In this article we study the residual lifetime of a coherent system after the rth failure, i.e. the time elapsed from the rth failure until the system failure given that the system operates at the time of the rth failure. We provide a mixture representation for the corresponding residual...

The problem of estimating order-restricted scale parameters of two Gamma distributions is considered under the Pitman closeness criterion. A class of isotonic estimators including the MLE is proposed. Some properties of this class of isotonic estimators is given under the Pitman closeness...

We present a new generalized family of skew two-piece skew-elliptical (GSTPSE) models and derive some its statistical properties. It is shown that the new family of distribution may be written as a mixture of generalized skew elliptical distributions. Also, a new representation theorem for a...