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Exact expressions for the weights used in least-squares regression estimation for the log-logistic and Weibull distribution

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  • J. Martin van Zyl

Abstract

Estimation for the log-logistic and Weibull distributions can be performed by using the equations used for probability plotting, and this technique outperforms the maximum likelihood (ML) estimation often in small samples. This leads to a highly heteroskedastic regression problem. Exact expressions for the variances of the residuals are derived which can be used to perform weighted regression. In large samples, the ML performs best, but it is shown that in smaller samples, the weighted regression outperforms the ML estimation with respect to bias and mean square error.

Suggested Citation

  • J. Martin van Zyl, 2017. "Exact expressions for the weights used in least-squares regression estimation for the log-logistic and Weibull distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1720-1730, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:4:p:1720-1730
    DOI: 10.1080/03610926.2015.1026995
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