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Maximum likelihood estimation for the Erlang integer parameter

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  • Miller, Gregory K.

Abstract

The maximum likelihood estimator for the integer-valued parameter of the Erlang density is derived. The estimator is easily obtained by solving a simple nonlinear equation, requiring no calculus. Asymptotic theory is provided to show that the estimator is consistent in the discrete sense, i.e. for increasingly large samples one can estimate the true value of the parameter exactly with probability approaching one. A brief simulation study shows that the estimator is quite accurate for even small samples. Applications to both queueing and reliability are provided.

Suggested Citation

  • Miller, Gregory K., 1999. "Maximum likelihood estimation for the Erlang integer parameter," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 335-341, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:4:p:335-341
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