Preservation of classes of life distributions under weighting with a general weight function

In the paper a representation of weighted distributions is used to obtain some results concerning their relations with life distributions. Extensions of the results by Gupta [Gupta, R.C., Keating, J.P., 1986. Relations for the reliability measures under length biased sampling. Scand. J. Statist. 13, 49–56], Jain et al. [Jain, K., Singh, H., Bagai, I., 1989. Relations for the reliability measures of weighted distributions. Comm. Statist. Theory Methods 18, 4393–4412] and Bartoszewicz and Skolimowska [Bartoszewicz, J., Skolimowska, M., 2006. Preservation of classes of life distributions and stochastic orders under weighting. Statist. Probab. Lett. 76, 587–596] are given.