Loss Distribution | cost per payment $Y = alpha X + (1 - alpha)(X-d)+$, Find CDF , PDF and mean of $Y$
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For an insurance policy loss $𝑋$, we define the cost per payment: $𝑌=𝛼𝑋+(1−𝛼)(𝑋−𝑑)+$, for $𝛼∈(0,1)$ and $𝑑>0$. Compute the cdf, pdf and mean of $𝑌$.
actuarial-science
asked Nov 19 at 16:41
M.F
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For an insurance policy loss $𝑋$, we define the cost per payment: $𝑌=𝛼𝑋+(1−𝛼)(𝑋−𝑑)+$, for $𝛼∈(0,1)$ and $𝑑>0$. Compute the cdf, pdf and mean of $𝑌$.
actuarial-science
asked Nov 19 at 16:41
M.F
11
I think you have to mention how X Is distributed.
– Thomas
Nov 19 at 17:41
Any distribution. But if important we say X~EXP(λ)
– M.F
Nov 19 at 18:00
So expanding what you write $Y=X-d(1-alpha)$, so the distribution of $Y$ is just the distribution of $X$ shifted but maybe I am not getting your question...
– Thomas
Nov 19 at 19:09
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
For an insurance policy loss $𝑋$, we define the cost per payment: $𝑌=𝛼𝑋+(1−𝛼)(𝑋−𝑑)+$, for $𝛼∈(0,1)$ and $𝑑>0$. Compute the cdf, pdf and mean of $𝑌$.
actuarial-science
asked Nov 19 at 16:41
M.F
11
For an insurance policy loss $𝑋$, we define the cost per payment: $𝑌=𝛼𝑋+(1−𝛼)(𝑋−𝑑)+$, for $𝛼∈(0,1)$ and $𝑑>0$. Compute the cdf, pdf and mean of $𝑌$.
actuarial-science
actuarial-science
asked Nov 19 at 16:41
M.F
11
asked Nov 19 at 16:41
M.F
11
edited Nov 19 at 18:04
asked Nov 19 at 16:41
M.F
11
asked Nov 19 at 16:41
M.F
11
asked Nov 19 at 16:41
M.F
11
11
I think you have to mention how X Is distributed.
– Thomas
Nov 19 at 17:41
Any distribution. But if important we say X~EXP(λ)
– M.F
Nov 19 at 18:00
So expanding what you write $Y=X-d(1-alpha)$, so the distribution of $Y$ is just the distribution of $X$ shifted but maybe I am not getting your question...
– Thomas
Nov 19 at 19:09
add a comment |
I think you have to mention how X Is distributed.
– Thomas
Nov 19 at 17:41
Any distribution. But if important we say X~EXP(λ)
– M.F
Nov 19 at 18:00
So expanding what you write $Y=X-d(1-alpha)$, so the distribution of $Y$ is just the distribution of $X$ shifted but maybe I am not getting your question...
– Thomas
Nov 19 at 19:09
I think you have to mention how X Is distributed.
– Thomas
Nov 19 at 17:41
I think you have to mention how X Is distributed.
– Thomas
Nov 19 at 17:41
Any distribution. But if important we say X~EXP(λ)
– M.F
Nov 19 at 18:00
Any distribution. But if important we say X~EXP(λ)
– M.F
Nov 19 at 18:00
So expanding what you write $Y=X-d(1-alpha)$, so the distribution of $Y$ is just the distribution of $X$ shifted but maybe I am not getting your question...
– Thomas
Nov 19 at 19:09
So expanding what you write $Y=X-d(1-alpha)$, so the distribution of $Y$ is just the distribution of $X$ shifted but maybe I am not getting your question...
– Thomas
Nov 19 at 19:09
add a comment |
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I think you have to mention how X Is distributed.
– Thomas
Nov 19 at 17:41
Any distribution. But if important we say X~EXP(λ)
– M.F
Nov 19 at 18:00
So expanding what you write $Y=X-d(1-alpha)$, so the distribution of $Y$ is just the distribution of $X$ shifted but maybe I am not getting your question...
– Thomas
Nov 19 at 19:09