Intuitive inference about normally distributed populations.

1968 ◽  
Vol 78 (2, Pt.1) ◽  
pp. 269-275 ◽  
Author(s):  
Wesley M. DuCharme ◽  
Cameron R. Peterson
Keyword(s):  
Normally Distributed

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

scholarly journals Learning Subject-Generalized Topographical EEG Embeddings Using Deep Variational Autoencoders and Domain-Adversarial Regularization

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1792
Author(s):  
Juan Hagad ◽  
Tsukasa Kimura ◽  
Ken-ichi Fukui ◽  
Masayuki Numao
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
Emotion Classification ◽  
Limited Data ◽  
Neural Network Architecture ◽  
Building Models ◽  
The Subject ◽  
Data Constraints ◽  
Input Level ◽  
Normally Distributed

Two of the biggest challenges in building models for detecting emotions from electroencephalography (EEG) devices are the relatively small amount of labeled samples and the strong variability of signal feature distributions between different subjects. In this study, we propose a context-generalized model that tackles the data constraints and subject variability simultaneously using a deep neural network architecture optimized for normally distributed subject-independent feature embeddings. Variational autoencoders (VAEs) at the input level allow the lower feature layers of the model to be trained on both labeled and unlabeled samples, maximizing the use of the limited data resources. Meanwhile, variational regularization encourages the model to learn Gaussian-distributed feature embeddings, resulting in robustness to small dataset imbalances. Subject-adversarial regularization applied to the bi-lateral features further enforces subject-independence on the final feature embedding used for emotion classification. The results from subject-independent performance experiments on the SEED and DEAP EEG-emotion datasets show that our model generalizes better across subjects than other state-of-the-art feature embeddings when paired with deep learning classifiers. Furthermore, qualitative analysis of the embedding space reveals that our proposed subject-invariant bi-lateral variational domain adversarial neural network (BiVDANN) architecture may improve the subject-independent performance by discovering normally distributed features.

Thermoelasticity of a moving disk heated by a moving normally distributed heat flux

1987 ◽  
Vol 23 (1) ◽  
pp. 70-75
Author(s):  
Yu. M. Kolyano ◽  
I. I. Bernar
Keyword(s):  
Heat Flux ◽  
Normally Distributed

Statistical Considerations When Assessing Short Latency Stretch Reflexes in the Human Soleus Muscle

Motor Control ◽  
2015 ◽  
Vol 19 (4) ◽  
pp. 253-270 ◽  
Author(s):  
Asger Roer Pedersen ◽  
Peter William Stubbs ◽  
Jørgen Feldbæk Nielsen
Keyword(s):  
Ankle Joint ◽  
Soleus Muscle ◽  
Stretch Reflex ◽  
Short Latency ◽  
Response Magnitude ◽  
Variance Heterogeneity ◽  
Stretch Reflexes ◽  
Response Characteristics ◽  
Normally Distributed

The aim was to investigate trial-by-trial response characteristics in the short-latency stretch reflex (SSR). Fourteen dorsiflexion stretches were applied to the ankle joint with a precontracted soleus muscle on 2 days. The magnitude and variability of trial-by-trial responses of the SSR were assessed. The SSR was log-normally distributed and variance heterogeneous between subjects. For some subjects, the magnitude and variance differed between days and stretches. As velocity increased, variance heterogeneity tended to decrease and response magnitude increased. The current study demonstrates the need to assess trial-by-trial response characteristics and not averaged curves. Moreover, it provides an analysis of SSR characteristics accounting for log-normally distributed and variance heterogeneous trial-by-trial responses.

Optimization problem with normally distributed uncertain parameters

AIChE Journal ◽  
2013 ◽  
Vol 59 (7) ◽  
pp. 2471-2484 ◽  
Author(s):  
Gennady M. Ostrovsky ◽  
Nadir N. Ziyatdinov ◽  
Tatiana V. Lapteva
Keyword(s):  
Optimization Problem ◽  
Uncertain Parameters ◽  
Normally Distributed

On random divisions of a convex set

1978 ◽  
Vol 15 (3) ◽  
pp. 645-649 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Elementary Proof ◽  
Convex Set ◽  
Limiting Distribution ◽  
Independent Identically Distributed ◽  
Normally Distributed

This paper gives an elementary proof that, under some general assumptions, the number of parts a convex set in Rd is divided into by a set of independent identically distributed hyperplanes is asymptotically normally distributed. An example is given where the distribution of hyperplanes is ‘too singular' to satisfy the assumptions, and where a different limiting distribution appears.

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