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A note on recovering the distributions from exponential moments
Robert M Mnatsakanov1, Khachatur Sarkisian2
1Department of Statistics, West Virginia University, P.O. Box 6330, Morgantown, WV 26506, USA ; Biostatistics and Epidemiology Branch, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, WV 26505, USA.
Applied Mathematics and Computation
|October 20, 2015
Summary
This study introduces a method for approximating cumulative distribution functions using scaled Laplace transform inversion. It provides a uniform upper bound for the approximation and explores its application to compound Poisson distributions.
Area of Science:
- Probability and Statistics
- Applied Mathematics
- Statistical Inference
Background:
- Recovering distribution functions is crucial in statistical analysis.
- Laplace transform inversion is a complex mathematical technique.
- Compound Poisson distributions model specific types of random events.
Purpose of the Study:
- To develop and analyze an approximation method for cumulative distribution functions.
- To investigate the application of this method to compound Poisson distributions.
- To determine optimal parameters for the proposed inversion technique.
Main Methods:
- Scaled Laplace transform inversion is employed for function recovery.
- A uniform upper bound for the approximation error is mathematically derived.
- Simulation studies are conducted to evaluate performance and parameter selection.
Main Results:
- A novel approximation for cumulative distribution functions is presented.
- The method is shown to be applicable for approximating compound Poisson distributions.
- The study provides insights into selecting the optimal scaling parameter for accuracy.
Conclusions:
- The proposed scaled Laplace transform inversion offers a viable approach for distribution function approximation.
- The findings are relevant for statistical estimation problems involving compound Poisson processes.
- Simulation results guide the practical implementation and parameter tuning of the method.
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