Fisher Information in Weighted Distributions

Authors

Satish Iyengar
Paul H. Kvam, University of RichmondFollow
Harshinder Singh

DOI

10.2307/3316134

Abstract

Standard inference procedures assume a random sample from a population with density f_μ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density f_μ^w(x) that is proportional to w(x)f_μ(x). In this paper, we assume that f_μ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the k^th order statistic of a random sample of size m, (ii) observations from the stationary distribution of the residual lifetime of a renewal process, and (iii) truncated distributions. We give general conditions under which the weighted distribution has greater Fisher information than the original distribution, and specialize to the normal, gamma, and Weibull distributions. These conditions involve the distributions' hazard rate and the reversed hazard rate functions.

Document Type

Post-print Article

Publication Date

1999

Publisher Statement

Copyright © 1999 Statistical Society of Canada.

DOI: 10.2307/3316134

The definitive version is available at: https://onlinelibrary.wiley.com/doi/abs/10.2307/3316134

Full Citation:

Iyengar, Satish, Paul Kvam, and Harshinder Singh. "Fisher Information in Weighted Distributions." Canadian Journal of Statistics 27, no. 4 (1999): 833-841. doi:10.2307/3316134.

Recommended Citation

Iyengar, Satish; Kvam, Paul H.; and Singh, Harshinder, "Fisher Information in Weighted Distributions" (1999). Department of Math & Statistics Faculty Publications. 191.
https://scholarship.richmond.edu/mathcs-faculty-publications/191