Estimating Distributions using the Theory of Relative Increment Functions

Estimating Distributions using the Theory of Relative Increment Functions

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Sereko Kooepile-Reikeletseng

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University of Botswana

Estimating Distributions using the Theory of Relative Increment Functions

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Abstract

Bounded growth processes can be modelled, approximately by different mathematical models. The challenge for statisticians and mathematicians is finding suitable models for these processes. In this paper we illustrate a non-parametric method, using the the theory of relative increment functions, of estimating density functions of these processes. For a long time, mathematicians attempted to describe the cumulative prevalence of caries with the assumption that there is a mathematical model that would describe the caries prevalence and may be used for predicting caries incidences. In 1960 Porter and Dudman [12] introduced The relative increment function and called it the relative increment of decay as they designed it to compare dental caries increments among children. Further studies of this led to the motivation that the best suitable model for describing the cumulative prevalence of caries should be chosen from a set of distributions that have relative increment functions with the same monotonic behaviour as the relative increment of decay [1]. We illustrate how relative increment functions may be used to estimate the unknown indefinitely smooth probability density function of unimodal populations.

References

18 Cites in Article

Reference Format

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

sereko_kooepile-reikeletseng. 2021. \u201cEstimating Distributions using the Theory of Relative Increment Functions\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 21 (GJSFR Volume 21 Issue F2).

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GJSFR Volume 21 Issue F2

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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Classification

GJSFR-F Classification MSC 2010: 12E12

Submission ReceivedJanuary 28, 2021
Peer Review Double Blind
Handling Editor
Accepted February 25, 2021
Published March 9, 2021

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v1.2

Issue date

April 16, 2021

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