Temporal and spatially heterogeneous finite length runs analysis
type: Item
instance of: scholarly article
title: Temporal and spatially heterogeneous finite length runs analysis
author: Zekai Şen
published in: Mathematical \& Computational Applications
publication date: 2018-07-05T00:00:00Z
review text: Summary: Various problems in physics and engineering lead to the problem of run-length probability distribution function (pdf) in a finite time series. In this study to find the pdf of run-lengths in such a series, first infinite sequence properties are reviewed and then finite series run length pdf is derived on the basis of simple set theory. This paper presents the derivation of exact run length pdf in finite length dependent series. In the derivation, two different definitions of runs are considered as the integration method for infinite series and combinatorial analysis for finite time series. The analytical derivations are solved numerically and the results are presented in forms of cumulative pdf, expectation, variance and higher order moment changes with the sample lengths. On the other hand, homogenous run properties based on Bernoulli trials are used in many physical and engineering applications for many decades. Heterogeneous regional Bernoulli trial probability distribution model is not available so far in applications and numerical calculations. Herein, a plausible, rational and logical mathematical derivation of the heterogeneous case is derived, which reduces to the classical homogeneous Bernoulli trial case. This paper provides regional probabilistic success and failure period areal coverage modeling, which is useful for temporal and spatial pattern recognition of spatial risk predictions and parameter assessments. The basis of the methodology is mutually exclusive and independent sub-areal (site) success and failure occurrences' heterogeneous probabilities.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 6898838
zbMATH Keywords: Bernoulli trials
zbMATH Keywords: combinatorial
zbMATH Keywords: finite sample
zbMATH Keywords: heterogeneity
zbMATH Keywords: random field
zbMATH Keywords: runs
MaRDI profile type: Publication
full work available at URL: mca18030221
OpenAlex ID: W2315333650
DOI: 10.3390/MCA18030221
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description: scientific article; zbMATH DE number 6898838