We propose a class of Bayesian cure rate models by incorporating a baseline density function as well as multiplicative and additive covariate structures. Our model naturally accommodates zero and non-zero cure rates, which provides an objective way to examine the existence of a survival fraction in the failure time data. An inherent parameter constraint needs to be incorporated into the model f...

Monotone Lévy processes with additive increments are defined and studied. It is shown that these processes have natural Markov structure and their Markov transition semigroups are characterized using the monotone Lévy-Khintchine formula. 17 Monotone Lévy processes turn out to be related to classical Lévy processes via Attal's " remarkable transformation. " A monotone analogue of the family of e...

In the present paper we propose to describe gene networks in biological systems using probabilistic algorithms. We describe gene duplication in the process of biological evolution using introduction of the replica procedure for probabilistic algorithms. We construct the examples of such a replica procedure for hidden Markov models. We introduce the family of hidden Markov models where the set o...

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

this paper is devoted to the study of determining optimal process mean in system production with the two markets for the sale of goods. in this paper, we developed an absorbing markov chain model in production systems where all items are inspected %100 for conformance with their specification limits. when the value of the quality characteristic of an item falls below a lower limit, the item is ...

For any α-stable Lévy process with jumps on both sides, where α ∈ (1, 2), we find the Mellin transform of the first hitting time of the origin and give an expression for its density. This complements existing work in the symmetric case and the spectrally one-sided case; cf. [38, 19] and [33, 36], respectively. We appeal to the Lamperti– Kiu representation of Chaumont et al. [16] for real-valued...