Comparisons of smallest order statistics from Weibull distributions with different scale and shape parameters

Weibull distribution is a very flexible family of distributions which has been applied in a vast number of disciplines. In this work, we investigate stochastic properties of the smallest order statistics from two independent heterogeneous Weibull random variables with different scale and shape parameters. Furthermore, we study the hazard rate order of the smallest order statistics from lower-truncated Weibull distributions due to, in general, Weibull random variables are not ordered according to this ordering in the shape parameter.