| dc.description.abstract | This thesis is mainly concerned with study of some generalizations of Cauchy
distribution. The distributions commonly used for modelling of insurance losses,
financial returns, file sizes on the network servers, etc. are subject to some sort
of deficiencies. Also, there are only few probability distributions capable of
modelling heavy tailed data sets and none of them are flexible enough to provide
greater accuracy in fitting complex forms of data. Furthermore, in financial and
actuarial risk management problems, the data sets are usually unimodal, skewed
to the right, and possess thick right tail. The distributions that exhibit such
characteristics can be used quite effectively to model insurance loss data to
estimate the business risk level.
To address the problems stated above, we have an interest in defining new
families of distributions through different approaches such as introducing
additional, location, scale, shape, and transmuted parameters, to generalize the
existing distributions.
We adopted six estimation approaches for estimating parameters of our
models, and assess the performance of these estimators. Therefore, this study is
addressed scientific computation challenge by performing numerical comparison
between several estimators for the model parameters and identified which of them
perform better in terms of estimation efficiency. The comparison is based on
Monte Carlo simulations and the outcomes of a real data analysis. The simplicity
of the proposed distributions and the great flexibility in modelling real life data
will attract researchers to use these distributions as an alternative of the Cauchy
distribution in modelling different scenarios. Our proposed families are useful for
modelling insurance claim data sets, better models for financial returns because
the normal model does not capture the large fluctuations seen in real assets. Also,
our families of distributions have received considerable attention due to the heavy
tail property. | en_US |
