Narrow Results

It's important to filter off noise component and keep the figure's geometry configuration during the disposal of the image. Smooth filter algorithm of noise image is used in this paper to eliminate noise commendably and intensify the image edge without blurring the image edge and damaging the detail inside the image.

The following sections are included:

• INTRODUCTION

• MEASURES OF CENTRAL TENDENCY
  • The Arithmetic Mean
  • The Geometric Mean
  • The Median
  • The Mode³

• MEASURES OF DISPERSION
  • The Variance and the Standard Deviation
  • The Mean Absolute Deviation
  • The Range
  • The Coefficient of Variation

• MEASURES OF RELATIVE POSITION
  • Percentiles, Quartiles, and Interquartile Range
  • Box and Whisker Plots: Graphical Descriptions Based on Quartiles
  • Z Scores

• MEASURES OF SHAPE
  • Skewness
  • Kurtosis

• CALCULATING CERTAIN SUMMARY MEASURES FROM GROUPED DATA (Optional)
  • The Mean
  • The Median
  • The Mode
  • Variance and Standard Deviation
  • Percentiles

• APPLICATIONS
  • Statistical Analysis of a Soda Survey
  • Stock Rates of Return for GM, Ford, and the Market
  • 3-Month Treasury Bill Rate and Prime Rate
  • GNP, Personal Consumption, and Disposable Income

• Summary

• Appendix 4A Short-Cut Formulas for Calculating Variance and Standard Deviation

• Appendix 4B Short-Cut Formulas for Calculating Group Variance and Standard Deviation

• Appendix 4C Financial Ratio Analysis for Three Auto Firms
  • Current Ratio
  • Inventory Turnover Ratio
  • Total Debt/Total Asset Ratio
  • Net Profit Margin
  • Return on Total Assets
  • Price/Earnings (P/E) Ratios
  • Payout Ratio

• Questions and Problems

• Project I Project for Descriptive Statistics

An ODE model of HTLV-I infection with CD4⁺ T cells is considered and analyzed. The model system has three equilibria: infection free equilibrium, uninfected equilibrium with leukemia cell only and infected equilibrium. It is observed that the infection persists (infected equilibrium is g.a.s.) if basic reproduction number is bigger than one. This model is further modified by introducing discrete time delay to account for the latent period of infection and it is shown that this delay has no destabilizing effect on the local stability of infected equilibrium. Again, this delay model system is extended to corresponding stochastic model considering the randomness in proliferation of leukemia cells. It is done by introducing white noise term in proliferation rate of Leukemia cells and corresponding stochastic delay differential equation model is analyzed using Fourier Transform technique. We observe fluctuations only in Leukemia cells populations and corresponding variations are obtained analytically. A numerical experimentation is performed to analyse and explain the outcomes. We observe that the fluctuations in Leukemia cells’ population are contributed by white noise perturbation of proliferation rate and this has no impact of both uninfected and infected CD4⁺ T cells.

In this and next two chapters, we will use advanced calculus to formalize and extend the probability theory introduced in Chapter 2. The use of calculus enables us to investigate probability more deeply. A number of quantitative-oriented probability concepts will be introduced. In this chapter, we first introduce the concept of a random variable and characterize the probability distributions of a random variable and functions of a random variable by the cumulative distribution function, the probability mass function or probability density function, the moment generating function and the characteristic function, respectively. We also introduce a class of moments and discuss their relationships with a probability distribution. This chapter focuses on univariate distributions.

To select an optimal solution from the Pareto frontier based on decision-maker preference or responses priority may not be the best practice and may lead to unexpected results in practice due to the variability that is inherent to some optimal solutions. The assessment of optimal solutions reproducibility has been ignored so far, though this information is critical for the decision-maker in the optimal solution selection process. This chapter explores the Quality of Prediction metric usefulness to help him/her in selecting a solution for multiresponse problems. Results from two case studies show that quality of prediction value cannot be ignored.

This paper studies variance estimators of cross-validation estimators of the generalization error. Three estimators are discussed, and their performance is evaluated in a variety of data models and data sizes. It is shown that the standard error associated with the moment approximation estimator is smaller than that associated with the other two. The effect of training and test set size on these estimators is discussed.

The following sections are included:

• PROBABILITY
• EXPECTATIONS
• DISTRIBUTIONS
• STATISTICAL ESTIMATION
• STATISTICAL TESTING
• DATA TYPES
• PROBLEM SET
• FURTHER RECOMMENDED READINGS