  Advanced science and technology provide a wealth of big data from different
sources for extreme value analysis. Classical extreme value theory was extended
to obtain an accelerated max-stable distribution family for modelling competing
risk-based extreme data in Cao and Zhang (2021). In this paper, we establish
probability models for power normalized maxima and minima from competing risks.
The limit distributions consist of an extensional new accelerated max-stable
and min-stable distribution family (termed as the accelerated p-max/p-min
stable distribution), and its left-truncated version. The consistency and
asymptotic normality are obtained for the maximum likelihood estimation of the
parameters involved in the accelerated p-max and p-min stable distributions
when it exists. The limit types of distributions are determined principally by
the sample generating process and the interplay among the competing risks,
which are illustrated by common examples. Further, the statistical inference
concerning the maximum likelihood estimation and model diagnosis of this model
was investigated. Numerical studies show first the efficient approximation of
all limit scenarios as well as its comparable convergence rate in contrast with
those under linear normalization, and then present the maximum likelihood
estimation and diagnosis of accelerated p-max/p-min stable models for simulated
data sets. Finally, two real datasets concerning annual maximum of ground level
ozone and survival times of Stanford heart plant demonstrate the performance of
our accelerated p-max and accelerated p-min stable models.
