IJSRP JUNE 2012 Online Print Version - IJSRP.ORG

International Journal of Scientific and Research Publications, Volume 2, Issue 6, June 2012 43
ISSN 2250-3153
Survival function for -th concomitant of order statistics for bivariate pseudo WIGD is
The conditional hazard rate of given is
Which is decreasing function in and .
Again the conditional survival function
is decreasing function in , therefore according to properties given by Tahmasebi and Behboodian, (2010) it follows that has
increasing failure rate (IFR) distribution and (entropy ordering) for and is stochastically decreasing and is
denoted by SD( .
Extention to Bivariate Concomitant from Trivariate Pseudo Distributions
The trivariate pseudo WIGD has been defined as a compound distribution of three random variables. Suppose that the random
variable has WIGD with pdf given in equation (2.1) and the r.v. and also has WIGD with parameter and
respectively with pdf
And
Then the compound distribution of equations (2.1), (4.1) and (4.2) gives trivariate pseudo WIGD as
Using and , the density given in (4.3) becomes
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