# Distributome Resource Database
#
# http://Distributome.org
# http://Distributome.org/jars/implementedDistributome.txt
# current Node format is "id; name; type,type; formula_id; url; keywords; references"
# current Edge format is "label; name; type,type; formula_id; from_nodeId; to_nodeId; references"
#
# Node (distribution) Types will be (full-name & abbreviation):
# 0 No Type Given
# 1 Convolution (Conv)
# 2 Memoryless (Mless)
# 3 Inverse (Inv)
# 4 Linear Combination (LinComb)
# 5 Minimum (min)
# 6 Maximum (max)
# 7 Product (Prod)
# 8 Conditional Residual (CondRes)
# 9 Scaling (Scale)
# 10 Simulate (Sim)
# 11 Variate Generation(VGen)
#
# Edge Types (directional distribution relations) will be:
# 0 No Type Given
# 1 Special Case (SC)
# 2 Transform (T)
# 3 Limiting (Lim)
# 4 Bayesian (Bayes)
#Version Info
[otherInfo]
version = 1.0
# Node syntax format is "id; name; type,type; formula_id; url; keywords; references"
[nodes]
url_prefix = http://socr.ucla.edu/htmls/dist/
Node = 1; Standard Normal; 0; 1; Normal_Distribution.html; continuous, symmetric, infinite, exponential; 1, 2, 3
Node = 2; General Normal; 1,4,9;2; Normal_Distribution.html; continuous, symmetric, infinite, exponential; 1, 2, 3, 4
Node = 3; Chi; 0; 3; Chi_Distribution.html; continuous, nonsymmetric, positive; 2, 3
Node = 4; Chi-Square; 1; 4; ChiSquare_Distribution.html; continuous, nonsymmetric, positive; 2, 3, 4
Node = 5; Gamma; 1,9;5; Gamma_Distribution.html; continuous, nonsymmetric, positive, exponential; 2, 3, 6
Node = 6; Beta; 0;6; Beta_Distribution.html; continuous, nonsymmetric, finite; 2, 3, 5, 6
Node = 7; Student's T; 0; 7; StudentT_Distribution.html; continuous, symmetric, infinite; 2, 3
Node = 8; Poisson; 1; 8 ; Poisson_Distribution.html; discrete, nonsymmetric, positive; 2, 3
Node = 9; General Cauchy; 1,3,9,10; 9; GeneralCauchy_Distribution.html; continuous, symmetric, infinite; 2, 3
Node = 10; Cauchy; 3,9,10; 10; Cauchy_Distribution.html; continuous, symmetric, infinite; 2, 3
Node = 11; Exponential; 2,5,8,9,10; 11; Exponential_Distribution.html; continuous, nonsymmetric, positive, exponential; 2, 3
Node = 12; Fisher's F; 3; 12 ; Fisher_Distribution.html; continuous, nonsymmetric, infinite ; 2, 3, 5
Node = 13; Bernoulli; 5,6,7; 13; Bernoulli_Distribution.html; discrete, nonsymmetric, positive; 2, 3
Node = 14; Binomial; 1; 14; Binomial_Distribution.html; discrete, nonsymmetric, positive; 2, 3
Node = 15; Negative Binomial; 1; 15 ; NegativeBinomial_Distribution.html; discrete, nonsymmetric, positive; 2, 3
Node = 16; Geometric; 2,5,11; 16 ; Geometric_Distribution.html; discrete, nonsymmetric, positive; 2, 3
Node = 17; Erlang; 9; 17 ; Erlang_Distribution.html; continous, positive, nonsymmetric, exponential; 2, 3
Node = 18; Laplace; 11; 18; Laplace_Distribution.html; continuous, symmetric, infinite, exponential; 2, 3
Node = 19; Continuous Uniform; 8,11;19; ContinuousUniform_Distribution.html; continuous, symmetric, positive, finite; 2, 3
Node = 20; Discrete Uniform; 8,11;20; DiscreteUniform_Distribution.html; discrete, symmetric, positive, finite; 2, 3
Node = 21; Logarithmic-Series; 0;21; LogarithmicSeries_Distribution.html; discrete, nonsymmetric, infinite; 2, 7
Node = 22; Logistic; 9, 11;22; Logistic_Distribution.html; continuous, symmetric, infinite; 2, 3
Node = 23; Logistic-Exponential; 9;23; LogisticExponential_Distribution.html; continuous, infinite; 2, 8
Node = 24; Power-Function; 6,9;24; PowerFunction_Distribution.html; continuous, nonsymmetric, finite; 2, 12
Node = 25; Benford's Law; 0;25; Benford_Distribution.html; continuous, nonsymmetrical, infinite; 2, 10
Node = 26; Pareto; 5; 26;Pareto_Distribution.html; continuous, nonsymmetric, finite; 2, 3
Node = 27; Student's T Non-Central; 0; 27;StudentT_Distribution.html; continuous, symmetric, infinite; 2
Node = 28; ArcSine; 0; 28;ArcSine_Distribution.html; continuous, symmetric, finite; 2,3
Node = 29; Half Circle; 0; 29;Circle_Distribution.html; continuous, symmetric, finite; 0
Node = 30; U-Quadratic; 0; 30;UQuadratic_Distribution.html; continuous, symmetric, finite; 0
Node = 31; Standard Uniform; 0; 31; ContinuousUniform_Distribution.html; continuous, symmetric, finite; 2, 3
Node = 32; Zipf; 0; 32; ZipfMandelbrot_Distribution.html; continuous, nonsymmetric, finite; 3
Node = 33; Inverted Gamma; 0; 33; InverseGamma_Distribution.html; continuous, nonsymmetric, finite, positive; 2
Node = 34; Fisher-Tippett; 0; 34; FisherTippett_Distribution.html; continuous, nonsymmetric, finite, positive; 0
Node = 35; Gumbel; 0; 35; Gumbel_Distribution.html; continuous, nonsymmetric, finite, positive; 0
Node = 36; Hypergeometric; 0; 36; HyperGeometric_Distribution.html; discrete, nonsymmetric, finite, positive; 2,3
Node = 37; Log-Normal; 7; 37; LogNormal_Distribution.html; continuous, nonsymmetric, infinite, positive; 2, 3
Node = 38; Gibrat's; 0; 38; Gilbrats_Distribution.html; continuous, nonsymmetric, finite, positive; 0
Node = 39; Hyperbolic Secant; 10; 39; HyperbolicSecant_Distribution.html; continuous, symmetric, infinite, positive; 2
Node = 40; Gompertz; 0; 40; Gompertz_Distribution.html; continuous, nonsymmetric, finite, positive; 0
Node = 41; Standard Cauchy; 3,9,10; 41; Cauchy_Distribution.html; continuous; symmetric, finite; 2, 3
# Edge syntax format is "label; name; type,type; formula_id; from_nodeId; to_nodeId; references"
[edges]
Edge = 1; Standard Normal to General Normal Transformation; 1,2; 1001; 1; 2; 1, 2, 3
Edge = 2; General Normal to Standard Normal Transformation; 2; 1002; 2; 1; 1, 2, 3
Edge = 3; Standard Normal to Chi Transformation; 2; 1003; 1; 3; 2, 3
Edge = 4; Standard Normal to Chi-Square Transformation; 2; 1004; 1; 4; 2, 3, 4
Edge = 5; Gamma to Normal Transformation; 3; 1005; 5; 2; 2, 3
Edge = 6; Gamma to Exponential Transformation; 1; 1006; 5; 11; 2, 3
Edge = 7; Gamma to Beta Transformation; 2; 1007; 5; 6; 2, 3, 6
Edge = 8; Student's T to Standard Normal Transformation; 3; 1008; 7; 1; 2, 3
Edge = 9; Student's T to Cauchy Transformation; 1; 1009; 7; 10; 2, 3
Edge = 10; Cauchy to General Cauchy Transformation; 1,2; 1010; 10; 9; 2, 3
Edge = 11; General Cauchy to Cauchy Transformation; 2; 1011; 9; 10; 2, 3
Edge = 12; Fisher's F to Student's T Transformation; 2; 1012; 12; 7; 2, 3
Edge = 13; Student's T to Fisher's F Transformation; 2; 1013; 7; 12; 2, 3
Edge = 14; Bernoulli to Binomial Transformation; 1,2; 1014; 13; 14; 2, 3
Edge = 15; Binomial to Bernoulli Transformation; 1,2; 1015; 14; 13; 2, 3
Edge = 16; Binomial to General Normal Transformation; 3; 1016; 14; 2; 2, 3
Edge = 17; Binomial to Poisson Transformation; 3; 1017; 14; 2; 2, 3
Edge = 18; Negative Binomial to Geometric Transformation; 1; 1018; 15; 16; 2, 3
Edge = 19; Erlang to Exponential Transformation; 1; 1019; 17; 11; 2, 3
Edge = 20; Erlang to Chi-Squared Transformation; 1; 1020; 17; 4; 2 ,3
Edge = 21; Laplace to Exponential Transformation; 1, 2; 1021; 18; 11; 2, 3
Edge = 22; Exponential to Laplace Transformation; 1; 1022; 11; 18; 2, 3
Edge = 23; Beta to Arcsine Transformation; 0; 1023; 6; 28; 2, 3
Edge = 24; Noncentral Student's T to Normal; 3; 1024; 27; 2; 2,3
Edge = 25; Noncentral Student's T to Student's T; 1; 1025; 27; 7; 2,3
Edge = 26; Pareto to Exponential; 2; 1026; 26; 11; 2,3
Edge = 27; Logistic Exponential to Exponential; 1; 1027; 23; 11; 2, 8
Edge = 28; Standard Uniform to Pareto; 2; 1028; 31; 26; 2
Edge = 29; Standard Uniform to Benford; 2; 1029; 31; 25; 2
Edge = 30; Standard Uniform to Exponential; 2,3; 1030; 31; 11; 2, 3
Edge = 31; Standard Uniform to Logistic Exponential; 2; 1031; 31; 23; 2
Edge = 32; Standard Uniform to Beta; 1; 1032; 31; 6; 2, 3
Edge = 33; Continuous Uniform to Standard Uniform; 1; 1033; 19; 31; 2, 3
Edge = 34; Zipf to Discrete Uniform; 1; 1034; 32; 20; 2
Edge = 35; Poisson to Normal; 3; 1035; 8; 1; 2, 3
Edge = 36; Binomial to Poisson; 3; 1036; 14; 8; 2, 3
Edge = 37; Gamma to Inverted Gamma; 2; 1037; 5; 33; 2
Edge = 38; Fisher-Tippett to Gumbel; 1; 1038; 34; 35; 0
Edge = 39; Hypergeometric to Binomial; 3; 1039; 36; 14; 2,3
Edge = 40; Log-Normal to Normal; 2; 1040; 37; 2; 2,3
Edge = 41; Normal to Log-Normal; 2; 1041; 2; 37; 2,3
Edge = 42; Log-Normal to Gibrat's; 1; 1042; 37; 38; 0
Edge = 43; Cauchy to Standard Cauchy; 1; 1043; 10; 41; 2,3
Edge = 44; Standard Cauchy to Cauchy; 2; 1044; 41; 10; 2,3
Edge = 45; Standard Cauchy to Hyperbolic Secant; 2; 1045; 41; 39; 2
# Formula syntax format is "id; density; formula;"
[formulas]
density_prefix = http://wiki.stat.ucla.edu/socr/uploads/math/
Formula = 1; 0/c/a/0cab65bf1790276ad1d97ab46a40567f.png; f(x)= {e^{-x^2} \over \sqrt{2 \pi}}
Formula = 2; 9/8/7/987fd149835d1de389765cdf2d03e247.png; f(x)= {e^{{-(x-\mu)^2} \over 2\sigma^2} \over \sqrt{2 \pi\sigma^2}}
Formula = 3; d/7/1/d71a0585ec10d96b0398de15a17647d9.png; \frac{2^{1-k/2}x^{k-1}e^{-x^2/2}}{\Gamma(k/2)}
Formula = 4; b/e/f/bef279b2cb4f25a855b38092b3dc671b.png; \frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}\,
Formula = 5; 2/b/1/2b123f5be4f5c152db65389455d3e2de.png; x^{k-1} \frac{\exp{\left(-x/\theta\right)}}{\Gamma(k)\,\theta^k}\,\!
Formula = 6; 5/8/b/58b0965234c4a32bf55111fe2ad12535.png; \frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\, x^{\alpha-1}(1-x)^{\beta-1}\!
Formula = 7; f/6/d/f6dbd1429a3d5f065980c11ed57254b1.png; \frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{x^2}{\nu} \right)^{-(\frac{\nu+1}{2})}\!
Formula = 8; 9/9/2/9928c50bbeac8192fa2414d10faf1377.png; \frac{e^{-\lambda} \lambda^k}{k!}\!
Formula = 9; a/9/2/a9260c6814d86ac3231f3934db752577.png; \frac{1}{\pi\gamma \left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}
Formula = 10; a/9/2/a9260c6814d86ac3231f3934db752577.png; \frac{1}{\pi\gamma \left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}
Formula = 11; 1/7/6/1764a5aca4ec3b78d60d46a724dcd5ec.png; \lambda e^{-\lambda x},\; x \ge 0
Formula = 12; b/b/b/bbb4079319994e3d46d43ae12510e74b.png; \frac {(\frac {d_1 x}{d_1 x + d_2})^{ d_1/2} ( 1 - \frac {d_1 x} {d_1 x + d2}) ^ {d_2/2}} { xB(d_1/2 , d_2/2) }
Formula = 13; 8/6/7/867103cbcf2d8f2a84e015ae4297df74.png; f(k;p) \begin{cases} \mbox{p if k = 1,} \mbox{1 - p if k = 0,} \mbox{0 otherwise} \end{cases}
Formula = 14; 4/6/f/46faf4c680409bf76d69404e34a678d0.png; \begin{pmatrix} n \\ k \end{pmatrix} p^k (1-p)^{n-k}
Formula = 15; 8/1/f/81f96673ef90b51ab48d3ca77f310ac8.png; \begin{pmatrix} k + r - 1 \\ k \end{pmatrix} p^r(1-p)^k
Formula = 16; a/4/a/a4a4a23832ba0edbdaf9e226c2ac02c1.png;\begin{pmatrix} 1-p \end{pmatrix} ^{k-1}p
Formula = 17; a/0/2/a0244739ba01e615049257a28de4fdd5.png; \frac {\lambda x^{k-1}e^{-\lambda x}} {(k-1)!}
Formula = 18; a/d/3/ad36da6a4fcc7c6f4acd08062ca9fdab.png; \frac {1}{2b} \exp (- \frac{|x-\mu|}{b})
Formula = 19; 8/6/6/8669d896dcbf0134e37cff56ff424f61.png; f(x) = \begin{cases} \frac{1}{b-a} \mbox{ for } a \le x \le b \\ 0 \mbox{ for } x < a \mbox{ or } x > b \end{cases}
Formula = 20; 2/5/7/2579584dc45cf3f73dea42ba8265062e.png; f(x) = \begin{cases} 1/n \mbox{ for } a \le x \le b, \\ 0 \mbox{ otherwise} \end{cases}
Formula = 21; f/2/0/f2061904fabaa091a2a6de94d67ad00d.png; f(k) = \frac{-1}{ln(1-p)} \frac{p^k}{k}
Formula = 22; 5/3/a/53ad61d172e22491bbd974961830ed60.png; f(x;u,s) = \frac{e^{-(x-\mu)/s}} {s(1+e^{-(x-\mu)/s})^2}
Formula = 23; c/0/b/c0bbb7c859640450d9e0f2598a4565c9.png; f(x;\beta) = \frac { \beta e^x(e^x - 1)^{\beta-1}} {(1+(e^x-1)^\beta))^2} \mbox{ }\mbox{ }x, \beta > 0
Formula = 24; c/8/3/c83d7f43422655121c3a3a5c2adb4037.png; f(x) = \frac {\alpha(x-a)^{\alpha-1}} {(b-a)^\alpha}
Formula = 25; e/2/e/e2e118712196bf2670a51e0e59655f6f.png; P(d) = \log_b(d + 1)- \log_b(d) = \log_b(\frac{d + 1}{d})
Formula = 26; 5/d/2/5d2eb18ae43752138f3189ca9f7e7f8e.png; \frac {kx^k_m} {x^{k+1}}
Formula = 27; e/3/7/e37a9ea8dea4ca3d0d7d55f76aaa430b.png; f(t)=\frac{\nu^{\nu/2}e^{-\nu\mu^2/2(t^2+\nu)}} {\sqrt{\pi}\Gamma(\nu/2)2^{(\nu-1)/2}(t^2+\nu)^{(\nu+1)/2}} \times\int\limits_0^\infty x^\nu\exp\left[-\frac{1}{2}\left(x-\frac{\mu t}{\sqrt{t^2+\nu}}\right)^2\right]dx
Formula = 28; 1/4/7/147aa81e110d81ed11d1f3d51169bc78.png; f(x) = \frac{1}{\pi \sqrt{x(1-x)}}
Formula = 29; 4/5/a/45a7876ef35972bf28385be926c52b62.png; f(x)={2\sqrt{r^2 - x^2}\over \pi r^2 }, \forall x \in [-r , r]
Formula = 30; f/f/7/ff76cc91a9caab7bead2efe8e5d9402f.png; \alpha \left ( x - \beta \right )^2
Formula = 31; 8/d/e/8dea828028c02208956348d4f00bb3e3.png; U(0,1) = f(x) = \begin{cases} {1} \mbox{ for } 0 \le x \le 1 \\ 0 \mbox{ for } x < 0 \mbox{ or } x > 1 \end{cases}
Formula = 32; d/9/7/d97d3fd7535620600d05c161b9864817.png; \frac{1/k^s}{H_{N,s}}
Formula = 33; 6/c/1/6c1d1b87912709db4a5adb09e5ed05bb.png; \frac{\beta^\alpha}{\Gamma(\alpha)} x^{-\alpha - 1} \exp \left(\frac{-\beta}{x}\right)
Formula = 34; 5/3/d/53dee9edf9ef4de0fe9f8b9db33c0518.png; \frac{z\,e^{-z}}{\beta}\!
where