# 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
 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
 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
 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
 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
 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: 06/05/2001
Last updated: 09/20/2016