Can i graduate?

Graduation

Part I
When I first thought about it, yes, I had the same thoughts as you. Would I be able to graduate? So far the 2 subjects that I have sat the exams for, were pretty screwed up. Scratch that. It WAS TOTALLY SCREWED UP. But somehow, I don't feel the stress. But goodness me, it's my last year isn't it? It's like how can someone, who has been studying in university for 3 years fail?? I guess the worst thing of it all is how slack I have become. My computer here is such a darling that I can't live without it. Knowing that the exams creep near, I have successfully repelled the immense desire to continue on Phoenix Wright: Trials and Tribulations which would take up hours. Unfortunately, this game called Free cell and Hexic has now happily got me distracted so easily again. =x Am I able to graduate? I wonder.

Part II
This, my friend, is where it gets technical. But then again, given that I hate jargon myself, I love trying to explain things simply, which gets me nowhere because that's not the specific terms that lecturers are looking for when they mark exam scripts do they?

Graduation -
i) Whittaker-Henderson Graduation Method
This formula is amazing as it allows us to choose between smoothness and adherence to data when graduating crude rates. (simple words, in a sample, this method allows us to adjust data to remove random errors through ensuring smooth transitions between data as well as portraying the important features of the mortality rates)

ii) Graphical Method of Graduation (MOST DIFFICULT)
- used to 'tidy up' graduation performed using other methods.

method applied: fit a curve by hand that has the same function as (i) without the mathematics.

If data is scanty, we are allowed to group them and calculate them using weighted mean age.

Logarithmic scale is suggested.

Advantages:
1) useful for scanty data
2) allows for use of judgment
3) can hand polish to get good results

Disadvantages:
1) difficult to apply! (requires experience)
2) hard to achieve high degree of smoothness - cant be used to produce standard table
3) no unique solution

iii) Univariate Delta Method

Making use of Taylor series expanded about X = μ

f (X) ≈ f(μ) + f ' (μ)(X-μ) + ...

where μ = E(X)

E(f(X)) = f(u)

Var(f(X)) = (f ' (μ))²*Var(X)

iv) Graduation by mathematical formula

This is the most complicated graduation which most likely would come up in the exams!

step 1:
Obtain estimates

step 2:
choose mathematical function. E.g. Gompertz' Law (remember to check for linearity)

step 3:
Parameter Estimation using
a) Maximum Likelihood Estimation
b) Weighted least squares ∑ w_{x (}q_{x - F(x))}2
c) Minimum Chi-Squared

step4:
Calculate graduated values - aka substitution

step5:
Test the fit of the graduation

tests include:
1) chi-squared distribution
2) individualised standardised deviations (ISD) test (with range)
3) cumulative standardised deviations test (no overlapping ages!)
4) signs test (N~bin(n,1/2))
5) runs test

v) Graduation by reference to standard table
most useful if:
- little data
- similar mortality experience
- for select rates

To find relationship between our data and standard table's data, plot a simple graph (linearity)

parameters a,b can be found using
1) plotting
2) methods of least squares
3) weighted least squares

vi) Graduation using Cubic Spline (special case of mathematical formula)

Alrighty! That was 25% of the material to be covered in the exams. Easy to just say this but to understand it. ... Going to have to look through it .. again.. and again.. and again.

Breakfast appointment in 7 hours time. I should sleep for 6. Good night all.