Area-biased one-parameter exponential distribution with financial applications

Abdullah Hardan; Loai Alzoubi

doi:https://doi.org/10.59139/stattrans-2025-026

Area-biased one-parameter exponential distribution with financial applications

Abdullah Hardan Department of Accounting, The world Islamic Sciences and Education University, Amman (11947), Jordan ORCID:https://orcid.org/0009-0007-2545-7719 , Loai Alzoubi 2Department of Mathematics, Al al-Bayt University, Mafraq (25113), Jordan ORCID:https://orcid.org/0000-0002-8795-4100 Statistics in Transition new series, vol. 26, 2025, 3, pages: 35-58 Published online: 5 September 2025 https://doi.org/10.59139/stattrans-2025-026 Citation: Hardan A., Alzoubi L., 2025. Area-biased one-parameter exponential distribution with financial applications. Statistics in Transition new series, 26(3), pp. 35- 58 https://doi.org/10.59139/stattrans-2025-026

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ABSTRACT

Area-biased distributions are special cases of size-biased distributions. We have used the idea of area-biased distributions in this paper to propose a generalisation of a one-parameter linear exponential distribution. The concept is called the area-biased one-parameter linear exponential distribution. Its various characteristics are deduced and thoroughly explored. Some numerical studies are implemented which demonstrate that the distribution is skewed to the right with heavier tail than the normal distribution. The mean waiting and residual life time are also studied. Six methods of estimation are employed to estimate the parameters distribution. A simulation study is conducted which shows that the estimators are approximately unbiased and consistent. Three financial real data sets are applied. They represent the earning per share in the financial, industry and service sectors at the Amman Stock Exchange. The study shows that the suggested distribution has the best fit for these data sets compared to some competence distributions.

KEYWORDS

one-parameter linear exponential distribution, area-biased, methods of estimation, earning per share.

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