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Some approximations of the logistic distribution with application to the covariance matrix of logistic regression

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  • Pingel, Ronnie

Abstract

In this paper, we show that a two-component normal mixture model provides a good approximation to the logistic distribution. This model is an improvement over using the normal distribution and is comparable with using the t-distribution as approximating distributions. The result from using the mixture model is exemplified by finding an approximative analytic expression for the covariance matrix of logistic regression with normally distributed random regressors.

Suggested Citation

  • Pingel, Ronnie, 2014. "Some approximations of the logistic distribution with application to the covariance matrix of logistic regression," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 63-68.
    • Handle: RePEc:eee:stapro:v:85:y:2014:i:c:p:63-68
    DOI: 10.1016/j.spl.2013.11.007
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    References listed on IDEAS

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    1. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, Enero-Abr.
    2. repec:cup:cbooks:9780521822893 is not listed on IDEAS
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    1. Pingel, Ronnie & Waernbaum, Ingeborg, 2015. "Correlation and efficiency of propensity score-based estimators for average causal effects," Working Paper Series 2015:3, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    2. Arthur Pewsey, 2018. "Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 147-172, March.

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