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Hi,

I am doing work that requires me to take the derivative of an integral over a distribution. I believe I calculated it correctly, but when I simulate the results in matlab, the plot for the integral and its derivative don't match up.

Here is the equation:

[tex]

$\int_{-\infty }^{\infty }\left[ p[1-G(p-y)]+\int_{-\infty }^{p-y}zg(z)dz\right] f(y)dy$

[/tex]

where G is the cdf of z with g the associated pdf, and F is the CDF of y with f the associated pdf.

I believe the derivative is the following:

[tex]

$\int_{-\infty }^{\infty }\left[ [1-G(p-y)]-yg(p-y)dz\right] $

[/tex]

But, when I simulate the two in matlab the graphs don't match up. See attached pdf.

Thanks for your help.

Any insight would be greatly appreciated.

All the best,

Bob

I am doing work that requires me to take the derivative of an integral over a distribution. I believe I calculated it correctly, but when I simulate the results in matlab, the plot for the integral and its derivative don't match up.

Here is the equation:

[tex]

$\int_{-\infty }^{\infty }\left[ p[1-G(p-y)]+\int_{-\infty }^{p-y}zg(z)dz\right] f(y)dy$

[/tex]

where G is the cdf of z with g the associated pdf, and F is the CDF of y with f the associated pdf.

I believe the derivative is the following:

[tex]

$\int_{-\infty }^{\infty }\left[ [1-G(p-y)]-yg(p-y)dz\right] $

[/tex]

But, when I simulate the two in matlab the graphs don't match up. See attached pdf.

Thanks for your help.

Any insight would be greatly appreciated.

All the best,

Bob

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