CT 3 IFoA April 2005 Q12

[Sunil Sanga]

In this question part (iii) a
What is the reason to use degree of freedom 5-1-1=3 instead of using 5-1=4 since parameter value is given we didn't estimate.

However I found similar question in Ch 12 page 63. Also a note given why DF 4-1=3 is used here since the parameter value is given already in question

Please clarify

 

[Sunil Sanga]

Anyone please help me on this

 

[suraj]

In this question part (iii) a
What is the reason to use degree of freedom 5-1-1=3 instead of using 5-1=4 since parameter value is given we didn't estimate.

(iii) The following table gives the numbers of occupants in 2,423 cars observed on a road junction during a certain time period on a weekday morning.
Number of occupants 1 2 3 4 5 6
Frequency of cars 1,486 694 195 37 10 1

The above data were modelled by a zero-truncated Poisson distribution as given in (i).
The maximum likelihood estimate of θ is 0.8925 and the Cramer-Rao lower bound on variance is 5.711574 * 10^ -4 (you do not need to verify these results.)

 

[Sunil Sanga]

So the estimate wording is identification as in Ch 12 question only a parameter value is given.
So whenever this estimate wording present...we can subtract 1 degree of freedom by assumption that parameter is estimated...

Correct?

 

[suraj]

So the estimate wording is identification as in Ch 12 question only a parameter value is given.
So whenever this estimate wording present...we can subtract 1 degree of freedom by assumption that parameter is estimated...

Correct?

Only if the parameter is estimated from the same data, which is the case in this question.