Statistics with Maxima

Edwin (Ted) Woollett


Edwin (Ted) Woollett Maxima by Example Economic Analysis with Maxima Computational Physics with Maxima or R

Statistics with Maxima, Ch. 0, Probability

Chapter 0 Topics

  1. Probability in General
  2. Rules of Probability
  3. Conditional Probability Examples
  4. Empirical Probability
  5. Subjective Probability
  6. Bayes' Theorem in Particle Physics
  7. Bayes' Theorem in Epidemiology
  1. --Stat00-Probability.wxmx : A wxMaxima notebook on the concept and use of probability, May 24, 2024
  2. --Stat00-Probability.pdf : An approximate pdf translation of Stat00-Probability-fit.wxmx, an edited version created to allow
    "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F,
    25 pages, Nov. 28, 2024

Statistics with Maxima, Ch. 1, The Discrete Geometric (p) Distribution

Chapter 1 Topics

  1. Discrete Distributions Defined
  2. What Is a Discrete Random Variable?
  3. Mean and Variance of a Discrete Data Set
  4. The Discrete Geometric (p) Distribution
  5. pdf_geometric (k, p)
  6. cdf_geometric (k, p)
  7. geomCalc (k, p)
  8. mean_geometric (k, p)
  9. var_geometric (k, p)
  10. std_geometric (k, p)
  11. quantile_geometric (q, p)
  12. random_geometric (p), random_geometric (p, n)
  13. discrete_freq (data)
  14. Real Life Examples of Use of the Geometric Distribution
  1. --Stat01-Geometric.wxmx : A wxMaxima notebook on the Discrete Geometric (p) Distribution, April 1, 2024
  2. --Stat01-Geometric.pdf : An approximate pdf translation of Stat01-Geometric-fit.wxmx, an edited version created to allow
    "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F,
    27 pages, April 1, 2024

Statistics with Maxima, Ch. 2, The Discrete Binomial (n, p) Distribution

Chapter 2 Topics

  1. Discrete Distributions Defined
  2. What Is a Discrete Random Variable?
  3. Mean and Variance of a Discrete Data Set
  4. The Discrete Binomial (n, p) Distribution
  5. pdf_binomial(x, n, p)
  6. mean_binomial (n, p)
  7. var_binomial (n, p)
  8. std_binomial (n, p)
  9. cdf_binomial (x, n, p)
  10. quantile_binomial (q, n, p)
  11. binomialCalc (x, n, p)
  12. confidence (q, m, s)
  13. Real Life Examples of Use of the Binomial Distribution
  14. Number of Missiles to Launch for Even Chance of Penetration of Defenses
  15. random_binomial (n, p), random_binomial (n, p, m)
  16. discrete_freq (data)
  1. --Stat02-Binomial.wxmx : A wxMaxima notebook on the Discrete Binomial(n, p) Distribution, April 10, 2024
  2. --Stat02-Binomial.pdf : An approximate pdf translation of Stat02-Binomial-fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 44 pages, April 10, 2024

Statistics with Maxima, Ch. 3, The Discrete Poisson (λ) Distribution

Chapter 3 Topics

  1. Discrete Distributions Defined
  2. What Is a Discrete Random Variable?
  3. Mean and Variance of a Discrete Data Set
  4. The Discrete Poisson (λ) Distribution
  5. pdf_poisson (n, λ), mean_poisson (λ)
  6. std_poisson(λ), cdf_poisson (n, λ)
  7. quantile_poisson (q, λ)
  8. poissonCalc (n, λ)
  9. random_poisson (λ), random_poisson (λ, n)
  10. discrete_freq (data)
  11. Real Life Examples of Use of the Poisson Distribution
  1. --Stat03-Poisson.wxmx : A wxMaxima notebook on the Discrete Poisson (λ) Distribution, April 19, 2024
  2. --Stat03-Poisson.pdf : An approximate pdf translation of Stat03-Poisson-fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 32 pages, April 19, 2024
Statistics with Maxima, Ch. 4, The Normal (Gaussian) Distribution

Updated June 14, 2024

Chapter 4 Topics

  1. The Normal (Gaussian) Distribution
  2. The 68%, 95%, 99.7% Rule
  3. mean (data), std (data), fracData (data, a, b)
  4. pdf_normal (x, μ, σ ), cdf_normal (x1, μ, σ )
  5. quantile_normal (q, μ, σ), confidence (q, m, s)
  6. mean_normal (m,s), var_normal (m,s), std_normal (m,s)
  7. random_normal (m, s), random_normal (m, s, n)
  8. Real Life Examples of the Normal Distribution
  9. Statistical Significance of a Certain σ in Physics
  1. --Stat04-Normal.wxmx : A wxMaxima notebook on the Normal (μ, σ) Distribution, June 14, 2024
  2. --Stat04-Normal.pdf : An approximate pdf translation of Stat04-Normal-fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 30 pages, June 14, 2024
Statistics with Maxima, Ch. 5, Error Analysis Introduction

Chapter 5 Topics

  1. Basic Concepts in Error Analysis
  2. Spring-loaded Projectile Launcher Experiment
  3. Precision and Accuracy Defined
  4. 20% of measurements incorrectly logged example
  5. Rules of Thumb for Precision
  6. Achieving Accurate Measurements
  7. Measurement Errors and the Central Limit Theorem
  8. Why Errors are Gaussian
  9. Expectation E(F) and Variance V(F) Defined
  10. Justification of the Central Limit Theorem
  1. --Uncertainties01.wxmx : A wxMaxima notebook with an introduction to error analysis concepts, June 3, 2024
  2. --Uncertainties01.pdf : An approximate pdf translation of Uncertainties01-fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture almost all the content; not perfect but is searchable using Ctrl-F, 20 pages, June 3, 2024
Statistics with Maxima, Ch. 6A, Uncertainties

Chapter 6A Topics

  1. What is Error?
  2. Truth? What is Truth?
  3. Uncertainty of a Measuring Device: Rule of Thumb
  4. Sample and Parent Distribution
  5. Standard Error of the Mean σE, SDOM, Standard Error
  1. --Uncertainties02A.wxmx : A wxMaxima notebook with a discussion of uncertainty concepts, July 19, 2024
  2. --Uncertainties02A.pdf : An approximate pdf translation of Uncertainties02A-fit.wxmx, an edited version created to allow "print to pdf" in Windows 11 to capture almost all the content; not perfect but is searchable using Ctrl-F, 15 pages, July 19, 2024
Statistics with Maxima, Ch. 6B, Uncertainties, Contd.

Chapter 6B Topics

  1. The Standard Error of the Mean
  2. The Error in the Error
  3. Rounding and Significant Figures
  4. Confidence Intervals
  5. random_normal (μ, σ), random_normal (μ, σ, n)
  6. Comparisons: Experiment vs. Accepted Value
  1. --Uncertainties02B.wxmx : A wxMaxima notebook with a discussion of uncertainty concepts, July 30, 2024
  2. --Uncertainties02B.pdf : An approximate pdf translation of Uncertainties02B-fit.wxmx, an edited version created to allow "print to pdf" in Windows 11 to capture almost all the content; not perfect but is searchable using Ctrl-F, 20 pages, July 30, 2024
Statistics with Maxima, Ch. 7, Uncertainties, Contd.

Chapter 7 Topics

  1. Averaging Weighted Measurements
  2. Error Propagation in a single variable function
  3. Covariance
  4. Correlation
  5. Error Propagation in a function of two or more variables
  1. --Uncertainties03.wxmx : A wxMaxima notebook with a discussion of uncertainty concepts, Aug. 20, 2024
  2. --Uncertainties03.pdf : An approximate pdf translation of Uncertainties03-fit.wxmx, an edited version created to allow "print to pdf" in Windows 11 to capture almost all the content; not perfect but is searchable using Ctrl-F, 15 pages, Aug. 20, 2024
Statistics with Maxima, Ch. 8, Least Squares Fits

Chapter 8 Topics

  1. Error Bars
  2. Linear Correlation Coefficient r
  3. lsquares_estimates
  4. linear_regression
  5. Residual Analysis
  6. Two Parameter Ordinary Least Squares (OLS) Fit
  7. Use of Χ² Value To Evaluate a Fit of Data
  8. One Parameter Ordinary Least Squares (OLS) Fit
  9. Two Parameter Weighted Least Squares (WLS) Fit
  10. One Parameter Weighted Least Squares (WLS) Fit
  1. --LeastSquares01.wxmx : A wxMaxima notebook with a discussion of least squares fits with examples, Nov. 27, 2024
  2. --LeastSquares01.pdf : An approximate pdf translation of LeastSquares01fit.wxmx, an edited version created to allow "print to pdf" in Windows 11 to capture almost all the content; not perfect but is searchable using Ctrl-F, 63 pages, Nov. 27, 2024