normalq_ function(n,pi1,pi2,mu1,mu2,mu0=0)
{

# Test for homogeneity in a two-component normal location mixture, 
# in which each component has unit variance.  This is a QUICK test,
# not requiring the underlying data set itself, but estimates of
# the mixture parameters must be in hand.
#
# Scenario:
#  	H_0: There exists mu_0 such that
#		p_1 f(x | mu_1, sigma^2_1 = 1) + p_2 f(x | mu_2, sigma^2_2 = 1)
#	     	may be written as f(x | mu_0, sigma^2_0 = 1).
#	H_1: There is no such mu_0.
#
# Required Inputs:
#     n  is the size of the underlying data set ("sample size"). 
#     pi1, pi2, mu1, mu2  are estimates of the mixture parameters,
#		which could have been obtained in any way (e.g., method
#		of moments, unpenalized maximum likelihood, penalized
#		maximum likelihood).
#     It is assumed that the underlying data set was rescaled (if 
#		necessary) so that the presumption of unit variance within 
#		each component was tenable.  Such rescaling can be done
#		using  scaleunit.S  or  newscaleunit.S .
#
# Optional Input:
#     mu0  is an estimate of the overall mean.  If no value is 
#		provided by the user, mu0  defaults to  0.
#
# Outputs:
#	dk	D-Test statistic 
#	pvalue  large-sample p-value:  Technically speaking, this is 
# 	        appropriate only when the mixture parameter estimates were 
#		  obtained by penalized maximum likelihood, with the penalty 
#		  term as indicated in  normal.S.  If the mixture parameter 
#		  estimates were obtained by unpenalized maximum likelihood, 
#		  you can use normalc.S  to get estimated critical values.

 
dkp1_ (pi1^2 / (2 * sqrt(pi) ) ) + ( pi2^2 / (2 * sqrt(pi) ) ) + 1 / (2 * sqrt(pi)) 
dkp2a_ 2 * pi1 * exp(-0.5*((mu1^2)+(mu0^2)) + 0.5*((mu1+mu0)^2/(2)))
dkp2b_ 2 * pi2 * exp(-0.5*((mu2^2)+(mu0^2)) + 0.5*((mu2+mu0)^2/(2)))
dkp3_ 2 * pi1 * pi2 * exp(-0.5*((mu2^2)+(mu1^2)) + 0.5*((mu2+mu1)^2/(2)))
dk_ dkp1 - dkp2a/sqrt(4*pi) - dkp2b/sqrt(4*pi) + dkp3/sqrt(4*pi)



pvalue_ 'LARGE'
sdk_ (16/3)*sqrt(pi)*n*dk
if (sdk > .2749959) pvalue_ 0.5-0.5*pchisq(sdk,1)

return(dk,pvalue)
result
}