Abstraction of Expectation Functions Using Gaussian Distributions

Author(s):  
David Monniaux
1993 ◽  
Vol 32 (02) ◽  
pp. 175-179 ◽  
Author(s):  
B. Brambati ◽  
T. Chard ◽  
J. G. Grudzinskas ◽  
M. C. M. Macintosh

Abstract:The analysis of the clinical efficiency of a biochemical parameter in the prediction of chromosome anomalies is described, using a database of 475 cases including 30 abnormalities. A comparison was made of two different approaches to the statistical analysis: the use of Gaussian frequency distributions and likelihood ratios, and logistic regression. Both methods computed that for a 5% false-positive rate approximately 60% of anomalies are detected on the basis of maternal age and serum PAPP-A. The logistic regression analysis is appropriate where the outcome variable (chromosome anomaly) is binary and the detection rates refer to the original data only. The likelihood ratio method is used to predict the outcome in the general population. The latter method depends on the data or some transformation of the data fitting a known frequency distribution (Gaussian in this case). The precision of the predicted detection rates is limited by the small sample of abnormals (30 cases). Varying the means and standard deviations (to the limits of their 95% confidence intervals) of the fitted log Gaussian distributions resulted in a detection rate varying between 42% and 79% for a 5% false-positive rate. Thus, although the likelihood ratio method is potentially the better method in determining the usefulness of a test in the general population, larger numbers of abnormal cases are required to stabilise the means and standard deviations of the fitted log Gaussian distributions.


2018 ◽  
Vol 69 (10) ◽  
pp. 2826-2832
Author(s):  
Ioan Gabriel Sandu ◽  
Viorica Vasilache ◽  
Andrei Victor Sandu ◽  
Marin Chirazi ◽  
Cezar Honceriu ◽  
...  

The saline aerosols generated in gaseous media, as nanodispersions, behave, with respect to the concentration levels and the lifespan, as trimodal distributions (the three domains with Gaussian distributions: fine or Aitken under 50 �m, medium between 50 and 500 mm and, respectively, coarse or large between 500 and 1000 mm). The generation in latent state is dependent on the active surface of the source (number of generator centres, the size and position of the fluorescences, the porosity, size and shape of the source, etc.), the climatic parameters, but also on a series of other characteristics of the gaseous medium. Our team has demonstrated experimentally that saline aerosols, NaCl type, besides the ability to prevent and treat broncho-respiratory and cardiac conditions, through coassistance of saline aerosols of other cations than sodium, and of the iodine anion, have for certain levels of concentrations propitious effects over the immune, bone and muscular systems. Similarly proved has been the positive influence on the development of children, as well the determinant role in increasing athletic performance and of other human subjects performing intense activities.


2019 ◽  
Vol 4 (6) ◽  
Author(s):  
W. Sosa-Correa ◽  
R. M. Pereira ◽  
A. M. S. Macêdo ◽  
E. P. Raposo ◽  
D. S. P. Salazar ◽  
...  

2011 ◽  
Vol 26 (24) ◽  
pp. 1771-1782 ◽  
Author(s):  
H. C. EGGERS ◽  
M. B. DE KOCK ◽  
J. SCHMIEGEL

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.


2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.


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