Formulas
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* [http://en.wikipedia.org/wiki/Student's_t_distribution Noncentral Student's T to Normal Transformation]: <math> Z=\lim_{\nu\to\infty}T </math> | * [http://en.wikipedia.org/wiki/Student's_t_distribution Noncentral Student's T to Normal Transformation]: <math> Z=\lim_{\nu\to\infty}T </math> | ||
* [http://socr.ucla.edu/htmls/dist/StudentT_Distribution.html Noncentral Student's T to Student's T Transformation]: <math> \mu = 0 \ </math> | * [http://socr.ucla.edu/htmls/dist/StudentT_Distribution.html Noncentral Student's T to Student's T Transformation]: <math> \mu = 0 \ </math> | ||
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* [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Standard Uniform to Pareto Transformation]: <math> \lambda X ^{-1/K} \ </math> | * [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Standard Uniform to Pareto Transformation]: <math> \lambda X ^{-1/K} \ </math> | ||
* [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Standard Uniform to Benford Transformation]: <math> 10^X \ </math> | * [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Standard Uniform to Benford Transformation]: <math> 10^X \ </math> | ||
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* [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Standard Uniform to Logistic Exponential Transformation]: <math> \frac{log[1+(\frac{X}{1-X})^{1/K}]}{\lambda} </math> | * [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Standard Uniform to Logistic Exponential Transformation]: <math> \frac{log[1+(\frac{X}{1-X})^{1/K}]}{\lambda} </math> | ||
* [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Standard Uniform to Beta Transformation]: If X has a standard uniform distribution, <math> Y = 1 - X^{1/n} \ </math> has a beta distribution | * [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Standard Uniform to Beta Transformation]: If X has a standard uniform distribution, <math> Y = 1 - X^{1/n} \ </math> has a beta distribution | ||
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* [http://en.wikipedia.org/wiki/Beta_distribution Beta to Standard Uniform Transformation]: <math> \beta = \gamma = 1 </math> | * [http://en.wikipedia.org/wiki/Beta_distribution Beta to Standard Uniform Transformation]: <math> \beta = \gamma = 1 </math> | ||
* [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Continuous Uniform to Standard Uniform Transformation]: <math> a = 0, b = 1 \ </math> | * [http://socr.ucla.edu/htmls/dist/ContinuousUniform_Distribution.html Continuous Uniform to Standard Uniform Transformation]: <math> a = 0, b = 1 \ </math> | ||
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* [http://socr.ucla.edu/htmls/dist/Pareto_Distribution.html Pareto to Exponential]: <math> log(X/\lambda) \ </math> | * [http://socr.ucla.edu/htmls/dist/Pareto_Distribution.html Pareto to Exponential]: <math> log(X/\lambda) \ </math> | ||
* [http://socr.ucla.edu/htmls/dist/LogisticExponential_Distribution.html Logistic Exponential to Exponential]: <math> \beta = 1 \ </math> | * [http://socr.ucla.edu/htmls/dist/LogisticExponential_Distribution.html Logistic Exponential to Exponential]: <math> \beta = 1 \ </math> | ||
* [http://socr.ucla.edu/htmls/dist/ZipfMandelbrot_Distribution.html Zipf to Discrete Uniform]: <math> a = 0, a = 1, b = n \ </math> | * [http://socr.ucla.edu/htmls/dist/ZipfMandelbrot_Distribution.html Zipf to Discrete Uniform]: <math> a = 0, a = 1, b = n \ </math> | ||
* [http://socr.ucla.edu/htmls/dist/DiscreteUniform_Distribution.html Discrete Uniform to Rectangular]: <math> a = 0, b = n \ </math> | * [http://socr.ucla.edu/htmls/dist/DiscreteUniform_Distribution.html Discrete Uniform to Rectangular]: <math> a = 0, b = n \ </math> | ||
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* [http://socr.ucla.edu/htmls/dist/Poisson_Distribution.html Poisson to Normal]: <math> \sigma ^2 = \mu , \mu \to \infty </math> | * [http://socr.ucla.edu/htmls/dist/Poisson_Distribution.html Poisson to Normal]: <math> \sigma ^2 = \mu , \mu \to \infty </math> | ||
* [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial to Poisson]: <math> \mu = np, \mu \to \infty </math> | * [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial to Poisson]: <math> \mu = np, \mu \to \infty </math> | ||
- | + | * [http://en.wikipedia.org/wiki/Gamma_distribution Gamma to Inverted Gamma]: <math> \frac{1}{X} </math> | |
+ | * [http://socr.ucla.edu/htmls/dist/FisherTippett_Distribution.html Fisher-Tippett to Gumbel]: <math> \mu = 0, \beta = 1 \ </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/HyperGeometric_Distribution.html Hypergeometric to Binomial]: <math> p = \frac{n_1}{n_3}, n = n_2, n_3, n \to \infty \ </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/LogNormal_Distribution.html Log-Normal to Normal]: <math> log(X) \ </math> | ||
+ | * [http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Normal_Prob Normal to Log-Normal]: <math>e^X \ </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/LogNormal_Distribution.html Log-Normal to Gibrat's]: <math> \mu = 0, x = 1 \ </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/Cauchy_Distribution.html Cauchy to Standard Cauchy]: <math> \gamma = 1, x_0 = 0 \ </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/Cauchy_Distribution.html Standard Cauchy to Cauchy]: <math> x_0 + \gamma X \ </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/HyperbolicSecant_Distribution.html Standard Cauchy to Hyperbolic Secant]: <math> \frac{log|x|}{\pi} \ </math> | ||
<hr> | <hr> |
Revision as of 12:38, 1 December 2008
Probability Density Functions (PDFs)
- Standard Normal PDF:
- General Normal PDF:
- Chi-Square PDF:
- Gamma PDF:
- Beta PDF:
- Student's T PDF:
- Poisson PDF:
- Chi PDF:
- Cauchy PDF:
- Exponential PDF:
- F Distribution PDF:
- Bernoulli PMF:
- Binomial PMF:
- Negative Binomial PMF:
- Geometric PMF:
- Erlang PDF:
- Laplace PDF:
- Continuous Uniform PDF:
- Discrete Uniform PMF:
- Logarithmic PDF:
- Logistic PDF:
- Logistic-Exponential PDF:
- Power Function PDF:
- Benford's Law:
- Pareto PDF:
- Non-Central Student T PDF:
- ArcSine PDF:
- Circle PDF:
- U-Quadratic PDF:
- Standard Uniform PDF:
- Zipf:
- Inverse Gamma:
- Fisher-Tippett:
where - Gumbel:
- HyperGeometric:
- Log-Normal:
- Gilbrats:
- Hyperbolic Secant:
- Gompertz:
- Standard Cauchy:
Transformations
- Standard Normal to General Normal Transformation:
- General Normal to Standard Normal Transformation:
- Standard Normal to Chi Transformation:
- Standard Normal to Chi-Square Transformation:
- Gamma to General Normal Transformation:
- Gamma to Exponential Transformation: The special case of is equivalent to exponential Exp(λ).
- Gamma to Beta Transformation: .
- Student's T to Standard Normal Transformation:
- Student's T to Cauchy Transformation:
- Cauchy to General Cauchy Transformation:
- General Cauchy to Cauchy Transformation:
- Fisher's F to Student's T:
- Student's T to Fisher's F: X2
- Bernoulli to Binomial Transformation: (iid)
- Binomial to Bernoulli Transformation:
- Binomial to General Normal Transformation:
- Binomial to Poisson Transformation:
- Negative Binomial to Geometric Transformation:
- Erlang to Exponential Transformation:
- Erlang to Chi-Square Transformation:
- Laplace to Exponential Transformation:
- Exponential to Laplace Transformation:
- Beta to Arcsine Transformation:
- Noncentral Student's T to Normal Transformation:
- Noncentral Student's T to Student's T Transformation:
- Standard Uniform to Pareto Transformation:
- Standard Uniform to Benford Transformation:
- Standard Uniform to Exponential Transformation:
- Standard Uniform to Log Logistic Transformation:
- Standard Uniform to Standard Triangular Transformation: X1 − X2
- Standard Uniform to Logistic Exponential Transformation:
- Standard Uniform to Beta Transformation: If X has a standard uniform distribution, has a beta distribution
- Beta to Standard Uniform Transformation: β = γ = 1
- Continuous Uniform to Standard Uniform Transformation:
- Pareto to Exponential:
- Logistic Exponential to Exponential:
- Zipf to Discrete Uniform:
- Discrete Uniform to Rectangular:
- Poisson to Normal:
- Binomial to Poisson:
- Gamma to Inverted Gamma:
- Fisher-Tippett to Gumbel:
- Hypergeometric to Binomial:
- Log-Normal to Normal:
- Normal to Log-Normal:
- Log-Normal to Gibrat's:
- Cauchy to Standard Cauchy:
- Standard Cauchy to Cauchy:
- Standard Cauchy to Hyperbolic Secant:
- SOCR Home page: http://www.socr.ucla.edu
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