Formulas
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* [http://socr.ucla.edu/htmls/dist/HyperbolicSecant_Distribution.html Hyperbolic Secant]:<math>\frac12 \; \operatorname{sech}\!\left(\frac{\pi}{2}\,x\right)\!</math> | * [http://socr.ucla.edu/htmls/dist/HyperbolicSecant_Distribution.html Hyperbolic Secant]:<math>\frac12 \; \operatorname{sech}\!\left(\frac{\pi}{2}\,x\right)\!</math> | ||
* [http://socr.ucla.edu/htmls/dist/Gompertz_Distribution.html Gompertz]: <math>b e^{-bx} e^{-\eta e^{-bx}}\left[1 + \eta\left(1 - e^{-bx}\right)\right]</math> | * [http://socr.ucla.edu/htmls/dist/Gompertz_Distribution.html Gompertz]: <math>b e^{-bx} e^{-\eta e^{-bx}}\left[1 + \eta\left(1 - e^{-bx}\right)\right]</math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/Cauchy_Distribution.html Standard Cauchy]: <math> f(x; 0,1) = \frac{1}{\pi (1 + x^2)}. \!</math> | ||
==Transformations== | ==Transformations== |
Revision as of 12:08, 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:
- SOCR Home page: http://www.socr.ucla.edu
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