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Chapter 2. Statistical Distributions and Functions

Table of Contents

Statistical Distributions Tutorial
Overview of Distributions
Headers and Namespaces
Distributions are Objects
Generic operations common to all distributions are non-member functions
Complements are supported too - and when to use them
Parameters can be calculated
Summary
Worked Examples
Distribution Construction Examples
Student's t Distribution Examples
Calculating confidence intervals on the mean with the Students-t distribution
Testing a sample mean for difference from a "true" mean
Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test
Comparing the means of two samples with the Students-t test
Comparing two paired samples with the Student's t distribution
Chi Squared Distribution Examples
Confidence Intervals on the Standard Deviation
Chi-Square Test for the Standard Deviation
Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation
F Distribution Examples
Binomial Distribution Examples
Binomial Coin-Flipping Example
Binomial Quiz Example
Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution
Estimating Sample Sizes for a Binomial Distribution.
Geometric Distribution Examples
Negative Binomial Distribution Examples
Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution
Estimating Sample Sizes for the Negative Binomial.
Negative Binomial Sales Quota Example.
Negative Binomial Table Printing Example.
Normal Distribution Examples
Some Miscellaneous Examples of the Normal (Gaussian) Distribution
Inverse Chi-Squared Distribution Bayes Example
Non Central Chi Squared Example
Tables of the power function of the chi2 test.
Error Handling Example
Find Location and Scale Examples
Find Location (Mean) Example
Find Scale (Standard Deviation) Example
Find mean and standard deviation example
Comparison with C, R, FORTRAN-style Free Functions
Using the Distributions from Within C#
Random Variates and Distribution Parameters
Discrete Probability Distributions
Statistical Distributions Reference
Non-Member Properties
Distributions
Bernoulli Distribution
Beta Distribution
Binomial Distribution
Cauchy-Lorentz Distribution
Chi Squared Distribution
Exponential Distribution
Extreme Value Distribution
F Distribution
Gamma (and Erlang) Distribution
Geometric Distribution
Hypergeometric Distribution
Inverse Chi Squared Distribution
Inverse Gamma Distribution
Inverse Gaussian (or Inverse Normal) Distribution
Laplace Distribution
Logistic Distribution
Log Normal Distribution
Negative Binomial Distribution
Noncentral Beta Distribution
Noncentral Chi-Squared Distribution
Noncentral F Distribution
Noncentral T Distribution
Normal (Gaussian) Distribution
Pareto Distribution
Poisson Distribution
Rayleigh Distribution
Skew Normal Distribution
Students t Distribution
Triangular Distribution
Uniform Distribution
Weibull Distribution
Distribution Algorithms
Extras/Future Directions

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