Trivariate Distribution 3D Interactive Calculator

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Instructions

• Use the Distribution type section to select what distributions you would like to be displayed
• Use the Variable Settings section to input the distribution parameters and correlation coefficient
• Use the Control section to input appropriate bivariate limits for X, Y and Z variables
• Use the Graph Settings sections to indicate what type of Marginal Distribution and Joint Bivariate Distribution to view. You can select to view either the Marginal functions of each variable, the Conditional distributions at the limits of variables, or the CDF functions for the Marginal Distribution graph, while the PDF, conditional PDF and the CDF are available for the Joint Bivariate Distribution plot.
• Please note that the "Trivariate Isosurface PDF" may take a long time to generate!
• Once done, click the X button to close the Graph Settings Section. The graph may take a few seconds to update.

Rules

• Normal Distribution: mean can take any value, but the standard deviation must be greater than 0
• Poisson Distribution limits: the value of lambda must be a non-negative number. Also, the X or Y limits must also be non-negative
• Gamma Distribution: both the shape (k) and the scale (θ) values must be greater than 0. Also, the X or Y limits must also be non-negative
• Chi-Square Distribution: the number of degrees of freedom must be a natural number. Also, the X or Y limits must also be non-negative
• Student's t-distribution: the number of degrees of freedom must be a positive number
• F-distribution: the values for the degrees of freedom D1 and D2 must be positive integers. Also, the X or Y limits must also be non-negative
• Beta Distribution: the values for α and β must be positive numbers. Also, the limits must be within the 0 to 1 range
• Weibull Distribution: the values for the shape (k) and scale (λ) must be greater than 0. Also, the X or Y limits must also be non-negative
• Pareto distribution: the values for the shape (α) and scale (Xm or Ym or Zm) must be greater than 0. Also, the X or Y limits must also be non-negative
• Logistic distribution: while the value for the location (μ) may be any real number, the value for s must be greater than 0
• Log-normal distribution: μ must be a non-negative value and σ must be breater than 0. Also, the X or Y limits must also be non-negative
• Gumbel distribution: while the value for the location (μ) may be any real number, the value for scale (β) must be greater than 0
• Uniform distribution: while the values for both a and b can be any real number, b must be greater than a. Also, the limits for X or Y must be no less than a-2 and no greater than b+2
• Birthday distribution: the value for days and sample must be a positive integer. Also, The limits for X or Y must be non-negative
• U-Quadratic distribution: while the values for a and b can be any real number, b must be greater than a
• Arcsine distribution: the X or Y limits must be between 0 and 1
• Semicircle distribution: the value for the radius (R) must be greater than 0
• Max Distance Walked distribution: the value for N must be a positive integer. Also, the X or Y limits must be non-negative
• Final Position on a Walk distribution: the value for N must be a positive integer. Also, the X or Y limits must be non-negative
• Cauchy distribution: the value for scale (γ) must be a positive number. Also, the X or Y limits must be non-negative
• Hyperbolic Secant distribution: while the value for the location may be any real number, the value for scale must be greater than 0
• Irwin-Hall distribution: the value for N must be a positive integer. Also, the X or Y limits must be non-negative
• Laplace distribution: while the value for the location (μ) may be any real number, the value for scale (b) must be greater than 0
• Benford-Mantissa distribution: the value for b must be greater than 2. Also, the X or Y limits must be non-negative
• Exponential-Logarithmic distribution: the value for p must be greater than 0 but less than 1, while the value for β must be greater than 0. Also, the X or Y limits must be non-negative
• Beta Prime distribution: the values for α and β must be positive numbers. Also, the X or Y limits must be non-negative
• Zeta distribution: the value for s must be an integer greater than 1. Also, the X or Y limits must be non-negative
• Log Logistic distribution: the values for α and β must be positive numbers. Also, the X or Y limits must be non-negative
• Maxwell–Boltzmann distribution: the value for a must be greater than 0. Also, the X or Y limits must be non-negative
• Logarithmic distribution: the value for p must be greater than 0 but less than 1. Also, the X or Y limits must be non-negative
• Binomial distribution: the value for Prob must be greater than 0 but less than 1, while the value for N must be a positive integer. Also, the X or Y limits must be non-negative
• Negative Binomial distribution: the value for Prob must be greater than 0 but less than 1, while the value for K must be a positive integer. Also, the X or Y limits must be non-negative
• Hypergeometric distribution: the value for N (population size) must be a positive integer, while the values for k and n must be positive integers no greater than N. Also, the X or Y limits must be non-negative
• Polya: the value for r (number of successes) must be a positive integer, while the values for p must be between 0 and 1. Also, the X or Y limits must be non-negative
• Finite Order distribution: the value for m (population size) must be a positive integer, the value for n must be a positive integer no greater than m, and the value for k must be a positive integer no greater than n. Also, the X or Y limits must be non-negative
• Matching Hats distribution: the value for the number of hats must be a positive integer. Also, the X or Y limits must be non-negative
• Triangular distribution: while all of the parameters can be any real number, Right must be greater than Left, while Middle must be in between Left and Right.
• Coupon Collector distribution: both m and k must be positive integers, but k must be no greater than m. Also, the X or Y limits must be non-negative
• Benford's Digit distribution: the value for b must be greater than 1. Also, the X or Y limits must be non-negative
• Beta Binomial distribution: the value for n must be a positive integer, while a and b must be positive real numbers. Also, the X or Y limits must be non-negative
• Beta Negative Binomial distribution: the value for k must be a positive integer, the value for a must be greater than 2 while b must be a positive real number. Also, the X or Y limits must be non-negative and greater than k

Distribution type
Distribution X	Arcsine Benford's Digit Benford-Mantissa Beta Beta Binomial Beta Negative Binomial Beta Prime Binomial Birthday Cauchy Chi-Square Coupon Collector Exponential-Logarithmic F-distribution Final Position on a Walk Finite Order Gamma Gumbel Hyperbolic Secant Hypergeometric Irwin-Hall Laplace Logarithmic Logistic Log Logistic Log-normal Matching Hats Max Distance Walked Maxwell-Boltzmann Negative Binomial Normal Pareto Poisson Semicircle Student's t Triangular Uniform U-Quadratic Weibull Zeta
Distribution Y	Arcsine Benford's Digit Benford-Mantissa Beta Beta Binomial Beta Negative Binomial Beta Prime Binomial Birthday Cauchy Chi-Square Coupon Collector Exponential-Logarithmic F-distribution Final Position on a Walk Finite Order Gamma Gumbel Hyperbolic Secant Hypergeometric Irwin-Hall Laplace Logarithmic Logistic Log Logistic Log-normal Matching Hats Max Distance Walked Maxwell-Boltzmann Negative Binomial Normal Pareto Poisson Semicircle Student's t Triangular Uniform U-Quadratic Weibull Zeta
Distribution Z	Arcsine Benford's Digit Benford-Mantissa Beta Beta Binomial Beta Negative Binomial Beta Prime Binomial Birthday Cauchy Chi-Square Coupon Collector Exponential-Logarithmic F-distribution Final Position on a Walk Finite Order Gamma Gumbel Hyperbolic Secant Hypergeometric Irwin-Hall Laplace Logarithmic Logistic Log Logistic Log-normal Matching Hats Max Distance Walked Maxwell-Boltzmann Negative Binomial Normal Pareto Poisson Semicircle Student's t Triangular Uniform U-Quadratic Weibull Zeta

Variable Settings
ρXY = 0.5	ρXZ = 0.5	ρYZ = 0.5
μX = 0	μY = 0	μZ = 0
σX = 1	σY = 1	σZ = 1
N/A	N/A	N/A
N/A	N/A	N/A

Controls

-4 < X < 4

-4 < Y < 4

-4 < Z < 4

Marginal Distribution Settings
Marginal of X	Marginal of Y	Marginal of Z
Bivariate Conditional of X given Y given Z given Y = Ymin Y = Ymax Z = Zmin Z = Zmax
Trivariate Conditional of X given Y given Z given Y = Ymin Y = Ymax ∩ Z = Zmin Z = Zmax
CDF of X	CDF of Y	CDF of Z
Joint Bivariate Distribution
Bivariate XY PDF	Bivariate XZ PDF	Bivariate YZ PDF
Bivariate XY CDF	Bivariate XZ CDF	Bivariate YZ CDF
Trivariate Conditional of XY|Z = Z XZ|Y = Y YZ|X = X min max
Joint Trivariate Distribution
Trivariate Point Cloud PDF	Trivariate Isosurface PDF	Trivariate CDF