Abstract
We investigate the equivalence of weak convergence and moment convergence of life distributions in a family which is larger than the HNBUE family. Also, we point out that within the HNBUE family the exponential distribution can be characterized by one value of its Laplace-Stieltjes transform.
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Lin, G.D. On equivalence of weak convergence and moment convergence of life distributions. Ann Inst Stat Math 46, 587–592 (1994). https://doi.org/10.1007/BF00773519
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DOI: https://doi.org/10.1007/BF00773519