Conflations of Probability Distributions
| dc.creator | Hill, Theodore P. | |
| dc.date | 2008-08-13 | |
| dc.date | 2009-05-25 | |
| dc.date.accessioned | 2026-07-07T13:17:23Z | |
| dc.date.available | 2026-07-07T13:17:23Z | |
| dc.description | The conflation of a finite number of probability distributions P_1,..., P_n is a consolidation of those distributions into a single probability distribution Q=Q(P_1,..., P_n), where intuitively Q is the conditional distribution of independent random variables X_1,..., X_n with distributions P_1,..., P_n, respectively, given that X_1= ... =X_n. Thus, in large classes of distributions the conflation is the distribution determined by the normalized product of the probability density or probability mass functions. Q is shown to be the unique probability distribution that minimizes the loss of Shannon Information in consolidating the combined information from P_1,..., P_n into a single distribution Q, and also to be the optimal consolidation of the distributions with respect to two minimax likelihood-ratio criteria. When P_1,..., P_n are Gaussian, Q is Gaussian with mean the classical weighted-mean-squares reciprocal of variances. A version of the classical convolution theorem holds for conflations of a large class of a.c. measures. | |
| dc.description | Additional reference, revised abstract, revised introduction (idempotency), revised title, and revised introduction to section 7; these changes plus converting the manuscript from plain tex to latex shortened the paper to 23 pages | |
| dc.identifier | https://arxiv.org/abs/0808.1808 | |
| dc.identifier | http://arxiv.org/abs/0808.1808 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/231096 | |
| dc.subject | Probability | |
| dc.subject | 60A05, 62B10, 94A15, 62B15 | |
| dc.title | Conflations of Probability Distributions | |
| dc.type | text |