TY - JOUR
T1 - A note on the harmonic law: A two-parameter family of distributions for ratios
AU - Puig, Pedro
PY - 2008/2/15
Y1 - 2008/2/15
N2 - 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. © 2007 Elsevier B.V. All rights reserved.
AB - 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. © 2007 Elsevier B.V. All rights reserved.
KW - Characterization of distributions
KW - Gauss's principle
KW - Generalized inverse Gaussian distribution
KW - Halphen distribution
KW - Harmonic distribution
U2 - 10.1016/j.spl.2007.07.024
DO - 10.1016/j.spl.2007.07.024
M3 - Article
SN - 0167-7152
VL - 78
SP - 320
EP - 326
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -