Moments from an Empirical Distribution

This function calculates a moment from an empirical distribution function.

wdistr - the input distribution wave
n - the moment (-2 - rms, 0 - most probable, 1 - mean, 2 - second, 3 ...)
xmax - optional x limit for the calculations
wdistrX - optional x wave for distribution (for calculations with non-scaled waves)

Function calc_DistributionMoment(wave wdistr, variable n [variable xmax, wave wdistrX])

	variable rtnv, scaled=1, limited=0, pmax
	
	if (!ParamIsDefault(wdistrX))
		scaled = 0
	endif
	if (!ParamIsDefault(xmax))
		limited=1
		if (scaled)
			pmax = x2pnt(wdistr,xmax)
		else
			pmax = x2pnt(wdistrX,xmax)
		endif
	else
		pmax = numpnts(wdistr) - 1
		if (scaled)
			xmax = pnt2x(wdistr,pmax)
		endif
	endif
	
	switch(n)
		case -2:	// rms
			duplicate/FREE wdistr, iwave, iMwave
			if (scaled)
				integrate/METH=1 iwave
				iMwave = wdistr*x^2
				integrate/METH=1 iMwave
			else
				integrate/METH=1 iwave /X=wdistrX
				iMwave = wdistr*wdistrX^2
				integrate/METH=1 iMwave /X=wdistrX
			endif
			rtnv = sqrt(iMwave[pmax]/iwave[pmax])
			break		
		case 0:	// most probable
			if (scaled)
				if (limited)
					WaveStats/M=1/Q/R=(0,xmax) wdistr
				else
					WaveStats/M=2/Q wdistr
				endif
				rtnv = v_maxloc
			else
				if (limited)
					WaveStats/P/M=2/Q/R=[0,pmax] wdistr
				else
					WaveStats/P/M=2/Q wdistr
				endif
				rtnv = wdistrX[v_maxRowLoc]
			endif
			break
		default:	// all others (1-mean, 2-second, 3...)
			duplicate/FREE wdistr, iwave, iMwave
			if (scaled)
				iwave = wdistr*x^(n-1)
				integrate/METH=1 iwave
				iMwave = wdistr*x^n
				integrate/METH=1 iMwave
			else
				iwave = wdistr*wdistrX^(n-1)
				integrate/METH=1 iwave /X=wdistrX
				iMwave = wdistr*wdistrX^n
				integrate/METH=1 iMwave /X=wdistrX
			endif
			rtnv = iMwave[pmax]/iwave[pmax]
			break
	endswitch
	
	return rtnv
end

This would be used by example to obtain the requisite values from polymer molar mass distributions or particle size distributions.