Exact statistical inference for quantities of loggamma distribution

Bowen Liu; Malwane M. A. Ananda; Bowen Liu; Malwane M. A. Ananda

doi:10.3934/era.2026119

Electronic Research Archive

2026, Volume 34, Issue 4: 2572-2589. doi: 10.3934/era.2026119

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Exact statistical inference for quantities of loggamma distribution

Bowen Liu ^{1
,
,},
Malwane M. A. Ananda ²

1.
School of Science and Engineering, University of Missouri-Kansas City, 5110 Rockhill Road, Kansas City, MO 64110, USA
2.
Department of Mathematical Sciences, University of Nevada, Las Vegas, 4505 S Maryland Pkwy, Las Vegas, NV 89154, USA

Received: 28 November 2025 Revised: 14 February 2026 Accepted: 03 March 2026 Published: 24 March 2026

Transformed gamma distributions are widely used in various fields such as survival analysis, reliability engineering, and environmental studies. Statistical inference for the quantities of the transformed gamma distributions is of great importance in these applications. However, traditional inference methods often rely on large sample approximations, which is not accurate for small sample sizes. To address this issue, we introduced an exact statistical inference framework for quantities of the transformed gamma distributions and applied the framework to loggamma distribution. The performance of the proposed framework was extensively evaluated via comprehensive simulation studies. The results showed that the proposed framework outperforms the parametric bootstrapping method in terms of coverage probability and type 1 error rate. Two real data applications are provided for illustrative purposes.
- generalized inference,
- exact inference,
- parametric inference,
- gamma distribution,
- loggamma distribution
Citation: Bowen Liu, Malwane M. A. Ananda. Exact statistical inference for quantities of loggamma distribution[J]. Electronic Research Archive, 2026, 34(4): 2572-2589. doi: 10.3934/era.2026119

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Abstract

Transformed gamma distributions are widely used in various fields such as survival analysis, reliability engineering, and environmental studies. Statistical inference for the quantities of the transformed gamma distributions is of great importance in these applications. However, traditional inference methods often rely on large sample approximations, which is not accurate for small sample sizes. To address this issue, we introduced an exact statistical inference framework for quantities of the transformed gamma distributions and applied the framework to loggamma distribution. The performance of the proposed framework was extensively evaluated via comprehensive simulation studies. The results showed that the proposed framework outperforms the parametric bootstrapping method in terms of coverage probability and type 1 error rate. Two real data applications are provided for illustrative purposes.

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