Dataplot Distributions
|
Types of Probability Functions
|
Dataplot has an extensive library of built-in probability
distributions. There are four types of probability functions
provided:
- Cumulative Distribution Functions (CDF)
- Probability Density (or Mass) Functions (PDF)
- Percent Point (or inverse CDF) Functions (PPF)
- Hazard Functions
- Cumulative Hazard Functions
- 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
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).
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|
Dataplot Distributions 9/2002
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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
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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
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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
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NU, LOC, SCALE
|
Semi-
Circular
|
YES
|
YES
|
N/A
|
YES
|
YES
|
YES
|
NO
|
NO
|
None
|
Triangular
|
YES
|
YES
|
YES
|
YES
|
YES
|
YES
|
NO
|
NO
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C, LOC, SCALE
|
Von
Mises
|
NO
|
YES
|
YES
|
YES
|
YES
|
YES
|
NO
|
NO
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B, LOC
|
Cosine
|
YES
|
YES
|
N/A
|
YES
|
YES
|
YES
|
NO
|
NO
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LOC, SCALE
|
Anglit
|
YES
|
YES
|
N/A
|
YES
|
YES
|
YES
|
NO
|
NO
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LOC, SCALE
|
Hyperbolic
Secant
|
YES
|
YES
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N/A
|
YES
|
YES
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YES
|
NO
|
NO
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LOC, SCALE
|
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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
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U, SD
|
Truncated
Normal
|
NO
|
YES
|
N/A
|
YES
|
YES
|
YES
|
NO
|
NO
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A, B, U, SD
|
Chi-
Square
|
YES
|
YES
|
YES
|
YES
|
YES
|
YES
|
NO
|
NO
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NU, LOC, SCALE
|
Chi
|
NO
|
YES
|
YES
|
YES
|
YES
|
YES
|
NO
|
NO
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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
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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
|
|
Bivariate/
Multivariate
|
|
Discrete Distributions
|
|
Date created: 6/5/2001
Last updated: 9/23/2002
Please email comments on this WWW page to
sedwww@cam.nist.gov.
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