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Search: Posts Made By: mathematicalhype
Forum: Short-Term Actuarial Math 04-29-2017, 10:22 PM
Replies: 1
Views: 501
Posted By mathematicalhype
Bump

Bump
Forum: Short-Term Actuarial Math 04-26-2017, 01:11 PM
Replies: 1
Views: 501
Posted By mathematicalhype
Modification to 1999 C4 Sample: 38

Original question asks:
You are given a random sample of 4 values from a distribution F: 4,5,9,14
You estimate E[X] using hte estimator g(X1,X2,X3,X4) = X1.
Determine the bootstrap approximation...
Forum: Short-Term Actuarial Math 04-26-2017, 01:06 PM
Replies: 2
Views: 476
Posted By mathematicalhype
agreed

agreed
Forum: Short-Term Actuarial Math 03-20-2017, 09:45 PM
Replies: 41
Views: 121,892
Posted By mathematicalhype
Soa Sample Question 11: Losses on a company’s...

Soa Sample Question 11:
Losses on a company’s insurance policies follow a Pareto distribution with
probability density function: f(x/theta) = theta / (x+theta)^2.
For half of the company’s...
Forum: Short-Term Actuarial Math 02-12-2017, 03:10 PM
Replies: 4
Views: 769
Posted By mathematicalhype
I set it up as 1-e^-12/theta to get theta...

I set it up as 1-e^-12/theta to get
theta equals 22.6391. I understand that the expected value of the exponential in this case will be theta 22.6391.
I used .41143* 22.6391 as the "extrapolation...
Forum: Short-Term Actuarial Math 02-11-2017, 06:18 PM
Replies: 4
Views: 769
Posted By mathematicalhype
Help?

Help?
Forum: Short-Term Actuarial Math 02-11-2017, 06:17 PM
Replies: 1
Views: 631
Posted By mathematicalhype
Question to Pass

I understand there are 35 questions, and 5 are pilot?
So to pass, I would safely need to answer correctly:
30 questions * .67 + 5 pilot questions = 25.1?

This is because if you get a pilot...
Forum: Short-Term Actuarial Math 02-10-2017, 03:19 PM
Replies: 2
Views: 612
Posted By mathematicalhype
Exponential MoM with incomplete data (memoryless property)

Example 30I from ASML
An automobile collision coverage has a deductible of 500. Claims for losses less than 500 are not submitted. You observe a sample of 20 losses totaling 18,000 including the...
Forum: Short-Term Actuarial Math 02-10-2017, 02:45 PM
Replies: 2
Views: 398
Posted By mathematicalhype
So in the empirical variance formula, Var (X) =...

So in the empirical variance formula,
Var (X) = (S(x) * (1-S(x)))/ n

In this example we should not set S(x) as the Product Limit Estimator of S(x) , but as the true S(x)? And it is easier to...
Forum: Short-Term Actuarial Math 02-10-2017, 01:14 PM
Replies: 2
Views: 398
Posted By mathematicalhype
Another Product Lim Est. question - variance

Question 26.5 from ASM:
From a 2 year mortality study of 1000 lives beginning at age 40, you are given:

i. observed deaths are distributed uniformly over the interval (40,42]
ii. Greenwood's...
Forum: Short-Term Actuarial Math 02-10-2017, 09:58 AM
Replies: 4
Views: 769
Posted By mathematicalhype
Product Limit Estimator Question

Ex 25C in ASM:
IN a mortality study, 10 lives are under observation.
one death a piece occurs at times 3, 4, and 7, and 2 deaths at 11. Withdrawals occur at times 5 and 10. Study concludes at time...
Forum: Short-Term Actuarial Math 02-10-2017, 09:50 AM
Replies: 5
Views: 574
Posted By mathematicalhype
Thank you!

Thank you!
Forum: Short-Term Actuarial Math 02-09-2017, 02:55 PM
Replies: 5
Views: 574
Posted By mathematicalhype
Another Agg loss question

20.8 from ASM:

The number of snowstorms in January has a binomial distribution with m=8, q=.5. The distribution of the number of inches of snow is:

Inches Probability
1 .2
2 .3
3 .2
4 .1
5...
Forum: Short-Term Actuarial Math 02-09-2017, 02:51 PM
Replies: 3
Views: 487
Posted By mathematicalhype
THanks, both!

THanks, both!
Forum: Short-Term Actuarial Math 02-09-2017, 02:31 PM
Replies: 3
Views: 487
Posted By mathematicalhype
Aggregate models

Exercise 20.9 in ASM
You are given
The number of claims follows a binomial distribution with m=3, q=.2.
Claim sizes follow the following distribution:
claim size claim probability
0 .2
1 ...
Forum: Short-Term Actuarial Math 02-08-2017, 10:32 PM
Replies: 3
Views: 746
Posted By mathematicalhype
Thanks both for the helpful responses.

Thanks both for the helpful responses.
Forum: Short-Term Actuarial Math 02-07-2017, 07:21 PM
Replies: 3
Views: 746
Posted By mathematicalhype
Deductibles example question, 6.37 in ASM

We are given a lognormal distribution with parameters m and sigma
The insurance agent for the risk settles all claims under 5000. (claims of 5000 or more are settled by the insurer not the agent)
...
Forum: Short-Term Actuarial Math 01-29-2017, 05:37 PM
Replies: 1
Views: 519
Posted By mathematicalhype
Information matrix - algebra question...

From page 655 of ASM, solving for variance of 2 param pareto with censored data...


We are told that
dl/da = m/a + (8 ln5500 - sum from i=1 to m of ln (5000 + x_i) - (8-m)*(ln 15,000)
where we...
Forum: Short-Term Actuarial Math 01-29-2017, 04:28 PM
Replies: 1
Views: 480
Posted By mathematicalhype
lognormal distribution

Can someone explain why for a lognormal distribution:

1. The expected value of ln x_i - mu = 0?
2. The expected value of (ln x_i - mu)^2 is sigma ^ 2?


These are from page 653 in ASM.
Forum: Short-Term Actuarial Math 01-28-2017, 01:25 PM
Replies: 1
Views: 431
Posted By mathematicalhype
Buhlmann Cred Cont. Prior, ASM 52.13

You are given the following:
a. The number of claims for a single risk follows a Poisson distribution with mean λ.
b. The amount of an individual claim is always 1,000λ.
c. λ is a random variable...
Forum: Short-Term Actuarial Math 01-28-2017, 01:18 PM
Replies: 4
Views: 1,107
Posted By mathematicalhype
Thanks for the insight. Let me ask though -...

Thanks for the insight.
Let me ask though - are you sure Mu will be H(t) or S(t)? Can you provide the reference of this either in the source material or ASM manual? Sorry for being particular, but...
Forum: Short-Term Actuarial Math 01-25-2017, 02:47 PM
Replies: 1
Views: 381
Posted By mathematicalhype
Bay Credibility: Bernoulli/Beta Ex 48B ASM

Annual claim counts follow a binomial distribution with parameters m=3 and Q. Q is beta with a=2, b=8, and theta =1. A policyholder submits 4 claims in 2 years.
Calculate the posterior expected...
Forum: Short-Term Actuarial Math 01-19-2017, 02:07 PM
Replies: 1
Views: 492
Posted By mathematicalhype
Mode of monotonically increasing function

On page 905, the ASM manual talks about loss functions.
Focusing on the zero-one loss function, we are provided an example which states:
...It is clear that the posterior function, a constant times...
Forum: Short-Term Actuarial Math 01-15-2017, 09:52 PM
Replies: 1
Views: 566
Posted By mathematicalhype
Classical Credibility Question

Question 42.15 from ASM asks:
i. For each individual insured, the number of claims follows a Poisson distribution
ii. The mean claim count varies by insured, and the distribution of mean claim...
Forum: Short-Term Actuarial Math 01-08-2017, 12:15 AM
Replies: 1
Views: 471
Posted By mathematicalhype
Weibull distn mle, ASM 33.56

You are given the following:
4 obs have been made of a RV having the density function
f(x)=2 λxe^- λx^2 , x>0
only one of the observations was less than 2.
determine the mle of λ.

In the...
Showing results 1 to 25 of 270

 

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