Real question on material for Course 4

[Actuary321]

This was sent on the CAS course 4 email list. Any responses?

Okay, enough general questions. [:-)] Here are a few difficulties I have run into so far. If anyone is able to help or shed light on them, I'd really appreciate it.

My questions are:

1. s2 = 1/n * summation of (Xi - Xmean)2 (the formula for the variance of an empirical distribution.
Is this biased or unbiased? I think I've seen text refer to it both ways.

2. In the ASM manual, example 4.1, the density function is identified as a 2-param-Pareto wtih theta = 1 but that doesn't look like a pareto to me. Any clue here? It looks like a pareto times X. Is that the same as a pareto? Confused.

3. In the ASM solution to it's problem 5.8, it uses a formula: Even if you lack the manual, Is this Formula Familiar to you?

Var [Fm(500)] = Fn(500) * [ 1 - Fn(500) ]

Where does this formula come from? Is it specific to exponential distributions only? I can't find a source anywhere.

[New at pd]

On 2002-01-22 15:16, Actuary321 wrote:
This was sent on the CAS course 4 email list. Any responses?

Okay, enough general questions. [:-)] Here are a few difficulties I have run into so far. If anyone is able to help or shed light on them, I'd really appreciate it.

My questions are:

1. s2 = 1/n * summation of (Xi - Xmean)2 (the formula for the variance of an empirical distribution.
Is this biased or unbiased? I think I've seen text refer to it both ways.

>>I believe that it is biased, since with that summation there are (n-1) df. However, it is asymptotically unbiased.

2. In the ASM manual, example 4.1, the density function is identified as a 2-param-Pareto wtih theta = 1 but that doesn't look like a pareto to me. Any clue here? It looks like a pareto times X. Is that the same as a pareto? Confused.

>>Sorry, I don't have it in front of me.

3. In the ASM solution to it's problem 5.8, it uses a formula: Even if you lack the manual, Is this Formula Familiar to you?

Var [Fm(500)] = Fn(500) * [ 1 - Fn(500) ]

Where does this formula come from? Is it specific to exponential distributions only? I can't find a source anywhere.

>>If I remember correctly, you consider a Bernoulli trial with prob. of success
p = Fn(500). So, the var is p(1-p). This is a general method, applying to all distributions, not just the exponential.



Hope this helps.

<font size=-1>[ This Message was edited by: New at c6 on 2002-01-23 07:38 ]</font>