Is there a software that solves this equation.

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I have a series of equations of the form:
$p int_0^infty f(x) dx = int_delta^infty g(x) dx$
where p is a probability (between 0 and 1).



In other words, I have some fraction of the area under the curve, being equal to the area under the curve of another function, starting at point delta, rather then 0. Please note that the two functions are not the same.



I'd like to set the values of p and delta such that the equations balance. This can be fixing, say p, to a constant and solving for delta or vice versa ( I have small set of values of special interest for each) but even better would be a function or a plot that shows when the equation balances.



My question is is there a softwareor a webservice where I can input my equation and it would return this functionplotvalues?



Thanks




math-software line-integrals




share|cite|improve this question



















  • Depending on how the integrands behave you may need a quadrature.
    – Sean Roberson
    Jul 31 at 22:15










  • what is a quadrature?
    – Rafa
    Jul 31 at 22:16










  • It's any type of numerical integration rule.
    – Sean Roberson
    Jul 31 at 22:17










  • If $f$ and $g$ are common probability density functions this would be easy enough in R. For example if $f$ was the density of a normal distribution with mean $4$ and standard deviation $3$, and $g$ the density of an exponential distribution with rate $2$ and $p=0.7$ then $delta$ could be found with something like the following code: qexp(1 - 0.7 * (1 - pnorm(0, mean=4, sd=3)), rate=2) while if $delta=0.226$ then $p$ could be found with (1 - pexp(0.226, rate=2)) / (1 - pnorm(0, mean=4, sd=3))
    – Henry
    Jul 31 at 22:22











  • Two unknowns makes this tricky. Hard to say exactly what $(p,delta)$ looks like without knowing your functions $f$ and $g$. Wolfram alpha can integrate $f$ from zero to infinity however... depending on how nice a function $f$ is..
    – Mason
    Jul 31 at 22:34















up vote
0
down vote

favorite












I have a series of equations of the form:
$p int_0^infty f(x) dx = int_delta^infty g(x) dx$
where p is a probability (between 0 and 1).



In other words, I have some fraction of the area under the curve, being equal to the area under the curve of another function, starting at point delta, rather then 0. Please note that the two functions are not the same.



I'd like to set the values of p and delta such that the equations balance. This can be fixing, say p, to a constant and solving for delta or vice versa ( I have small set of values of special interest for each) but even better would be a function or a plot that shows when the equation balances.



My question is is there a softwareor a webservice where I can input my equation and it would return this functionplotvalues?



Thanks




math-software line-integrals




share|cite|improve this question



















  • Depending on how the integrands behave you may need a quadrature.
    – Sean Roberson
    Jul 31 at 22:15










  • what is a quadrature?
    – Rafa
    Jul 31 at 22:16










  • It's any type of numerical integration rule.
    – Sean Roberson
    Jul 31 at 22:17










  • If $f$ and $g$ are common probability density functions this would be easy enough in R. For example if $f$ was the density of a normal distribution with mean $4$ and standard deviation $3$, and $g$ the density of an exponential distribution with rate $2$ and $p=0.7$ then $delta$ could be found with something like the following code: qexp(1 - 0.7 * (1 - pnorm(0, mean=4, sd=3)), rate=2) while if $delta=0.226$ then $p$ could be found with (1 - pexp(0.226, rate=2)) / (1 - pnorm(0, mean=4, sd=3))
    – Henry
    Jul 31 at 22:22











  • Two unknowns makes this tricky. Hard to say exactly what $(p,delta)$ looks like without knowing your functions $f$ and $g$. Wolfram alpha can integrate $f$ from zero to infinity however... depending on how nice a function $f$ is..
    – Mason
    Jul 31 at 22:34













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have a series of equations of the form:
$p int_0^infty f(x) dx = int_delta^infty g(x) dx$
where p is a probability (between 0 and 1).



In other words, I have some fraction of the area under the curve, being equal to the area under the curve of another function, starting at point delta, rather then 0. Please note that the two functions are not the same.



I'd like to set the values of p and delta such that the equations balance. This can be fixing, say p, to a constant and solving for delta or vice versa ( I have small set of values of special interest for each) but even better would be a function or a plot that shows when the equation balances.



My question is is there a softwareor a webservice where I can input my equation and it would return this functionplotvalues?



Thanks




math-software line-integrals




share|cite|improve this question











I have a series of equations of the form:
$p int_0^infty f(x) dx = int_delta^infty g(x) dx$
where p is a probability (between 0 and 1).



In other words, I have some fraction of the area under the curve, being equal to the area under the curve of another function, starting at point delta, rather then 0. Please note that the two functions are not the same.



I'd like to set the values of p and delta such that the equations balance. This can be fixing, say p, to a constant and solving for delta or vice versa ( I have small set of values of special interest for each) but even better would be a function or a plot that shows when the equation balances.



My question is is there a softwareor a webservice where I can input my equation and it would return this functionplotvalues?



Thanks





math-software line-integrals





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 31 at 22:12









Rafa

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1021











  • Depending on how the integrands behave you may need a quadrature.
    – Sean Roberson
    Jul 31 at 22:15










  • what is a quadrature?
    – Rafa
    Jul 31 at 22:16










  • It's any type of numerical integration rule.
    – Sean Roberson
    Jul 31 at 22:17










  • If $f$ and $g$ are common probability density functions this would be easy enough in R. For example if $f$ was the density of a normal distribution with mean $4$ and standard deviation $3$, and $g$ the density of an exponential distribution with rate $2$ and $p=0.7$ then $delta$ could be found with something like the following code: qexp(1 - 0.7 * (1 - pnorm(0, mean=4, sd=3)), rate=2) while if $delta=0.226$ then $p$ could be found with (1 - pexp(0.226, rate=2)) / (1 - pnorm(0, mean=4, sd=3))
    – Henry
    Jul 31 at 22:22











  • Two unknowns makes this tricky. Hard to say exactly what $(p,delta)$ looks like without knowing your functions $f$ and $g$. Wolfram alpha can integrate $f$ from zero to infinity however... depending on how nice a function $f$ is..
    – Mason
    Jul 31 at 22:34

















  • Depending on how the integrands behave you may need a quadrature.
    – Sean Roberson
    Jul 31 at 22:15










  • what is a quadrature?
    – Rafa
    Jul 31 at 22:16










  • It's any type of numerical integration rule.
    – Sean Roberson
    Jul 31 at 22:17










  • If $f$ and $g$ are common probability density functions this would be easy enough in R. For example if $f$ was the density of a normal distribution with mean $4$ and standard deviation $3$, and $g$ the density of an exponential distribution with rate $2$ and $p=0.7$ then $delta$ could be found with something like the following code: qexp(1 - 0.7 * (1 - pnorm(0, mean=4, sd=3)), rate=2) while if $delta=0.226$ then $p$ could be found with (1 - pexp(0.226, rate=2)) / (1 - pnorm(0, mean=4, sd=3))
    – Henry
    Jul 31 at 22:22











  • Two unknowns makes this tricky. Hard to say exactly what $(p,delta)$ looks like without knowing your functions $f$ and $g$. Wolfram alpha can integrate $f$ from zero to infinity however... depending on how nice a function $f$ is..
    – Mason
    Jul 31 at 22:34
















Depending on how the integrands behave you may need a quadrature.
– Sean Roberson
Jul 31 at 22:15




Depending on how the integrands behave you may need a quadrature.
– Sean Roberson
Jul 31 at 22:15












what is a quadrature?
– Rafa
Jul 31 at 22:16




what is a quadrature?
– Rafa
Jul 31 at 22:16












It's any type of numerical integration rule.
– Sean Roberson
Jul 31 at 22:17




It's any type of numerical integration rule.
– Sean Roberson
Jul 31 at 22:17












If $f$ and $g$ are common probability density functions this would be easy enough in R. For example if $f$ was the density of a normal distribution with mean $4$ and standard deviation $3$, and $g$ the density of an exponential distribution with rate $2$ and $p=0.7$ then $delta$ could be found with something like the following code: qexp(1 - 0.7 * (1 - pnorm(0, mean=4, sd=3)), rate=2) while if $delta=0.226$ then $p$ could be found with (1 - pexp(0.226, rate=2)) / (1 - pnorm(0, mean=4, sd=3))
– Henry
Jul 31 at 22:22





If $f$ and $g$ are common probability density functions this would be easy enough in R. For example if $f$ was the density of a normal distribution with mean $4$ and standard deviation $3$, and $g$ the density of an exponential distribution with rate $2$ and $p=0.7$ then $delta$ could be found with something like the following code: qexp(1 - 0.7 * (1 - pnorm(0, mean=4, sd=3)), rate=2) while if $delta=0.226$ then $p$ could be found with (1 - pexp(0.226, rate=2)) / (1 - pnorm(0, mean=4, sd=3))
– Henry
Jul 31 at 22:22













Two unknowns makes this tricky. Hard to say exactly what $(p,delta)$ looks like without knowing your functions $f$ and $g$. Wolfram alpha can integrate $f$ from zero to infinity however... depending on how nice a function $f$ is..
– Mason
Jul 31 at 22:34





Two unknowns makes this tricky. Hard to say exactly what $(p,delta)$ looks like without knowing your functions $f$ and $g$. Wolfram alpha can integrate $f$ from zero to infinity however... depending on how nice a function $f$ is..
– Mason
Jul 31 at 22:34
















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