Mixing
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 2 days ago
M.F
11
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up vote
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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 2 days ago
M.F
11
I think you have to mention how X Is distributed.
– Thomas
2 days ago
Any distribution. But if important we say X~EXP(λ)
– M.F
2 days ago
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
2 days ago
add a comment |
up vote
0
down vote
favorite
up vote
0
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 2 days ago
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 2 days ago
M.F
11
asked 2 days ago
M.F
11
edited 2 days ago
asked 2 days ago
M.F
11
asked 2 days ago
M.F
11
asked 2 days ago
M.F
11
11
I think you have to mention how X Is distributed.
– Thomas
2 days ago
Any distribution. But if important we say X~EXP(λ)
– M.F
2 days ago
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
2 days ago
add a comment |
I think you have to mention how X Is distributed.
– Thomas
2 days ago
Any distribution. But if important we say X~EXP(λ)
– M.F
2 days ago
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
2 days ago
I think you have to mention how X Is distributed.
– Thomas
2 days ago
I think you have to mention how X Is distributed.
– Thomas
2 days ago
Any distribution. But if important we say X~EXP(λ)
– M.F
2 days ago
Any distribution. But if important we say X~EXP(λ)
– M.F
2 days ago
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
2 days ago
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
2 days ago
add a comment |
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I think you have to mention how X Is distributed.
– Thomas
2 days ago
Any distribution. But if important we say X~EXP(λ)
– M.F
2 days ago
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
2 days ago