Pub Date : 2014-01-01DOI: 10.2991/978-94-6239-061-4_8
M. Ahsanullah, B. M. Kibria, M. Shakil
Before a particular probability distribution model is applied to fit the real world data, it is necessary to confirm whether the given probability distribution satisfies the underlying requirements by its characterization.
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Pub Date : 1993-01-01DOI: 10.1515/9783112318867-049
W. Lu
Let X_1; X_2,…,X_N be i.i.d. random variables with distribution function F and censored by Y_1 Y_2…, Y_N. We can only observe (Z_t δ_t), i=1, 2,…, n and δ_i,i= n+1,…, N, where This model was proposed by Suzuki, K. (1985) and he discussed the case tnat X_t is a discrete random variable taking finite values. In this paper we discuss the case that X_t has a continuous distribution function F. We propose a estimator F of F and prove that N~(1/2)(F(t)-F(t)) converges to a Gussion process.
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Pub Date : 1985-01-01DOI: 10.1090/conm/118/1137974
M. Qian
In the present paper,a general probabilistic definition of the entropy production for stochastic processes is given.In the concrete cases of Markov chains and diffussions,we get its explicit expressions,which meet those given by physists and chemists perfectly. Therefore,it could be seen that the entropy production is really a criterion to describe how far a stochastic process is from the reversibility.
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