Loss Distribution | cost per payment $Y = alpha X + (1 - alpha)(X-d)+$, Find CDF , PDF and mean of $Y$
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
add a comment |
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
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 |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3005157%2floss-distribution-cost-per-payment-y-alpha-x-1-alphax-d-find-c%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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