What question did this study set out to answer?

This research aims to develop confidence intervals for the mean of a two-parameter exponential distribution and evaluate their performance.

July 26, 2026SymmetryOpen Access

On the Joint Asymptotic Normality of the Method of Moments Estimators of the Two-Parameter Exponential Distribution

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Authors

WPWikanda PhaphanKing Mongkut's University of Technology North Bangkok NKNattawut KhansaiNational Science and Technology Development Agency AKApitad KraichokKing Mongkut's University of Technology North Bangkok

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Implication

Randomized trial examines confidence intervals for mean in the two-parameter exponential distribution, indicating improved performance with larger samples.

Key Points

This research aims to develop confidence intervals for the mean of a two-parameter exponential distribution and evaluate their performance.
Developed confidence intervals based on joint asymptotic normality using the Delta method.
Compared proposed intervals with Wald-type intervals regarding coverage probability and average width.
Evaluated performance using Monte Carlo simulation and real data from PM2.5 concentrations.
As sample size increases, estimators improve in bias and stability, yielding narrower confidence intervals.
For small samples, wider intervals and lower coverage probabilities were observed.
Large samples showed negligible bias, variances near theoretical values, and confidence intervals at nominal levels.

Cite This Study

Phaphan et al. (2026) studied this question.

synapsesocial.com/papers/6a65a660d3aea3239cd77c56 https://doi.org/10.3390/sym18081253

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Implication

Randomized trial examines confidence intervals for mean in the two-parameter exponential distribution, indicating improved performance with larger samples.

On the Joint Asymptotic Normality of the Method of Moments Estimators of the Two-Parameter Exponential Distribution

Discussion

Member takes

Implication

Key Points

Cite This Study

On the Joint Asymptotic Normality of the Method of Moments Estimators of the Two-Parameter Exponential Distribution

Discussion

Member takes

Implication

Key Points

Cite This Study

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