Page 244 - Special Topic Session (STS) - Volume 1

STS426 Asis K.C.
component analysis, to analyze GRB data set as well as a new kernel, which
makes the clustering results better in comparison with the other existing
kernels and gives three physically interpretable groups in GRBs. However
explanation of the sources of these three groups will be more prominent in
the future with more data collection.

4. Classification under bivariate gamma set up with incomplete
observation
The analysis of De, Bhattacharya and Chattopadhyay(2016) was based on
the sample of Globular clusters (GCs) of the early-type central giant elliptical
galaxy in the Centaurus group, NGC 5128, whose structural parameters have
been derived by Mclaughlin et al. The distance is that adopted by McLaughlin
et al. (2008), namely 3.8 MPc. The sample consists of 130 GCs whose available
structural and photometric parameters are tidal (Rtid,in pc), Core radius ( , in

pc), half light radius( ,in pc), central volume density ( ) in −3 ), .0
0
ℎ
⨀
(predicted line of sight velocity dispersion at the cluster center (in −1 )),
twobody relaxation time at the model projected half mass radius(trn,in years),
galactocentric radius (Rgc, in kpc), Concentration (c ∼ ( / ) ),

dimensionless central potential of the best fitting model ( ), extinction-
0
corrected central surface brightness in the F606W bandpass ( in
0
−2 ) , v surface brightness averaged over (< > h) in
ℎ

−2 , integrated model mass( in MJ), washington
1
magnitude, extinction corrected color ( − ) . and metallically ([Fe/H])index
1 0
determined from the color ( − ) . However, for their purpose, they have
1 0
considered only and . It was found that 127 among the 130 data
ℎ
points (i.e. 97.69%) satisfy the restriction < . Thus there was a
ℎ
clear indication of the order restriction among the realized values of
ℎ
and . These two variables were found to be jointly distributed as
bivariate Gamma. They have considered three forms of bivariate Gamma
distributions proposed by Mckay, Nadarajah & Gupta and a transformed form
proposed by the authors.
Hence the problem was to form the discriminant function for observations
coming out from some bivariate gamma distribution. In particular, considering
two groups, say Group 1 and Group 2 and a random observation (X,Y) such
that (X,Y ) ∼ (, ) under Group i=1,2, where (, ) is the density of a

bivariate gamma distribution the discrimination function was developed.
Assuming that ‘loss’ is the cost associated with misclassifying an observation,
they have denoted the loss for classifying an observation to group 1 when it
originally belonged to group 2 by c(1|2) = and the loss for classifying an
1
observation to group 2 when it originally belongs to group 1 by c(2|1) = .
2
Then one should classify (x,y) to Group 1 if

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