  Statistical Isotropy of the Cosmic Microwave Background (CMB) radiation has
been studied and debated extensively in recent years. Under this assumption,
the hot spots and cold spots of the CMB are expected to be uniformly
distributed over a 2-sphere. We use the orientation matrix, first proposed by
Watson (1965) and Scheidegger (1965) and associated shape and strength
parameters (Woodcock, 1977) to analyse whether the hot and cold spots of the
observed CMB temperature anisotropy field are uniformly placed. We demonstrate
the usefulness of our estimators by using simulated toy models containing
non-uniform data. We apply our method on several foreground minimized CMB maps
observed by WMAP and Planck over large angular scales. The shape and strength
parameters constrain geometric features of possible deviations from uniformity
(isotropy) and the power of the anomalous signal. We find that distributions of
hot or cold spots in cleaned maps show no unusual signature of clustering or
girdling. Instead, we notice a strikingly uniform distribution of hot spots
over the full sky. The signal remains robust with respect to the four cleaned
maps used and presence or absence of the non-Gaussian cold spot (NGCS). On the
partial sky with WMAP KQ75 and Planck U73 masks we find anomalously low
strength of non-uniformity for cold spots which is found to be robust with
respect to various cleaning methods, masks applied, instruments, frequencies,
and the presence or absence of the NGCS. Interestingly we find that the signal
of anomalously weak non-uniformity could be due to contributions from the
quadrupole and octupole and may be related with the low CMB temperature
variance anomaly.
