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Dataplot Distributions

Types of Probability Functions Dataplot has an extensive library of built-in probability distributions. There are six types of probability functions provided:
  1. Cumulative Distribution Functions (CDF)
  2. Probability Density (or Mass) Functions (PDF)
  3. Percent Point (or inverse CDF) Functions (PPF)
  4. Hazard Functions
  5. Cumulative Hazard Functions
  6. Sparsity Functions (SF)
Probability Plots, PPCC Plots, Goodness of Fit Tests, and Random Numbers In addition to the above probability functions, Dataplot also supports the following:
Tables of Supported Distributions The tables below lists which distributions and functions are available in Dataplot. If the hazard function is listed as yes, then the cumulative hazard function is also supported.

The tables also list the names of any shape parameters. Note that most of the distributions also support location and scale parameters. These are listed as LOC and SCALE in the tables below. In the probability functions (e.g., the PDF), the location and scale parameters are optional (default to 0 and 1) and come after any shape parameters for the distribution. The scale parameter always comes after the location parameter (i.e., you can give a location parameter without a scale parameter, but you cannot give a shape parameter without a location parameter).

Function Names The function name is a 1 to 3 character id combined with CDF, PDF, PPF, SF, HAZ, or CHA. The function will have an X argument (where the function is evaluated) and arguments for any shape, location, or scale parameters.

For example, the functions for the normal distribution are:

  • NORCDF(X,LOC,SCALE)
  • NORPDF(X,LOC,SCALE)
  • NORPPF(P,LOC,SCALE)
  • NORSF(P,LOC,SCALE)
  • NORHAZ(X,LOC,SCALE)
  • NORCHA(X,LOC,SCALE)
MINMAX Command The extreme value distributions (Weibull, EV1, EV2) support versions based on both the minimum and the maximum order statistics. This is specified by entering the command
    SET MINMAX <1/2>
before using these distributions.
Random Numbers are LET Sub-
Commands
Random numbers are LET subcommands as oppossed to functions. For example,
    LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 100
Required parameters are specified via LET commands before generating the random numbers. Location and scale parameters are not used, but can be generated simply. For example,
    LET GAMMA = 2
    LET Y = GAMMA RANDOM NUMBERS FOR I = 1 1 100
    LET LOC = 5
    LET SCALE = 10
    LET Y = LOC + SCALE*Y
Dataplot supports six different uniform random number generators. Random numbers for the other distributions are transformations of uniform random numbers. The desired generator can be set with the command SET RANDOM NUMBER GENERATOR.
Lower and Upper Limits For a few distributions, lower and upper limits are specified rather than location and scale parameters. These are referred to as LOWER and UPPER in the parameter lists.
LIST DISTRIBU for Up-to-Date List The information in this list may become somewhat out of date over time as new distributions are added to Dataplot (basically, the "YES" entries will still be available, but "NO" entries may become "YES" and there will be new entries). For an up-to-date table, enter the command LIST DISTRIBU from within Dataplot or view the file "help/distribu" in the Dataplot directory ("C:\DATAPLOT\HELP\DISTRIBU" on the PC, "/usr/local/lib/dataplot/help/distribu" on Unix).

Dataplot Distributions 9/2002

Symmetric and Continuous Distributions
Symmetric and Continuous Distributions
Name Random
Numbers
Probability
Plot
PPCC
Plot
CDF PDF PPF CHAZ
HAZ
SF Parameters
Uniform YES YES YES YES YES YES YES YES LOWER, UPPER
Normal YES YES N/A YES YES YES YES YES LOC, SCALE
Logistic YES YES N/A YES YES YES NO YES LOC, SCALE
Double
Exponential
YES YES N/A YES YES YES NO YES LOC, SCALE
Double
Weibull
YES YES YES YES YES YES NO NO GAMMA, LOC, SCALE
Double
Gamma
YES YES YES YES YES YES NO NO LOC, SCALE, GAMMA
Cauchy YES YES N/A YES YES YES NO YES LOC, SCALE
Tukey-
Lambda
YES YES YES YES YES YES NO YES LAMBDA, LOC, SCALE
T YES YES YES YES YES YES NO NO NU, LOC, SCALE
Semi-
Circular
YES YES N/A YES YES YES NO NO None
Triangular YES YES YES YES YES YES NO NO C, LOC, SCALE
Von
Mises
NO YES YES YES YES YES NO NO B, LOC
Cosine YES YES N/A YES YES YES NO NO LOC, SCALE
Anglit YES YES N/A YES YES YES NO NO LOC, SCALE
Hyperbolic
Secant
YES YES N/A YES YES YES NO NO LOC, SCALE
Skewed and Continuous Distributions
Skewed and Continuous Distributions
Name Random
Numbers
Probability
Plot
PPCC
Plot
CDF PDF PPF CHAZ
HAZ
SF Parameters
Lognormal YES YES YES YES YES YES YES NO SD, LOC, SCALE
Power
Lognormal
YES YES YES YES YES YES YES NO P, SD, LOC
Power
Normal
YES YES YES YES YES YES YES NO P, LOC, SCALE
Half-
Normal
YES YES N/A YES YES YES NO NO LOC, SCALE
Folded
Normal
YES YES N/A YES YES YES NO NO U, SD
Truncated
Normal
NO YES N/A YES YES YES NO NO A, B, U, SD
Chi-
Square
YES YES YES YES YES YES NO NO NU, LOC, SCALE
Chi NO YES YES YES YES YES NO NO NU, LOC, SCALE
Non-Central
Chi-Square
YES YES N/A YES YES YES NO NO NU, LAMBDA
F YES YES N/A YES YES YES NO NO NU1, NU2, LOC, SCALE
Non-Central
F
YES YES N/A YES NO YES NO NO NU1, NU2, LAMBDA
Doubly
Non-Central F
YES YES N/A YES NO YES NO NO NU1, NU2, LAMBDA1, LAMBDA2
Non-Central
T
NO YES N/A YES YES YES NO NO NU, LAMBDA
Doubly
Non-Central T
NO YES N/A YES NO YES NO NO NU1, NU2, LAMBDA1, LAMBDA2
Beta YES YES YES YES YES YES NO NO ALPHA, BETA, LOWER, UPPER
Non-Central
Beta
NO YES N/A YES NO YES NO NO ALPHA, BETA, LAMBDA
Power
Function
YES YES YES YES YES YES NO NO C, SCALE
Arcsin YES YES N/A YES YES YES NO NO LOC, SCALE
Gamma YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Generalized
Gamma
NO YES N/A YES YES YES NO NO GAMMA, C, LOC, SCALE
Inverted
Gamma
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Log-Gamma YES YES YES YES YES YES NO NO Gamma
Exponential YES YES N/A YES YES YES YES YES None
Truncated
Exponential
NO YES N/A YES YES YES NO NO X0, M, SD
Power
Exponential
YES YES N/A YES YES YES NO NO ALPHA, BETA, LOC
Generalized
Exponential
NO YES N/A YES YES YES NO NO LAMBDA1, LAMBDA12, S
Geometric
Extreme
Exponential
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Weibull
(minimum)
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Weibull
(maximum)
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Exponentiated
Weibull
YES YES YES YES YES YES YES NO GAMMA, THETA, LOC, SCALE
Inverted
Weibull
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
EV1 (Gumbel)
(minimum)
YES YES N/A YES YES YES YES NO LOC, SCALE
EV1 (Gumbel)
(maximum)
YES YES N/A YES YES YES YES NO LOC, SCALE
EV2 (Frechet)
(minimum)
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
EV2 (Frechet)
(minimum)
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Generalized
Extreme
Value
YES YES YES YES YES YES NO NO GAMMA, LOC, SCALE
Gompertz YES YES YES YES YES YES NO NO C, B, LOC, SCALE
Pareto
(first kind)
YES YES YES YES YES YES YES NO GAMMA, LOC
Pareto
(second kind)
NO YES YES YES YES YES NO NO GAMMA, LOC, SCALE
Generalized
Pareto
YES YES YES YES YES YES YES NO GAMMA, SCALE
Alpha YES YES YES YES YES YES YES NO ALPHA, BETA, LOC, SCALE
Inverse
Gaussian
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Wald YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Reciprocal
Inverse Gaussian
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Failure
Time
YES YES YES YES YES YES YES NO GAMMA, LOC, SCALE
Log-
Logistic
YES YES YES YES YES YES NO NO DELTA, LOC, SCALE
Half-
Logistic
YES YES N/A YES YES YES NO NO LOC, SCALE
Generalized
Half-Logistic
NO YES YES YES YES YES NO NO GAMMA. LOC, SCALE
Genaralized
Logistic
NO YES YES YES YES YES NO NO ALPHA, LOC, SCALE
Half-
Cauchy
YES YES N/A YES YES YES NO NO LOC, SCALE
Wrapped-Up
Cauchy
NO YES YES YES YES YES NO NO P, LOC
Folded
Cauchy
NO YES N/A YES YES YES NO NO M, SD
Mielke's
Beta-Kappa
NO YES N/A YES YES YES NO NO K, BETA, THETA, LOC, SCALE
Bradford YES YES YES YES YES YES NO NO BETA, LOC, SCALE
Reciprocal YES YES YES YES YES YES NO NO B, LOC, SCALE
Log
Double
Exponential
YES YES YES YES YES YES NO NO ALPHA, LOC, SCALE
Johnson
SB
YES YES YES YES YES YES NO NO ALPHA1, ALPHA2, LOC, SCALE
Johnson
SU
YES YES YES YES YES YES NO NO ALPHA1, ALPHA2, LOC, SCALE
Two-
Sided
Power
YES YES YES YES YES YES NO NO THETA, N, LOC, SCALE
Mixture
Distributions
Mixture Distributions
Name Random
Numbers
Probability
Plot
PPCC
Plot
CDF PDF PPF CHAZ
HAZ
SF Parameters
Normal
Mixture
YES YES N/A YES YES YES NO NO P, U1, SD1, U2, SD2
Bi-
Weibull
YES YES N/A YES YES YES YES NO SCALE1, GAMMA1, LOC2, SCALE2, GAMMA2
Bivariate/
Multivariate
Bivariate/Multivariate Distributions
Name Random
Numbers
Probability
Plot
PPCC
Plot
CDF PDF PPF CHAZ
HAZ
SF Parameters
Bivariate
Normal
YES N/A N/A YES YES N/A NO N/A P
Discrete Distributions
Discrete Distributions
Name Random
Numbers
Probability
Plot
PPCC
Plot
CDF PDF PPF CHAZ
HAZ
SF Parameters
Binomial YES YES N/A YES YES YES NO NO N, P
Geometric YES YES YES YES YES YES NO NO P
Poisson YES YES YES YES YES YES NO NO LAMBDA
Negative
Binomial
YES YES N/A YES YES YES NO NO P, N
Discrete
Uniform
YES YES NO YES YES YES NO NO N
Hypergeometric YES YES N/A YES YES YES NO NO L, K, N, M
Logarithmic
Series
YES YES NO YES YES YES NO NO THETA
Waring
(A=1 is Yule)
NO YES N/A YES YES YES NO NO C, A
Beta-
Binomial
NO YES N/A YES YES YES NO NO ALPHA, BETA

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Date created: 6/5/2001
Last updated: 10/30/2013

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