Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
The paper gives some basic ideas of both the construction and investigation of the properties of ... more The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol‐Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied via simulations in the special case.
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
The paper gives some basic ideas of both the construction and investigation of the properties of ... more The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol-Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied via simulations in the special case.
Asymptotic Properties of the Invariantly Optimal Estimator of Reliability in the Exponential Case
Statistics & Risk Modeling, 1983
In this note the asymptotic behaviour of the invariantly optimal estimator (IOE) of the reliabili... more In this note the asymptotic behaviour of the invariantly optimal estimator (IOE) of the reliability function in the case of an exponential parent distribution is studied. The IOE turns out to be asymptotically efficient. Further, in terms of asymptotic deficiency, the IOE is compared with the minimum variance unbiased estimator, the maximum likelihood estimator and a type of Bayes estimator of the reliability function. 1. Asymptotic properties of the invariantly optimal estimator. 1.1. Let ζη= ( , . .. , ?n) be a random variable with exponential distribution, independent components ξ i . e . each one -1 -χ/Θ with probability density x>->0 -e ' '""(ο,») (χ) · Θ>0. The corresponding reliability function x<-»R0 (x) =e-x/® will be considered as a function defined on (0,<*>) . By xn= (x-| ,. . . ,xn) realizations of AMS Classification Primary: 62F12 Secondary: 62G05, 62F15
On an estimation problem for type I censored spatial Poisson processes
Kybernetika -Praha-
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz In this paper we consider the problem of estimating the intensity of a spatial homo-geneous Poisuon process if a part of the observations (quadrat counts) is censored. The actual problem has occurred during a court case when one of the authors was a referee for the defense.
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Let {X(t)> t eT be a stochastic process and g be a real function. Suppose that E|X(t)-0| q+2-» 0 ... more Let {X(t)> t eT be a stochastic process and g be a real function. Suppose that E|X(t)-0| q+2-» 0 , q being a natural number and θ being a parameter. Under some smoothing conditions on g asymptotic expansions for Ε g(X(t)) and var g(X(t)) are derived with the remainder terms Ο(E|X(t)-6| g+1) and 0(E|x(t)-9| g+2) , respectively. The proofs use the idea of the method of statistical differentials. Function g may depend on t explicitely. A generalization to the multi-dimensional case is also given. The asymptotic formulas are applied to the problem of compa
Uploads
Papers by Jan Hurt