Actuarial Outpost Counting degree of freedom
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

#1
02-19-2009, 07:12 PM
 Sophie H. Member Join Date: Jan 2009 Studying for FAP FA Posts: 572
Counting degree of freedom

Case I: If given some distribution and provide parameters, df=n-1

Case II: If given some distribution and provide parameters, fitted from the data, df= n-r-1
From here,
given binomial n and q, df=n-2-1
given Pareto alpha and theta, df= n-2-1
given negative binomial, df= n-2-1

what if uniform distribution, so Ej will be total and equally divided, then df= n-??-1....?
----------------------------------------------------------------------------------------------
Let's assume 40.14 and 40.10 are really the case II. Then, what will their df's be?

40.14 is as follow:

The observed # of claims for a group of 50 risks has been recorded as:
# of claims // # of risks
0 // 7
1 // 10
2 // 12
3 // 17
4 // 4
Null hypothesis: the # of claims per risk follows a uniform distribution on 0,1,2,3 and 4.
So 50 risk equally divided into 5 groups is 10 each group. Can I assume 10 is a given parameter? So, df=5-1-1=3?

--------------------------------------------------------------------------------------------
40.10
100 observed losses have been recorded in thousands of dollars and are grouped as follow:
Interval // # of Losses
(0,1) // 15
[1,5) // 40
[5,10) // 20
[10,15) // 15
[15, infinity)// 10
Random variable X underlying observed losses, in thousands, is believed to have density function
f(x) = 0.2 e^(-0.2x)

Can I assume it's given as an exponential with theta=1/.2=5,
so df= 5-1-1=3?

Last edited by Sophie H.; 02-19-2009 at 07:52 PM..
#2
02-19-2009, 07:38 PM
 Actuarialsuck Member Join Date: Sep 2007 Posts: 5,334

How many parameters are fitted for uniform?

Maybe you should post 40.14
__________________
Quote:
 Originally Posted by Buru Buru i'm not. i do not troll.
#3
02-19-2009, 07:42 PM
 Sophie H. Member Join Date: Jan 2009 Studying for FAP FA Posts: 572

Another confusion -> 40.19.

"null hypothesis, H0, is the number of claims per risk follows a Poisson Distribution.
.........
min chi-square estimate of the mean of the Poisson distribution is .3055."

Case I: This is what I got. 4 groups down to 3 groups. df=3-1=2 because it doesn't said it's fitted from the data so it doesn't minus the given parameter (Poisson mean).

Case II: which is the solution. Is it because of this sentence? "min chi-square estimate of the mean of the Poisson distribution is .3055"

So, can I draw a conclustion that whenever a distribution parameter is given along with key words such as "chi-square estimate", "fitted by data", ...,etc, then we use df=n-r-1.
#4
02-19-2009, 08:21 PM
 Actuarialsuck Member Join Date: Sep 2007 Posts: 5,334

__________________
Quote:
 Originally Posted by Buru Buru i'm not. i do not troll.
#5
02-19-2009, 08:24 PM
 Actuarialsuck Member Join Date: Sep 2007 Posts: 5,334

Quote:
 Originally Posted by Sophie H. Another confusion -> 40.19. "null hypothesis, H0, is the number of claims per risk follows a Poisson Distribution. ......... min chi-square estimate of the mean of the Poisson distribution is .3055." Case I: This is what I got. 4 groups down to 3 groups. df=3-1=2 because it doesn't said it's fitted from the data so it doesn't minus the given parameter (Poisson mean). Case II: which is the solution. Is it because of this sentence? "min chi-square estimate of the mean of the Poisson distribution is .3055" So, can I draw a conclustion that whenever a distribution parameter is given along with key words such as "chi-square estimate", "fitted by data", ...,etc, then we use df=n-r-1.
You are told that a parameter is fitted! "chi square estimate of the mean..." and how is Poisson dist. determined? By lambda. And what does the mean = ?
__________________
Quote:
 Originally Posted by Buru Buru i'm not. i do not troll.
#6
02-20-2009, 12:54 PM
 Sophie H. Member Join Date: Jan 2009 Studying for FAP FA Posts: 572

Quote:
 Originally Posted by Actuarialsuck Have you had a chance to read this http://www.actuarialoutpost.com/actu...hlight=freedom

I'm still not getting everything for chi-square!

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 02:36 AM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top