in the same way with the frequency range contained in the line shape.
Applications:
Used in mechanical and electrical theory, physical anthropology and
measurement and calibration problems.In physics it is called a Lorentzian distribution, where it is the
distribution of the energy of an unstable state in quantum mechanics.Also used to model the points of impact of a fixed straight line of
particles emitted from a point source.
Source.
answered 10 hours ago
Matthew AndersonMatthew Anderson
1158 bronze badges
$endgroup$
$begingroup$
Thank you. The first sentence is pretty helpful. I am quite far from the physics, could you give any examples considering finance or machine learning?
$endgroup$
– Maria Lavrovskaya
10 hours ago
1
$begingroup$
It's not really used in finance or machine learning (practically); it's used in physics (99.9% of the time). I suppose that if someone wanted to model the ratio between two independent, normally distributed variables in finance, they would use the Cauchy distribution.
$endgroup$
– Matthew Anderson
10 hours ago
1
$begingroup$
A reason it could be useful in finance is that it has extremely heavy tails. It has no moments, so it doesn’t make sense to say that it has high kurtosis, but it is prone to extreme observations, both high and low.
$endgroup$
– Dave
9 hours ago
4
$begingroup$
It is used in machine learning, in particular as a prior distribution in Bayesian inference. In particular the half-Cauchy is used as a prior for certain scale variables.
$endgroup$
– Wayne
9 hours ago
2
$begingroup$
@Wayne Could you please give an example, maybe a reference?
$endgroup$
– Dave
8 hours ago
|
show 2 more comments
$begingroup$
The standard Cauchy distribution is derived from the ratio of two independent Normal Distributions. If $X sim N(0,1)$, and $Y sim N(0,1)$, then $tfracXY sim Cauchy(0,1)$.
The Cauchy distribution is important in physics (where it’s known as the Lorentz distribution) because it’s the solution to the differential equation describing forced resonance. In spectroscopy, it is the description of the shape of spectral lines which are subject to homogeneous broadening in which all atoms interact in the same way with the frequency range contained in the line shape.
Applications:
Used in mechanical and electrical theory, physical anthropology and
measurement and calibration problems.In physics it is called a Lorentzian distribution, where it is the
distribution of the energy of an unstable state in quantum mechanics.Also used to model the points of impact of a fixed straight line of
particles emitted from a point source.
Source.
answered 10 hours ago
Matthew AndersonMatthew Anderson
1158 bronze badges
$endgroup$
The standard Cauchy distribution is derived from the ratio of two independent Normal Distributions. If $X sim N(0,1)$, and $Y sim N(0,1)$, then $tfracXY sim Cauchy(0,1)$.
The Cauchy distribution is important in physics (where it’s known as the Lorentz distribution) because it’s the solution to the differential equation describing forced resonance. In spectroscopy, it is the description of the shape of spectral lines which are subject to homogeneous broadening in which all atoms interact in the same way with the frequency range contained in the line shape.
Applications:
Used in mechanical and electrical theory, physical anthropology and
measurement and calibration problems.In physics it is called a Lorentzian distribution, where it is the
distribution of the energy of an unstable state in quantum mechanics.Also used to model the points of impact of a fixed straight line of
particles emitted from a point source.
Source.
answered 10 hours ago
Matthew AndersonMatthew Anderson
1158 bronze badges
answered 10 hours ago
Matthew AndersonMatthew Anderson
1158 bronze badges
answered 10 hours ago
Matthew AndersonMatthew Anderson
1158 bronze badges
answered 10 hours ago
Matthew AndersonMatthew Anderson
1158 bronze badges
1158 bronze badges
$begingroup$
Thank you. The first sentence is pretty helpful. I am quite far from the physics, could you give any examples considering finance or machine learning?
$endgroup$
– Maria Lavrovskaya
10 hours ago
1
$begingroup$
It's not really used in finance or machine learning (practically); it's used in physics (99.9% of the time). I suppose that if someone wanted to model the ratio between two independent, normally distributed variables in finance, they would use the Cauchy distribution.
$endgroup$
– Matthew Anderson
10 hours ago
1
$begingroup$
A reason it could be useful in finance is that it has extremely heavy tails. It has no moments, so it doesn’t make sense to say that it has high kurtosis, but it is prone to extreme observations, both high and low.
$endgroup$
– Dave
9 hours ago
4
$begingroup$
It is used in machine learning, in particular as a prior distribution in Bayesian inference. In particular the half-Cauchy is used as a prior for certain scale variables.
$endgroup$
– Wayne
9 hours ago
2
$begingroup$
@Wayne Could you please give an example, maybe a reference?
$endgroup$
– Dave
8 hours ago
|
show 2 more comments
$begingroup$
Thank you. The first sentence is pretty helpful. I am quite far from the physics, could you give any examples considering finance or machine learning?
$endgroup$
– Maria Lavrovskaya
10 hours ago
1
$begingroup$
It's not really used in finance or machine learning (practically); it's used in physics (99.9% of the time). I suppose that if someone wanted to model the ratio between two independent, normally distributed variables in finance, they would use the Cauchy distribution.
$endgroup$
– Matthew Anderson
10 hours ago
1
$begingroup$
A reason it could be useful in finance is that it has extremely heavy tails. It has no moments, so it doesn’t make sense to say that it has high kurtosis, but it is prone to extreme observations, both high and low.
$endgroup$
– Dave
9 hours ago
4
$begingroup$
It is used in machine learning, in particular as a prior distribution in Bayesian inference. In particular the half-Cauchy is used as a prior for certain scale variables.
$endgroup$
– Wayne
9 hours ago
2
$begingroup$
@Wayne Could you please give an example, maybe a reference?
$endgroup$
– Dave
8 hours ago
$begingroup$
Thank you. The first sentence is pretty helpful. I am quite far from the physics, could you give any examples considering finance or machine learning?
$endgroup$
– Maria Lavrovskaya
10 hours ago
$begingroup$
Thank you. The first sentence is pretty helpful. I am quite far from the physics, could you give any examples considering finance or machine learning?
$endgroup$
– Maria Lavrovskaya
10 hours ago
1
1
$begingroup$
It's not really used in finance or machine learning (practically); it's used in physics (99.9% of the time). I suppose that if someone wanted to model the ratio between two independent, normally distributed variables in finance, they would use the Cauchy distribution.
$endgroup$
– Matthew Anderson
10 hours ago
$begingroup$
It's not really used in finance or machine learning (practically); it's used in physics (99.9% of the time). I suppose that if someone wanted to model the ratio between two independent, normally distributed variables in finance, they would use the Cauchy distribution.
$endgroup$
– Matthew Anderson
10 hours ago
1
1
$begingroup$
A reason it could be useful in finance is that it has extremely heavy tails. It has no moments, so it doesn’t make sense to say that it has high kurtosis, but it is prone to extreme observations, both high and low.
$endgroup$
– Dave
9 hours ago
$begingroup$
A reason it could be useful in finance is that it has extremely heavy tails. It has no moments, so it doesn’t make sense to say that it has high kurtosis, but it is prone to extreme observations, both high and low.
$endgroup$
– Dave
9 hours ago
4
4
$begingroup$
It is used in machine learning, in particular as a prior distribution in Bayesian inference. In particular the half-Cauchy is used as a prior for certain scale variables.
$endgroup$
– Wayne
9 hours ago
$begingroup$
It is used in machine learning, in particular as a prior distribution in Bayesian inference. In particular the half-Cauchy is used as a prior for certain scale variables.
$endgroup$
– Wayne
9 hours ago
2
2
$begingroup$
@Wayne Could you please give an example, maybe a reference?
$endgroup$
– Dave
8 hours ago
$begingroup$
@Wayne Could you please give an example, maybe a reference?
$endgroup$
– Dave
8 hours ago
|
show 2 more comments
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