AbstractFor each n, X1(n),…Xn(n) are independent and identically distributed random variables, with common probability density function\documentclass{article}\pagestyle{empty}\begin{document}$$ f(x) = 0\,{\rm for}\,x < \theta $$\end{document}\documentclass{article}\pagestyle{empty}\begin{document}$$ f\left(x \right) = c\left({x - \theta } \right)^\alpha \left[{1 + r\left({x - \theta } \right)} \right]\,for\,x \ge \theta, $$\end{document}Wherec, θ, α, andr(y) are all unknown. It is shown that we can make asymptotic inferences aboutc, θ, and α, whenr(y) satisfies mild condi