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Estimation of the PDF and the CDF of exponentiated moment exponential distribution

Author

Listed:
  • Yogesh Mani Tripathi

    (Indian Institute of Technology Patna)

  • Tanmay Kayal

    (Indian Institute of Technology Patna)

  • Sanku Dey

    (St. Anthony’s College)

Abstract

This article addresses the different methods of estimation of the probability density function and the cumulative distribution function for the exponentiated moment exponential distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimators, maximum likelihood estimators, percentile estimators, least squares estimators, weighted least square estimators, maximum product of spacings estimators, Cramér–von-Mises estimators and Anderson–Darling estimators. Analytical expressions are derived for the bias and the mean squared error. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Simulation studies and real data applications show that the ML estimator performs better than others. Finally, one real data set has been analyzed for illustrative purposes.

Suggested Citation

  • Yogesh Mani Tripathi & Tanmay Kayal & Sanku Dey, 2017. "Estimation of the PDF and the CDF of exponentiated moment exponential distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1282-1296, November.
    • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-017-0599-3
    DOI: 10.1007/s13198-017-0599-3
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    Cited by:

    1. Sanku Dey & Tanmay Kayal & Yogesh Mani Tripathi, 2018. "Evaluation and Comparison of Estimators in the Gompertz Distribution," Annals of Data Science, Springer, vol. 5(2), pages 235-258, June.
    2. Sasikumar Padmini Arun & Christophe Chesneau & Radhakumari Maya & Muhammed Rasheed Irshad, 2023. "Farlie–Gumbel–Morgenstern Bivariate Moment Exponential Distribution and Its Inferences Based on Concomitants of Order Statistics," Stats, MDPI, vol. 6(1), pages 1-15, February.

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