On a simple unreferenced distribution with support [-1,1]

Christophe Chesneau

On a simple unreferenced distribution with support [-1,1]

Abstract

The notion of distributions is central to probability theory and statistics. Because so many already exist, it is difficult to find new distributions that combine simplicity and originality. In this article, however, we present one, described as a simple but not yet referenced one-parameter distribution with support $[-1,1]$. It can be seen as a modified and restricted version of the logistic distribution on the interval $[-1,1]$, and also as a generalization of the uniform distribution over $[-1,1]$. In particular, the forms of the corresponding probability density functions are monotonic, typical of those obtained by a cumulative distribution function and its vertically symmetric version. We discuss the main properties of this new distribution, focusing on those related to the quantile function and the moments. Some additional results contribute to the theory of distributions, including one that introduces the notion of opposite distributions. The article concludes with a short numerical study, part of which is devoted to the maximum likelihood estimation of the unique parameter involved. It also includes the analysis of score-type data.

Keywords

References

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Details

Primary Language

English

Subjects

Statistical Theory, Probability Theory

Journal Section

Research Article

Authors

Christophe Chesneau ^*
France

Publication Date

June 20, 2025

Submission Date

February 14, 2025

Acceptance Date

March 31, 2025

Published in Issue

Year 2025 Volume: 1 Number: 1

IZ

https://izlik.org/JA56MU64SN

Cite

RIS / Bibtex

APA

Chesneau, C. (2025). On a simple unreferenced distribution with support [-1,1]. Smyrna Journal of Natural and Data Sciences, 1(1), 1-25. https://izlik.org/JA56MU64SN

AMA

1.Chesneau C. On a simple unreferenced distribution with support [-1,1]. Smyrna Journal of Natural and Data Sciences. 2025;1(1):1-25. https://izlik.org/JA56MU64SN

Chicago

Chesneau, Christophe. 2025. “On a Simple Unreferenced Distribution With Support [-1,1]”. Smyrna Journal of Natural and Data Sciences 1 (1): 1-25. https://izlik.org/JA56MU64SN.

EndNote

Chesneau C (June 1, 2025) On a simple unreferenced distribution with support [-1,1]. Smyrna Journal of Natural and Data Sciences 1 1 1–25.

IEEE

[1]C. Chesneau, “On a simple unreferenced distribution with support [-1,1]”, Smyrna Journal of Natural and Data Sciences, vol. 1, no. 1, pp. 1–25, June 2025, [Online]. Available: https://izlik.org/JA56MU64SN

ISNAD

Chesneau, Christophe. “On a Simple Unreferenced Distribution With Support [-1,1]”. Smyrna Journal of Natural and Data Sciences 1/1 (June 1, 2025): 1-25. https://izlik.org/JA56MU64SN.

JAMA

1.Chesneau C. On a simple unreferenced distribution with support [-1,1]. Smyrna Journal of Natural and Data Sciences. 2025;1:1–25.

MLA

Chesneau, Christophe. “On a Simple Unreferenced Distribution With Support [-1,1]”. Smyrna Journal of Natural and Data Sciences, vol. 1, no. 1, June 2025, pp. 1-25, https://izlik.org/JA56MU64SN.

Vancouver

1.Christophe Chesneau. On a simple unreferenced distribution with support [-1,1]. Smyrna Journal of Natural and Data Sciences [Internet]. 2025 Jun. 1;1(1):1-25. Available from: https://izlik.org/JA56MU64SN