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Standard Deviation

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more...

Clearance Models: Noncompartmental Models

Clearance Models: Noncompartmental Models

Clearance is a pharmacokinetic parameter traditionally defined by compartment models, signifying the rate at which a drug is expelled from the body. However, a noncompartmental model offers an alternative method for assessing clearance, primarily employing empirical data obtained after administering a single drug dose.
The noncompartmental approach capitalizes on extensive sampling data, correlating the volume of distribution to systemic exposure and the administered dosage. This method enables...

Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches

Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches

Drug disposition in the body is a complex process and can be studied using two major approaches: the model and the model-independent approaches.
The model approach uses mathematical models to describe changes in drug concentration over time. Pharmacokinetic models help characterize drug behavior in patients, predict drug concentration in the body fluids, calculate optimum dosage regimens, and evaluate the risk of toxicity. However, ensuring that the model fits the experimental data accurately...

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...

Estimating Population Standard Deviation

Estimating Population Standard Deviation

When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...

Empirical Method to Interpret Standard Deviation

Empirical Method to Interpret Standard Deviation

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...

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Related Experiment Video

Updated: Jun 14, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Model for non-Gaussian intraday stock returns.

Austin Gerig¹, Javier Vicente, Miguel A Fuentes

¹School of Finance and Economics, University of Technology, Sydney, Broadway, New South Wales, Australia. gerig@santafe.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

This study models stock price fluctuations, revealing non-Gaussian dynamics and stable intraday return distributions. The model accurately predicts these patterns using a gamma distribution for volatility, explaining observed stock market behavior.

Related Experiment Videos

Last Updated: Jun 14, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

Quantitative Finance
Financial Econometrics
Statistical Modeling

Background:

Stock market prices exhibit complex, non-Gaussian dynamics, necessitating advanced models.
Understanding the origin of these dynamics is crucial for financial analysis and risk management.

Purpose of the Study:

To develop and validate a model explaining the shape and scaling of intraday stock return distributions.
To provide evidence for non-Gaussian and stable return distributions in stocks traded on the London Stock Exchange.

Main Methods:

Utilized a large database of intraday stock price data for London Stock Exchange-traded stocks.
Developed a model assuming constant intraday return volatility that varies over longer periods.
Modeled the inverse square of volatility using a gamma distribution, predicting Student-distributed returns.

Main Results:

Confirmed non-Gaussian and similar return distributions across multiple stocks.
Demonstrated the stability of these distributions over intraday time scales.
Showed excellent agreement between the model's predictions and empirical data across all return distribution regions.

Conclusions:

The proposed model successfully explains the observed non-Gaussian dynamics of intraday stock returns.
The gamma distribution of volatility provides a robust framework for understanding stock return distributions.
The findings offer valuable insights into the statistical properties of financial markets.