Maximum-Likelihood Method

  • Simon ŠircaEmail author
Part of the Graduate Texts in Physics book series (GTP)


The maximum-likelihood method offers a possibility to devise estimators of unknown population parameters by circumventing the calculation of expected values like average, variance and higher moments. The likelihood function is defined and its role in formulating the principle of maximum likelihood is elucidated. The variance and efficiency of maximum-likelihood estimators is discussed, in particular in the light of its information content and possible minimum variance bound. Likelihood intervals are introduced by analogy to the confidence intervals used in standard sample-based inference. The method is extended to the case when several parameters are determined simultaneously, and to likelihood regions as generalizations of likelihood intervals.


Likelihood Function Extreme Rainfall Typical Pair Likelihood Equation Corrosion Level 
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  1. 1.
    H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, 1946)zbMATHGoogle Scholar
  2. 2.
    C.R. Rao, Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81 (1945)MathSciNetzbMATHGoogle Scholar
  3. 3.
    S. Brandt, Data Analysis, 4th edn. (Springer, Berlin, 2014)CrossRefGoogle Scholar
  4. 4.
    A.G. Frodesen, O. Skjeggestad, H. Tøfte, Probability and Statistics in Particle Physics (Universitetsforlaget, Bergen, 1979)Google Scholar
  5. 5.
    S. Coles, An Introduction to Statistical Modeling of Extreme Values (Springer, Berlin, 2001)CrossRefzbMATHGoogle Scholar
  6. 6.
    R.L. Smith, J.C. Naylor, A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Appl. Stat. 36, 358 (1987)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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