Mixture Distributions

[decrement]

just wanted to know how u can tell when u have to do a mixture distribution calculation, doesnt seem obvious, but the method is simple
i refer to Q7 April 2002 as an example which uses it but doesnt explicity tell you to
what is it that gives it away?

 

[RyuVI]

The key is to note that the claim amounts on the portfolio of policies each have poisson distribution but the value for lamda (I'll call it 'k') is different for each individual policy.

Hence the no. of claims has a conditional distribution:
N l k ~ Poisson(k) as opposed to N ~ Poisson(k)
we then multiply by the density of k and integrate to get the unconditional distribution of N.

This question explicitly states that lambda is not the same for all policies so that's your hint.

Check out April 2001 Q4 for another mixture distribution; it says:

'In a group of policies, the monthly number of claims for a single policy has a poisson distribution.... where lambda is a random variable..."

So that's how I check it anyways; I hope that's correct.

p.s - do u think chpt 13 is coming up this year? I hope not!

 

[decrement]

so if it says lambda with individual policies u must mix 1st
otherwise go straight to ExEN

hopefully i remember to read the question properly


when u look at the ASET grid of papers it seems like they skewed towards Parts 3/4 always, dnt mind chapter 13 stuff, was told they cant ask it properly coz the questions would be too complex to ask in an exam...

also dnt u think that the 06 papers are far harder than 05, theyve made the wording far more complex

 

[RyuVI]

so if it says lambda with individual policies u must mix 1st
otherwise go straight to ExEN

hopefully i remember to read the question properly

Basically if the parameter is treated as a random variable and the question isn't asking for the posterior distribution then u know u gotta mix!

when u look at the ASET grid of papers it seems like they skewed towards Parts 3/4 always, dnt mind chapter 13 stuff, was told they cant ask it properly coz the questions would be too complex to ask in an exam...

also dnt u think that the 06 papers are far harder than 05, theyve made the wording far more complex

Yeah 06 papers are definitely harder - the credibility theory question on April 06 is ridiculous. Even after looking at the solution I have no idea what it's talking about! Good news about chpt 13 - any other 'insider tips'?

 

[decrement]

but in bayseian estimation isnt the lambda/watever treated as a random variable?

wat is the fundamenal difference between posterior and mixed distbns in questions?

as for other stuff, apparantly they will not ask convolutions, so completely ignore that section

 

[RyuVI]

wat is the fundamenal difference between posterior and mixed distbns in questions?

Posterior questions come up in bayesian estimation/credibility theory and will explicitly ask you to calculate the posterior. As far as i know, the only time they've asked for a mixture is in risk models.

 

[wossname]

wat is the fundamenal difference between posterior and mixed distbns in questions?

As I understand it, a posterior gives you the distribution of the lambda. A mixture gives you the distribution of the X.

So it depends what you want to find.

 

[RyuVI]

As I understand it, a posterior gives you the distribution of the lambda. A mixture gives you the distribution of the X.

So it depends what you want to find.

The posterior is the distribution of lambda given x

The distribution of lambda is the prior distribution. Anyways, mixture distribution won't be coming up (probably!) so let's not worry about it!