k[A_?NumericQ,b_?NumericQ,sigma_]:=NIntegrate[1/(Sqrt[2 Pi] sigma) Exp[-s^2/(2 sigma^2)] 1/(Sqrt[2 Pi] sigma) Exp[-ss^2/(2 sigma^2)] A/Pi ((1+b) Exp[-Sqrt[s-ss]]-b), {s,-Infinity,Infinity},{ss,-Infinity,s}]; (*用二重积分把东西写一起*)
data=Table[{sigma,k[2.5,-1.2,sigma]},{sigma,1,3,0.1}] (*假设一组数据*)
FindFit[data,k[A,b,sigma],{A,b},sigma] (*还原出参数的值（有点慢）*)