scholarly journals Serial Interval Distribution of SARS-CoV-2 Infection in Brazil

2020 ◽  
Author(s):  
Carlos A. Prete ◽  
Lewis Buss ◽  
Amy Dighe ◽  
Victor Bertollo Porto ◽  
Darlan da Silva Candido ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Probability Distribution ◽  
Ministry Of Health ◽  
Interval Probability ◽  
Serial Interval ◽  
The Mean ◽  
Two Parameters ◽  
Interval Distribution

AbstractUsing 65 transmission pairs of SARS-CoV-2 reported to the Brazilian Ministry of Health we estimate the mean and standard deviation for the serial interval to be 2.97 and 3.29 days respectively. We also present a model for the serial interval probability distribution using only two parameters.

A simple proof of Gauss's inequality.

1947 ◽  
Vol 7 (01) ◽  
pp. 38-41 ◽  
Author(s):  
Wilfred Perks
Keyword(s):  
Standard Deviation ◽  
Probability Distribution ◽  
Simple Proof ◽  
The Mean

Consider a continuous probability distribution of a variablexmeasured from its mean in units of its standard deviation, and suppose that deviations from the mean are taken irrespective of sign; letpxrepresent the ordinate applicable tox(this ordinate is, of course, the sum of the original ordinates at +xand —x). We then have, and we write.

scholarly journals Statistical Analysis of Basketball Teams Through Normal Distribution and R Programming

2020 ◽  
Vol 4 (9) ◽  
Author(s):  
Megan Wang
Keyword(s):  
Statistical Analysis ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Normal Distribution ◽  
Sports Analytics ◽  
R Programming Language ◽  
General Improvement ◽  
The Mean ◽  
R Programming ◽  
Two Parameters

Basketball has existed for almost 130 years, becoming one of the most famous sports worldwide by affecting millions of lives and having national and global tournaments. With the general improvement of people's concern and love for sports competition, sports analytics’ role will become more prominent. Hence, this paper combines the relevant knowledge of statistics and typical basketball competition cases from NBA, expounding the application of statistics in sports competition. The paper first examines the importance of normal distribution (also called Gaussian distribution) in statistics through its probability density function and the function's graph. The function has two parameters: the mean for the maximum and standard deviation for the distance away from the mean[1]. By compiling datasets of past teams and individuals for their basketball performances and making simple calculations of their standard deviation and mean, the paper constructs normal distribution graphs using the R programming language. Finally, the paper examines the Real Plus-Minus value and its importance in basketball.

scholarly journals The serial interval of COVID-19 from publicly reported confirmed cases

2020 ◽  
Author(s):  
Zhanwei Du ◽  
Xiaoke Xu ◽  
Ye Wu ◽  
Lin Wang ◽  
Benjamin J. Cowling ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Chinese Cities ◽  
Serial Interval ◽  
The Mean

Short AbstractWe estimate the distribution of serial intervals for 468 confirmed cases of COVID-19 reported in 93 Chinese cities by February 8, 2020. The mean and standard deviation are 3.96 (95% CI 3.53-4.39) and 4.75 (95% CI 4.46-5.07) days, respectively, with 12.6% of reports indicating pre-symptomatic transmission.One sentence summaryWe estimate the distribution of serial intervals for 468 confirmed cases of COVID-19 reported in 93 Chinese cities by February 8, 2020.

scholarly journals Transmission onset distribution of COVID-19

2020 ◽  
Author(s):  
June Young Chun ◽  
Gyuseung Baek ◽  
Yongdai Kim
Keyword(s):  
Standard Deviation ◽  
Incubation Period ◽  
Bayesian Methods ◽  
Symptom Onset ◽  
Onset Time ◽  
Preventive Measure ◽  
Credible Interval ◽  
Serial Interval ◽  
Interval Distribution ◽  
Key Parameter

AbstractObjectivesThe distribution of the transmission onset of COVID-19 relative to the symptom onset is a key parameter for infection control. It is often not easy to study the transmission onset time, as is difficult to know who infected whom exactly when.MethodsWe inferred transmission onset time from 72 infector-infectee pairs in South Korea, either with known or inferred contact dates by means of incubation period. Combining this data with known information of infector’s symptom onset, we could generate the transmission onset distribution of COVID-19, using Bayesian methods. Serial interval distribution could be automatically estimated from our data.ResultsWe estimated the median transmission onset to be 1.31 days (standard deviation, 2.64 days) after symptom onset with peak at 0.72 days before symptom onset. The pre-symptomatic transmission proportion was 37% (95% credible interval [CI], 16–52%). The median incubation period was estimated to be 2.87 days (95% CI, 2.33–3.50 days) and the median serial interval to be 3.56 days (95% CI, 2.72–4.44 days).ConclusionsConsidering the transmission onset distribution peaked with the symptom onset and the pre-symptomatic transmission proportion is substantial, the usual preventive measure might be too late to prevent SARS-CoV-2 transmission.

Using Skew for Classification

2015 ◽  
Vol 29 (03) ◽  
pp. 1551002
Author(s):  
Mark J. DeBonis
Keyword(s):  
Distribution Function ◽  
Standard Deviation ◽  
Probability Distribution ◽  
Principle Component Analysis ◽  
Probability Distribution Function ◽  
Error Rates ◽  
Binary Classifier ◽  
Data Set ◽  
Principle Component ◽  
The Mean

One classic example of a binary classifier is one which employs the mean and standard deviation of the data set as a mechanism for classification. Indeed, principle component analysis has played a major role in this effort. In this paper, we propose that one should also include skew in order to make this method of classification a little more precise. One needs a simple probability distribution function which can be easily fit to a data set and use this pdf to create a classifier with improved error rates and comparable to other classifiers.

scholarly journals Transmission interval estimates suggest pre-symptomatic spread of COVID-19

2020 ◽  
Author(s):  
Lauren C. Tindale ◽  
Michelle Coombe ◽  
Jessica E. Stockdale ◽  
Emma S. Garlock ◽  
Wing Yin Venus Lau ◽  
...  
Keyword(s):  
Incubation Period ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Interval Estimates ◽  
Secondary Infections ◽  
Serial Interval ◽  
Incubation Periods ◽  
Key Variables ◽  
The Mean ◽  
Interval Distribution

AbstractBackgroundAs the COVID-19 epidemic is spreading, incoming data allows us to quantify values of key variables that determine the transmission and the effort required to control the epidemic. We determine the incubation period and serial interval distribution for transmission clusters in Singapore and in Tianjin. We infer the basic reproduction number and identify the extent of pre-symptomatic transmission.MethodsWe collected outbreak information from Singapore and Tianjin, China, reported from Jan.19-Feb.26 and Jan.21-Feb.27, respectively. We estimated incubation periods and serial intervals in both populations.ResultsThe mean incubation period was 7.1 (6.13, 8.25) days for Singapore and 9 (7.92, 10.2) days for Tianjin. Both datasets had shorter incubation periods for earlier-occurring cases. The mean serial interval was 4.56 (2.69, 6.42) days for Singapore and 4.22 (3.43, 5.01) for Tianjin. We inferred that early in the outbreaks, infection was transmitted on average 2.55 and 2.89 days before symptom onset (Singapore, Tianjin). The estimated basic reproduction number for Singapore was 1.97 (1.45, 2.48) secondary cases per infective; for Tianjin it was 1.87 (1.65, 2.09) secondary cases per infective.ConclusionsEstimated serial intervals are shorter than incubation periods in both Singapore and Tianjin, suggesting that pre-symptomatic transmission is occurring. Shorter serial intervals lead to lower estimates of R0, which suggest that half of all secondary infections should be prevented to control spread.

scholarly journals PHENOTYPIC EXPRESSION OF A GENETIC PROPERTY INTRODUCED BY DEOXYRIBONUCLEATE

1959 ◽  
Vol 42 (4) ◽  
pp. 737-748 ◽  
Author(s):  
Maurice S. Fox
Keyword(s):  
Standard Deviation ◽  
Time Course ◽  
Distribution Curve ◽  
Phenotypic Expression ◽  
Normal Distribution Curve ◽  
Phenotypic Alteration ◽  
The Mean ◽  
Definition Of ◽  
Two Parameters ◽  
Mean Time

The time course of the appearance of cells showing a new phenotype, following treatment with a specific DNA, has been analyzed. A plot as a function of time of the number of cells showing the new property closely resembles the summation under a normal distribution curve. Describing the appearance of the new phenotype in these terms permits the definition of two parameters, the mean time, and the standard deviation of the distribution curve. This distribution is not affected either by the DNA concentration with which the transformable population has been treated, or by the streptomycin concentration with which the transformed population has been challenged. Interruptions of the expression process, by cooling to 20° or 0°C., serve only to displace the expression curves, without changing their shape, while small reductions in temperature change both the mean time of expression and the standard deviation of the distribution curve. On the basis of these observations a number of hypotheses have been examined concerning the mechanism whereby transforming DNA manifests a phenotypic alteration in the transformed cells. It can be concluded that there exist at least two stages in the process of expression. The completion of the first stage, causing the randomization, occurs with a mean time of about 60 minutes, and a terminal step, that of the transition of phenotype, occurs in less than 3 minutes.

Global Predictability of Chaotic Epidemiological Dynamics in Coupled Populations

2003 ◽  
Vol 10 (04) ◽  
pp. 311-320
Author(s):  
Matt Davison ◽  
C. Essex ◽  
J. S. Shiner
Keyword(s):  
Standard Deviation ◽  
Probability Distribution ◽  
Coupling Strength ◽  
Chaotic Dynamics ◽  
Statistical Measures ◽  
Sensitive Dependence ◽  
Strength Dependence ◽  
The Mean ◽  
Long Term Prediction

When the dynamics of an epidemic are chaotic, detailed prediction is effectively impossible, except perhaps in the short term. However, a probability distribution underlying the motion does allow for the long term prediction of statistical measures such as the mean or the standard deviation. Even this weaker long term predictability might be lost if distinct populations with chaotic dynamics are coupled. We show that such coupling can result in a phenomenon we call “sensitive dependence on neglected dynamics”. In light of this phenomenon, it is somewhat surprising that when two logistic maps are coupled, the long term predictability of the mean and standard deviation is maintained. This is true even though the probability distribution describing the time series depends on the coupling strength. The coupling-strength dependence does reveal itself in the loss of predictability of higher order moments such as skewness and kurtosis.

scholarly journals The Probability Distribution of Sea Surface Wind Speeds. Part I: Theory and SeaWinds Observations

2006 ◽  
Vol 19 (4) ◽  
pp. 497-520 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Surface Wind ◽  
Sea Surface ◽  
Wind Speeds ◽  
Sea Surface Wind ◽  
The Mean

Abstract The probability distribution of sea surface wind speeds, w, is considered. Daily SeaWinds scatterometer observations are used for the characterization of the moments of sea surface winds on a global scale. These observations confirm the results of earlier studies, which found that the two-parameter Weibull distribution provides a good (but not perfect) approximation to the probability density function of w. In particular, the observed and Weibull probability distributions share the feature that the skewness of w is a concave upward function of the ratio of the mean of w to its standard deviation. The skewness of w is positive where the ratio is relatively small (such as over the extratropical Northern Hemisphere), the skewness is close to zero where the ratio is intermediate (such as the Southern Ocean), and the skewness is negative where the ratio is relatively large (such as the equatorward flank of the subtropical highs). An analytic expression for the probability density function of w, derived from a simple stochastic model of the atmospheric boundary layer, is shown to be in good qualitative agreement with the observed relationships between the moments of w. Empirical expressions for the probability distribution of w in terms of the mean and standard deviation of the vector wind are derived using Gram–Charlier expansions of the joint distribution of the sea surface wind vector components. The significance of these distributions for improvements to calculations of averaged air–sea fluxes in diagnostic and modeling studies is discussed.

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