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Statistical Methods with Applications to Demography and Life Insurance
book

Statistical Methods with Applications to Demography and Life Insurance

by Estate V. Khmaladze
March 2013
Intermediate to advanced content levelIntermediate to advanced
242 pages
5h 47m
English
Chapman and Hall/CRC
Content preview from Statistical Methods with Applications to Demography and Life Insurance
16 Models of distribution functions F(x) and force of mortality µ(x)
where λ is the scale parameter and
Γ(k) =
Z
0
x
k1
e
x
dx
is the gamma function of “shape parameter” k. The gamma distribution
function is the integral
F(x) =
λ
k
Γ(k)
Z
x
0
y
k1
e
λy
dy, x 0. (2.9)
For the gamma function see, e.g., Abramowitz and Stegun [1964]; for
the gamma distribution function see, e.g., Johnson et al. [1994] and
Johnson et al. [1995]. When k = 1, F becomes an exponential distribu-
tion function while for k = n/2 with integer n and λ = 1/2 it becomes
a chi-square distribution function with n degrees of freedom. We use
both of these distributions in this book.
For integer values ...
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Publisher Resources

ISBN: 9781466505742