Chapter 0 and Chapter 1 Flashcards
Define survival analysis
Study of the distirbution of lifetimes or time from some initating event to a terminal event - can be applied to study of distribution of times from changing one state to another
Where are survival models used in actuarial
Life assurance
Annuties
Critical illness cover
Pension funds
Why is the difference in actuarial vs statistical notation so important?
In survival models actuaries are interested in financial significance vs statisticians statistical significance - something can be acceptable under actuarial criteria but not statistically so its key we understand the purpose of the model
Explain meaning of variable T
The future lifetime of a new born person is a random variable T which is continuously distirbuted over interval 0 to omega where omega is between 0 and infinity
Explain limiting age
Denoted omega - usually 100 - 200 years old and is the oldest or max age to live to.
Explain meaning of variable Tx
The future life of a person aged x is a random variable T describing future lifetime after age x of person who survives until age x. T0= T by convention
What is the only distirbution function we need to find all Fx(t)
F0(t)
What does tqx mean?
Rate of mortality : Probability of life age x dying before age x+t
What does tpx mean?
Probability of life age x surviving next t years
What does qx mean
Probability that a life alive at age x dies before age x+1
What is the probability of surviving for time s+t after age x? in terms of multiplying two probabilities
Multiplying probability of surviving for time s after age x and probability of then surviving for a further time t at age x+s
Desribe the force fo mortality in words
The instantaneous measure of mortality at age x - as in you’re alive at x but die instantly. This measure can be over 1 briefly for short periods of time
Define the complete expectation of life
The complete expectation of life at age x is defined as E(Tx) which is the expected future lifetime after age x. Often it is used to measure countries’ standard of living however this average can be skewed so the median would be a better measure.
Define the curtate expectation of life
Curtate expectation of life is the expectation of Kx random variable where Kx is age last birthday. IE E[Tx] - rounded down
How can the Curtate expectation of life be an non integer value
It is average. although Kx has to be an integer the average of a collection of integers can be a decimal
IF i have the force of mortality what can I work out about survival
Survival rates through lemma 5 or survival function
Why is the exponential model with constant hazard not realistic for humans
Mortality rates are independent of age in this model - not true in reality
How does the Weibull model relate to the exponential
If Beta = 1 then the hazard is constant and weibull model is the same as the exponential. However unlike exponential different values of beta alter the hazard to be monotonically increasing or decreasing with time
Discuss Gompertz law
Says with age force of mortality goes up and keeps going up, its entirely driven by age. This is a reasonable assumption for middle to older age groups.
Discuss makehams law
Includes a constant figure that can be interpreted as an allowance for accidental deaths not depending on age. - good approximation
What are life tables
These are routinely published by the profession - they summarise the mortality experience of a certain group of lives. The tables are usually refreshed with each census and there are lots of different tables with different uses
What does x denote int he tables
The exact age of the person on their last birthday
What does lx denote int he tables
Number of people surviving to exact age x out of original 100k aged 0
What does dx denote in the tables
number of deaths in year age x to x+1 out of the lx persons who enter that year
What does Lx denote in the tables
Population to be expected according to the Life Table aged between x and x+1 years, assuming deaths occur evenly over the year
What does Tx denote in the tablest
Expected number of person years to be lived byt eh survivors at age x
What does e^ox denote in the tables
Life expectancy at age x for each person surviving, or total future lifetime in years which an average is passed through by people aged exactly x - period life expectancy
Explain life expectancy
Average number of years a person would live if current mortality rates applied in the future.
Explain the difference between period life expectancy and cohort life expectancy
Period life expectancy assumes mortality rates remain constant into the future, while cohort life expectancy uses projected changes in future mortality rates
