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Sharp bounds on distribution functions and expectations of mixtures of ordered families of distributions

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  • Tomasz Rychlik

    (Polish Academy of Sciences)

Abstract

We compare two mixtures of arbitrary collection of stochastically ordered distribution functions with respect to fixed mixing distributions. Under the assumption that the first mixture distribution is known, we establish optimal lower and upper bounds on the latter mixture distribution function and present single families of ordered distributions which attain the bounds uniformly at all real arguments. Furthermore, we determine sharp upper and lower bounds on the differences between the expectations of the mixtures expressed in various scale units. General results are illustrated by several examples.

Suggested Citation

  • Tomasz Rychlik, 2019. "Sharp bounds on distribution functions and expectations of mixtures of ordered families of distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 166-195, March.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:1:d:10.1007_s11749-018-0604-4
    DOI: 10.1007/s11749-018-0604-4
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    References listed on IDEAS

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