In simple step-stress experiments under Type-II censoring with the cumulative exposure model and exponentially distributed lifetimes, maximum likelihood estimates (MLE) of the expected lifetimes may not exist due to the absence of failure times either before or after the stress change point. For...

A simple representation of the expectation of a renewal process mean with random time is obtained which leads to a renewal theoretic interpretation of certain premium calculation principles.

For order statistics Xi,n,Xj,n,Xk,n with 1[less-than-or-equals, slant]i<j<k[less-than-or-equals, slant]n, and an independent beta distributed random variable C the distributional equation is established for uniform distributions as well as seen to be characteristic.