exponentialq_ function(n,pi1,pi2,beta1,beta2,beta0)
{

# Test for homogeneity in a two-component exponential sacle mixture.
# 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 beta_0 such that
#		p_1 f(x | beta_1) + p_2 f(x | beta_2)
#	     	may be written as f(x | beta_0).
#	H_1: There is no such  beta_0.
#
# Required Inputs:
#     n  is the size of the underlying data set ("sample size"). 
#     pi1, pi2, beta1, beta2  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).
#
# Outputs:
#	dk	D-Test statistic, no weighting function
#	dk.w1      weighting function  w_1(x) = x
#	dk.w2      weighting function  w_2(x) = x^2
#	pvalue  large-sample p-value: 
#		  penalized maximum likelihood estimation scheme, no weighting function
#	pvalue.w1  weighting function  w_1(x) = x
#     pvalue.w2  weighting function  w_2(x) = x^2
#		  If the mixture parameter estimates were obtained by unpenalized 
#		  maximum likelihood, use exponentialc.S  to get estimated critical values.
#
# Caveat:  
#     The  p-values  are based on asymptotic theory that, although presumed
#	applicable, has not been rigorously justified in the exponential scale 
#	case.  The principal difficulty is that one of the regularity conditions 
#	(uniform boundedness) is violated in the exponential scale case, unless 
#	the parameter space is severely restricted.

  
dk0_ beta0/2 + pi1*pi1*beta1/2 + pi2*pi2*beta2/2 
dk1_ 2*pi1*beta0*beta1/(beta0+beta1)+2*pi2*beta0*beta2/(beta0+beta2)
dk2_ 2*pi1*pi2*beta1*beta2/(beta1+beta2)

dk_ dk0 - dk1 + dk2


# weighting function w_1(x) = x

dknew0_ 1/4 + pi1*pi1/4 + pi2*pi2/4
dknew1_ 2*pi1*beta0*beta1/((beta0+beta1)^2)+2*pi2*beta0*beta2/((beta0+beta2)^2)
dknew2_ 2*pi1*pi2*beta1*beta2/((beta1+beta2)^2)

dk.w1_ dknew0 - dknew1 + dknew2


# weighting function w_2(x) = x^2

dk00_ -1*-1*beta0*beta0/(beta0+beta0)^3 
dk01_ -1*pi1*beta0*beta1/(beta0+beta1)^3
dk02_ -1*pi2*beta0*beta2/(beta0+beta2)^3

dk10_ pi1*-1*beta1*beta0/(beta1+beta0)^3 
dk11_ pi1*pi1*beta1*beta1/(beta1+beta1)^3
dk12_ pi1*pi2*beta1*beta2/(beta1+beta2)^3

dk20_ pi2*-1*beta2*beta0/(beta2+beta0)^3 
dk21_ pi2*pi1*beta2*beta1/(beta2+beta1)^3
dk22_ pi2*pi2*beta2*beta2/(beta2+beta2)^3

dk.w2_ 2*(dk00+dk01+dk02+dk10+dk11+dk12+dk20+dk21+dk22)


pvalue_ 'LARGE'
s_ (16/3)*(1/beta0)*n*dk
if (s > .2749959) pvalue_ 0.5-0.5*pchisq(s,1)

pvalue.w1_ 'LARGE'
s.w1_ (32/3)*n*dk.w1
if (s.w1 > .2749959) pvalue.w1_ 0.5-0.5*pchisq(s.w1,1)

pvalue.w2_ 'LARGE'
s.w2_ (32/5)*beta0*n*dk.w2
if (s.w2 > .2749959) pvalue.w2_ 0.5-0.5*pchisq(s.w2,1)


return(dk,dk.w1,dk.w2,pvalue,pvalue.w1,pvalue.w2)
result
}