A model used in the construction of life tables is a piecewise, con- stant hazard rate model. Here the time axis is divided into k intervals, (7;-1, T,), i = 1, ..., k, with T, = 0 and T = 0, The hazard rate on the ith interval is a constant value, 60; that is

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Solve this, for part a, find the cumulative hazard function H(t), then use this to find the survival function.

Then proceed to solve part b and c

A model used in the construction of life tables is a piecewise, con
stant hazard rate model. Here the time axis is divided into k intervals,
(T;-1, T;), i = 1, ..., k, with T, = 0 and T = 0. The hazard rate on the
ith interval is a constant value, 0; that is
0< x< T
T1 <x< T2
b(x) =
O-1 Tk-2 <x< Th-1
x2 TL-1
(a) Find the survival function for this model.
(b) Find the mean residual-life function.
(c) Find the median residual-life function.
Transcribed Image Text:A model used in the construction of life tables is a piecewise, con stant hazard rate model. Here the time axis is divided into k intervals, (T;-1, T;), i = 1, ..., k, with T, = 0 and T = 0. The hazard rate on the ith interval is a constant value, 0; that is 0< x< T T1 <x< T2 b(x) = O-1 Tk-2 <x< Th-1 x2 TL-1 (a) Find the survival function for this model. (b) Find the mean residual-life function. (c) Find the median residual-life function.
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