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







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  • I think you have to mention how X Is distributed.
    – Thomas
    yesterday










  • Any distribution. But if important we say X~EXP(λ)
    – M.F
    yesterday










  • 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
    yesterday

















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







share|cite|improve this question
























  • I think you have to mention how X Is distributed.
    – Thomas
    yesterday










  • Any distribution. But if important we say X~EXP(λ)
    – M.F
    yesterday










  • 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
    yesterday















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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








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M.F

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11












  • I think you have to mention how X Is distributed.
    – Thomas
    yesterday










  • Any distribution. But if important we say X~EXP(λ)
    – M.F
    yesterday










  • 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
    yesterday




















  • I think you have to mention how X Is distributed.
    – Thomas
    yesterday










  • Any distribution. But if important we say X~EXP(λ)
    – M.F
    yesterday










  • 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
    yesterday


















I think you have to mention how X Is distributed.
– Thomas
yesterday




I think you have to mention how X Is distributed.
– Thomas
yesterday












Any distribution. But if important we say X~EXP(λ)
– M.F
yesterday




Any distribution. But if important we say X~EXP(λ)
– M.F
yesterday












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
yesterday






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
yesterday

















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