Singular distribution functions for random variables with stationary digits

Methodology and Computing in Applied Probability

Published On 2023/3

Let F be the cumulative distribution function (CDF) of the base-q expansion , where is an integer and is a stationary stochastic process with state space . In a previous paper we characterized the absolutely continuous and the discrete components of F. In this paper we study special cases of models, including stationary Markov chains of any order and stationary renewal point processes, where we establish a law of pure types: F is then either a uniform or a singular CDF on [0, 1]. Moreover, we study mixtures of such models. In most cases expressions and plots of F are given.

Journal

Methodology and Computing in Applied Probability

Published On

2023/3

Volume

25

Issue

1

Page

31

Authors

Jesper Møller

Jesper Møller

Aalborg Universitet

Position

Professor in Statistics

H-Index(all)

46

H-Index(since 2020)

23

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0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

Cited By

0

Research Interests

Mathematical Statistics

Probability Theory

University Profile Page

Ira Herbst

Ira Herbst

University of Virginia

Position

Professor of Mathematics

H-Index(all)

36

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14

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0

I-10 Index(since 2020)

0

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0

Citation(since 2020)

0

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0

Research Interests

Mathematical Physics

University Profile Page

Horia D. Cornean

Horia D. Cornean

Aalborg Universitet

Position

Professor of Mathematics Denmark

H-Index(all)

22

H-Index(since 2020)

13

I-10 Index(all)

0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

Cited By

0

Research Interests

spectral theory

scattering theory

quantum transport

ICT

University Profile Page

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Article Details
Jesper Møller

Jesper Møller

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Article Details
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Article Details
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Methodology and Computing in Applied Probability

Joint Reliability of Two Consecutive-(1, l) or (2, k)-out-of-(2, n): F Type Systems and Its Application in Smart Street Light Deployment

To investigate some complex practical systems, such as a smart street light system composed of symmetrically deployed lighting and sensing equipment on both sides of a road segment, two consecutive-(1,l) or (2,k)-out-of-(2,n): F type systems that share components are quite useful and are therefore studied in this paper. The joint reliability of the two systems is presented by using the finite Markov chain imbedding approach (FMCIA), which also presents a new computational method for joint signatures of such systems. Compared to the direct method, the new method is not only computationally more efficient, but also presents a unified mathematical form. Finally, some numerical examples are presented to show the computational process, and some further applications and extensions of the models and the methods developed here are mentioned.