Skip to main content
SpringerLink
Log in

On the Estimation of the Exponential Distribution of Parameters

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

In the present paper, the problem of estimation of the exponential distribution of parameters is investigated.

In Sec. 1, the ordinary exponential distribution is considered, and the parameter λ is estimated by means of censored observations by the pseudomaximal likelihood method. It is shown that the estimator is asymptotically consistent and effective.

In Sec. 2, the problem of estimation of parameters of the truncated exponential distribution is considered using the maximal likelihood method. The existence and uniqueness of the solution corresponding to the likelihood equation are shown.

The practical application of the obtained results with the aid of computer realization is given. In particular, a sample of size n = 1000 is selected, which is distributed by the truncated exponential law. The sample mean \( \overline{x} \) = 1.3435 and the solution θ ∗ = 2.004 of the corresponding likelihood control are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Faris M. Al-Athari, “Estimation of the mean of truncated exponential distribution,” J. Math. Stat., 4, No. 4, 284–288 (2008).

  2. G. Kulldorf, Contribution to the Theory of Estimation from Grouped and Partially Grouped Samples, Wiley, New York (1962).

    Google Scholar 

  3. E.L. Lehmann, Theory of Point Estimation, Springer-Verlag, New York (1997).

    MATH  Google Scholar 

  4. E. Nadaraya, M. Patsatsia, and G. Sokhadze, “On the maximum pseudo-likelihood estimations of distribution parameters by grouped observations with censoring,” Proc. Sukhumi State Univ., 7, 33–43 (2009).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. A. Tsereteli State University, Kutaisi, Georgia

    G. Lominashvili

Authors
  1. G. Lominashvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Lominashvili.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 94, Proceedings of the International Conference “Lie Groups, Differential Equations, and Geometry,” June 10–22, 2013, Batumi, Georgia, Part 1, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lominashvili, G. On the Estimation of the Exponential Distribution of Parameters. J Math Sci 216, 569–576 (2016). https://doi.org/10.1007/s10958-016-2916-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-016-2916-9

Search

Navigation