Parameter Estimation for
the Truncated Weibull Model Using the Ordinary Differential Equation

Authors

H. Hirose

Source

International Conference on Computers,
Networks, Systems, and Industrial Engineering (CNSI 2011),
pp.???-???, May 23-25, 2011, Jeju, Korea

Abstract

In
estimating the number of failures using the truncated data for
the Weibull model, we often encounter a case that the estimate
is smaller than the true one when we use the likelihood principle
to conditional probability.
In infectious disease predictions, the SIR model described by simultaneous ordinary
differential equations are often used, and this model can predict the final stage
condition, i.e., the total number of infected patients, well, even if the number
of observed data is small.
These two models have the same condition for the observed data: truncated to
the right.
Thus, we have investigated whether the number of failures in the Weibull model
can be estimated accurately using the ordinary differential equation. The positive
results to this conjecture are shown.

Key Words

Weibull
model; truncated data; number of failures; SIR model; differential
equation, best-backward solution.