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A note on the exponential Poisson distribution: A nested EM algorithm

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  • Karlis, Dimitris

Abstract

An EM type algorithm for estimating the parameters of the exponential Poisson distribution has recently been proposed. This algorithm uses a Newton Raphson approach at the M-step. An alternative approach, where the Newton Raphson step is replaced by another EM algorithm is described. This approach has simple closed form expressions, making use of a nested EM scheme where the M-step itself is solved with an EM algorithm. An advantage of this algorithm is that it provides estimates in the admissible range when the initial values are in the admissible range, and avoids overflow problems that may occur during Newton-Raphson iterations and, in certain cases, it can be faster. Some simulation evidence on the speed of the new approach compared to the one that uses Newton-Raphson is provided.

Suggested Citation

  • Karlis, Dimitris, 2009. "A note on the exponential Poisson distribution: A nested EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 894-899, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:894-899
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    References listed on IDEAS

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    1. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    2. Chong Ju Choi & Carla C. J. M. Millar & Caroline Y. L. Wong, 2005. "Knowledge and the State," Palgrave Macmillan Books, in: Knowledge Entanglements, chapter 0, pages 19-38, Palgrave Macmillan.
    3. Dankmar Böhning & Dieter Schön, 2005. "Nonparametric maximum likelihood estimation of population size based on the counting distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(4), pages 721-737, August.
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    Cited by:

    1. Cancho, Vicente G. & Louzada-Neto, Franscisco & Barriga, Gladys D.C., 2011. "The Poisson-exponential lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 677-686, January.
    2. Chahkandi, M. & Ganjali, M., 2009. "On some lifetime distributions with decreasing failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4433-4440, October.
    3. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    4. Bakouch, Hassan S. & Ristić, Miroslav M. & Asgharzadeh, A. & Esmaily, L. & Al-Zahrani, Bander M., 2012. "An exponentiated exponential binomial distribution with application," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1067-1081.

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