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A note on the harmonic law: A two-parameter family of distributions for ratios

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  • Puig, Pedro

Abstract

Consider two-parameter statistical models for positive continuous observations. Suppose that these models are closed under change of scale and under reciprocals, properties that are very appropriate when the observations are ratios of positive magnitudes. Additionally, suppose that the maximum likelihood estimator of the population mean is the sample mean (Gauss's principle). Surprisingly, only one statistical model satisfies these three properties and this is a special case of the generalized inverse gaussian family of distributions known as Harmonic Law.

Suggested Citation

  • Puig, Pedro, 2008. "A note on the harmonic law: A two-parameter family of distributions for ratios," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 320-326, February.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:3:p:320-326
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    References listed on IDEAS

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    1. Puig, Pedro & Valero, Jordi, 2006. "Count Data Distributions: Some Characterizations With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 332-340, March.
    2. Puig, Pedro, 2003. "Characterizing Additively Closed Discrete Models by a Property of Their Maximum Likelihood Estimators, With an Application to Generalized Hermite Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 687-692, January.
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    Cited by:

    1. Lucas O. F. Sales & André L. S. Pinho & Marcelo Bourguignon & F. Moisés C. Medeiros, 2022. "Control charts for monitoring the median in non-negative asymmetric data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 1037-1068, October.
    2. N. Balakrishnan & Helton Saulo & Marcelo Bourguignon & Xiaojun Zhu, 2017. "On moment-type estimators for a class of log-symmetric distributions," Computational Statistics, Springer, vol. 32(4), pages 1339-1355, December.

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