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Mean Absolute Deviation01:13

Mean Absolute Deviation

3.0K
The mean absolute deviation is also a measure of the variability of data in a sample. It is the absolute value of the average difference between the data values and the mean.
Let us consider a dataset containing the number of unsold cupcakes in five shops: 10, 15, 8, 7, and 10. Initially, calculate the sample mean. Then calculate the deviation, or the difference, between each data value and the mean. Next, the absolute values of these deviations are added and divided by the sample size to...
3.0K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

121
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
121
Regression Toward the Mean01:52

Regression Toward the Mean

6.6K
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
6.6K
Decision Making: P-value Method01:09

Decision Making: P-value Method

5.9K
The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim  is also stated. These statements can act as null and alternative hypotheses:  a null hypothesis would be a neutral statement while the alternative hypothesis can...
5.9K
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

9.0K
To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
9.0K
Weighted Mean00:57

Weighted Mean

5.7K
While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
5.7K

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Related Experiment Video

Updated: Oct 16, 2025

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
11:53

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

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Portfolio Optimization with a Mean-Absolute Deviation-Entropy Multi-Objective Model.

Weng Siew Lam1, Weng Hoe Lam1, Saiful Hafizah Jaaman2

  • 1Department of Physical and Mathematical Science, Faculty of Science, Kampar Campus, Universiti Tunku Abdul Rahman, Jalan Universiti, Bandar Barat, Kampar 31900, Perak, Malaysia.

Entropy (Basel, Switzerland)
|October 23, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a new portfolio optimization model that maximizes return, minimizes risk, and increases diversification through entropy. The proposed mean-absolute deviation-entropy model offers investors a superior performance ratio and better risk management.

Keywords:
entropygoal programmingoptimal portfolioreturnrisk

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Area of Science:

  • Quantitative Finance
  • Financial Engineering
  • Operations Research

Background:

  • Traditional portfolio optimization often balances return and risk using models like mean-absolute deviation (MAD).
  • Existing MAD models do not explicitly incorporate portfolio diversification through entropy maximization.
  • Higher entropy correlates with greater portfolio diversification, potentially reducing overall risk.

Purpose of the Study:

  • To propose a novel multi-objective optimization model for portfolio selection: the mean-absolute deviation-entropy (MADE) model.
  • To integrate the maximization of portfolio entropy alongside return maximization and risk minimization.
  • To utilize a goal-programming approach for optimizing multiple objective functions.

Main Methods:

  • Development of a multi-objective optimization model incorporating mean return, absolute deviation, and entropy.
  • Application of a goal-programming framework to handle the optimal values of the objective functions.
  • Empirical testing using stock return data from the Dow Jones Industrial Average.

Main Results:

  • The proposed MADE model demonstrates superior performance compared to the traditional MAD model and naive diversification strategies.
  • The MADE model achieved a higher performance ratio, indicating a better risk-return trade-off.
  • Portfolios optimized with the MADE model generated higher mean returns than those from the MAD model and naive diversification.

Conclusions:

  • The mean-absolute deviation-entropy model offers a more effective approach to portfolio optimization.
  • Incorporating entropy maximization enhances portfolio diversification and reduces unsystematic risk.
  • Investors can benefit from the MADE model for constructing well-diversified portfolios with improved performance.