Abstract:
In this paper two probability distributions are introduced compounding inverse Weibull distribution
with Poisson and geometric distributions. The distributions can be used to model lifetime of series
system where the lifetimes follow inverse Weibull distribution and the subgroup size being random follows either
geometric or Poisson distribution. Some of the important statistical and reliability properties of each of
the distributions are derived. The distributions are found to exhibit both monotone and non-monotone failure
rates. The parameters of the distributions are estimated using the maximum likelihood method and the
expectation-maximization algorithm. The potentials of the distributions are explored through three real life
data sets and are compared with similar compounded distributions, viz. Weibull-geometric, Weibull-Poisson,
exponential-geometric and exponential-Poisson distributions.
