Dataplot Vol 2 Vol 1

# Probability Distributions

The following commands operate on distributions:

For these commands, you may need to enter value of one or more shape parameters and/or values for location and scale parameters. For example,

LET GAMMA = 2.5
WEIBULL PROBABILITY PLOT Y

More specifically:

1. For the RANDOM NUMBERS command, you need to specify the values of any shape parameters. This command does not utilize location or scale parameters. However, you can transform the random numbers using the relation

Y = LOC + SCALE*Y

For example,

LET GAMMA = 2.5
LET LOC = 10
LET SCALE = 5
LET Y = WEIBULL RANDOM NUMBERS FOR I = 1 1 N
LET Y = LOC + SCALE*Y

2. For the PROBABILITY PLOT command, you need to specify the values for any shape parameters. For example,

LET GAMMA = 2.5
WEIBULL PROBABILITY PLOT Y

You can optionally specify location and scale parameters with the commands

LET PPLOC = <value>
LET PPSCALE = <value>

Note that the probability plot is invariant to location and scale (i.e., the linearity of the probability plot does not depend on the values of the location and scale parameters). PPLOC and PPSCALE are typically used when a non-PPCC method is used to estimate the location/scale parameters.

3. For the PPCC PLOT, ANDERSON DARLING PLOT, KOLMOGOROV SMIRNOV PLOT and CHI-SQUARE PLOT commands, you can optionally specify the range for the shape parameter(s) (default ranges will be used if they are not specified). For example,

LET GAMMA1 = 0.5
LET GAMMA2 = 5
WEIBULL PPCC PLOT Y

That is, you append a 1 (for the lower limit) and a 2 (for the upper limit) to the shape parameter name.

For the ANDERSON DARLING, KOLMOGOROV SMIRNOV, and CHI-SQUARE variants, you can optionally fix the values of the location/scale parameters with the commands

LET KSLOC = <value>
LET KSSCALE = <value>

4. For the GOODNESS OF FIT and the BOOTSTRAP/JACKNIFE PLOT commands, you need to specify the values for any shape parameters.

In addition, you can specify the values for the location/scale parameters with the commands (these will default to 0 and 1 if these commands are not given)

LET KSLOC = <value>
LET KSSCALE = <value>

Distributions that are bounded both above and below specify the lower and upper limits (rather than the location/scale) with the commands

LET A = <value>
LET B = <value>

Distributions that use A and B rather than KSLOC/KSSCALE will be denoted by the phrase "bounded distribution" in the tables below.

An example of using these commands:

LET GAMMA = 2.5
LET KSLOC = 5
LET KSSCALE = 10
WEIBULL ANDERSON DARLING GOODNESS OF FIT Y
BOOTSTRAP WEIBULL ANDERSON DARLING PLOT Y

The extreme value type 1 (Gumbel), extreme value type 2 (Frechet), generalized Pareto, generalized extreme value and the Weibull support "minimum" and "maximum" forms of the distribution. You can specify the minimum form with either of the following commands

SET MINMAX 1
SET MINMAX MINIMUM

You can specify the maximum form with either of the following commands

SET MINMAX 2
SET MINMAX MAXIMUM

The default is the "minimum" for the Weibull and "maximum" for the others.

This section documents the values you need to enter for the distributions supported in Dataplot.

CONTINUOUS DISTRIBUTIONS:

Location/Scale Distributions:

1. NORMAL
2. UNIFORM - bounded distribution
3. LOGISTIC
4. DOUBLE EXPONENTIAL
5. CAUCHY
6. SEMI-CIRCULAR
7. COSINE
8. ANGLIT
9. HYPERBOLIC SECANT
10. HALF-NORMAL
11. ARCSIN
12. EXPONENTIAL
13. EXTREME VALUE TYPE I (GUMBEL)
14. HALF-CAUCHY
15. SLASH
16. RAYLEIGH
17. MAXWELL
18. LANDAU

One Shape Parameter Distributions - name of shape parameter(s) listed:

 1. ALPHA: ALPHA 2. ASYMMETRIC DOUBLE EXPONENTIAL: K (or MU) 3. BRADFORD: BETA 4. BURR TYPE 2: R 5. BURR TYPE 7: R 6. BURR TYPE 8: R 7. BURR TYPE 10: R 8. BURR TYPE 11: R 9. CHI: NU 10. CHI-SQUARED: NU 11. DOUBLE GAMMA: GAMMA 12. DOUBLE WEIBULL: GAMMA 13. ERROR (SUBBOTIN): ALPHA 14. EXPONENTIAL POWER: BETA 15. EXTREME VALUE TYPE 2 (FRECHET): GAMMA 16. FATIGUE LIFE: GAMMA 17. FOLDED T: NU 18. GAMMA: GAMMA 19. GENERALIZED EXTREME VALUE: GAMMA 20. GENERALIZED HALF LOGISTIC: GAMMA 21. GENERALIZED LOGISTIC: ALPHA 22. GENERALIZED LOGISTIC TYPE 2: ALPHA 23. GENERALIZED LOGISTIC TYPE 3: ALPHA 24. GENERALIZED LOGISTIC TYPE 5: ALPHA 25. GENERALIZED PARETO: GAMMA 26. GEOMETRIC EXTREME EXPONENTIAL: GAMMA 27. INVERTED GAMMA: GAMMA 28. INVERTED WEIBULL: GAMMA 29. LOG DOUBLE EXPONENTIAL: ALPHA 30. LOG GAMMA: GAMMA 31. LOGISTIC-EXPONENTIAL: BETA 32. LOG LOGISTIC: DELTA 33. LOGNORMAL: SIGMA 34. MCLEISH: ALPHA 35. MUTH: BETA 36. OGIVE: N 37. PEARSON TYPE 3: GAMMA 38. POWER FUNCTION: C 39. POWER NORMAL: P, bounded distribution 40. RECIPROCAL: B 41. REFLECTED POWER: C, bounded distribution 42. SKEW DOUBLE EXPONENTIAL: LAMBDA 43. SKEW NORMAL: LAMBDA 44. SLOPE: ALPHA, bounded distribution 45. T: NU 46. TOPP AND LEONE: BETA, bounded distributin 47. TRIANGULAR: C, bounded distribution 48. TUKEY LAMBDA: LAMBDA 49. VON MISES: B 50. WALD: GAMMA 51. WEIBULL: GAMMA 52. WRAPPED CAUCHY: P

Two Shape Parameter Distributions:

 1. ASYMMETRIC LOG DOUBLE EXPONENTIAL: ALPHA, BETA 2. BETA: ALPHA, BETA, bounded distribution 3. BETA NORMAL: ALPHA, BETA 4. BURR TYPE 3: R, K 5. BURR TYPE 4: R, C 6. BURR TYPE 5: R, K 7. BURR TYPE 6: R, K 8. BURR TYPE 9: R, K 9. BURR TYPE 12: C, K 10. DOUBLY PARETO UNIFORM: M, N 11. EXPONENTIATED WEIBULL: GAMMA, THETA 12. F: NU1, NU2 13. FOLDED CAUCHY: LOC, SCALE 14. FOLDED NORMAL: MU, SD 15. G-AND-H: G, H 16. GENERALIZED ASYMMETRIC LAPLACE: K, TAU or K, MU 17. GENERALIZED GAMMA: ALPHA, C 18. GENERALZIED INVERSE GAUSSIAN: LAMBDA, OMEGA 19. GENERALIZED LOGISTIC TYPE 4: P, Q 20. GENERALIZED MCLEISH: ALPHA, A 21. GENERALIZED TOPP AND LEONE: ALPHA, BETA, bounded distribution 22. GENERALIZED TUKEY LAMBDA: LAMBDA3, LAMBDA4 23. GOMPERTZ: C, B or ALPHA, K 24. GOMPERTZ-MAKEHAM: ETA, ZETA (Meeker parameterization) 25. INVERSE GAUSSIAN: GAMMA, MU 26. INVERTED BETA: ALPHA, BETA 27. JOHNSON SB: ALPHA1, ALPHA2 28. JOHNSON SU: ALPHA1, ALPHA2 29. KAPPA: K, H 30. KUMARASWAMY: ALPHA, BETA bounded distribution 31. LOG-SKEW-NORMAL: LAMBDA, SD 32. MIELKE'S BETA-KAPPA: THETA, K 33. NON-CENTRAL T: NU, LAMBDA 34. NON-CENTRAL CHI-SQUARE: NU, LAMBDA 35. PARETO: GAMMA, A (A defaults to 1 if not specified) 36. PARETO SECOND KIND: GAMMA, A (A defaults to 1 if not specified) 37. POWER LOGNORMAL: P, SD 38. RECIPROCAL INVERSE GAUSSIAN: GAMMA, NU 39. REFLECTED GENERALIZED TOPP LEONE: ALPHA, BETA bounded distribution 40. TWO-SIDED OGIVE: THETA, N bounded distribution 41. TWO-SIDED POWER: THETA, N bounded distribution 42. TWO-SIDED SLOPE: THETA, ALPHA bounded distribution 43. SKEW T: LAMBDA, NU

Three or More Shape Parameter Distributions:

 1. BESSEL I-FUNCTION: SIGMA1SQ, SIGMA2SQ, NU or B, C, M 2. BESSEL K-FUNCTION: SIGMA1SQ, SIGMA2SQ, NU or B, C, M 3. BI-WEIBULL: GAMMA1, GAMMA2, SCALE1, SCALE2, LOC2 4. BRITTLE FRACTURE: ALPHA, BETA, R 5. DOUBLY NON-CENTRAL BETA: ALPHA, BETA, LAMBDA1, LAMBDA2 6. DOUBLY NON-CENTRAL F: NU1, NU2, LAMBDA1, LAMBDA2 7. DOUBLY NON-CENTRAL T: NU, LAMBDA1, LAMBDA2 8. GENERALIZED EXPONENTIAL: LAMBDA1, LAMBDA12, S 9. GENERALZIED TRAPEZOID: A, B, C, D, ALPHA, NU1, NU3 10. GOMPERTZ-MAKEHAM: CHI, LAMBDA, THETA or GAMMA, LAMBDA, K 11. LOG BETA: ALPHA, BETA, C, D 12. LOG-SKEW-T: NU, LAMBDA, SD 13. NON-CENTRAL BETA: ALPHA, BETA, LAMBDA 14. NON-CENTRAL F: NU1, NU2, LAMBDA 15. NORMAL MIXTURE: U1, SD1, U2, SD2, P 16. TRAPEZOID: A, B, C, D 17. TRUNCATED EXPONENTIAL: X0, M, SD (X0 assumed known for PPCC) 18. TRUNCATED NORMAL: MU, SD, A, B 19. TRUNCATED PARETO: GAMMA, A, NU 20. UNEVEN TWO-SIDED POWER: ALPHA, NU1, NU3, D bounded distribution 21. WAKEBY: GAMMA, BETA, DELTA, ALPHA, CHI (CHI and ALPHA are the location and scale parameters)

DISCRETE DISTRIBUTIONS:

 1. BETA-BINOMIAL: ALPHA, BETA, N 2. BETA GEOMETRIC: ALPHA, BETA 3. BETA NEGATIVE BINOMIAL: ALPHA, BETA, K 4. BINOMIAL: P, N 5. BOREL-TANNER: LAMBDA, K 6. CONSUL (GENERALIZED GEOMTRIC): THETA, BETA or MU, BETA 7. DISCRETE UNIFORM: N 8. DISCRETE WEIBULL: Q, BETA 9. GEETA: THETA, BETA or MU, BETA 10. GENERALIZED LOGARITHMIC SERIES: THETA, BETA 11. GENERALIZED LOST GAMES: P, J, A 12. GENERALIZED NEGATIVE BINOMIALS: THETA, BETA, M 13. GEOMETRIC: P 14. HERMITE: ALPHA, BETA 15. HYPERGEOMETRIC: L, K, N, M 16. KATZ: ALPHA, BETA 17. LAGRANGE-POISSON: LAMBDA, THETA 18. LEADS IN COIN TOSSING: N 19. LOGARITHMIC SERIES: THETA 20. LOST GAMES: P, R 21. MATCHING: K 22. NEGATIVE BIONOMIAL: P, N 23. POISSON: LAMBDA 24. POLYA-AEPPLI: THETA, P 25. QUASI BINOMIAL TYPE I: P, PHI 26. TRUNCATED GENE NEGATIVE BINOMIAL: THETA, BETA, B, N 27. WARING: C, A 28. YULE: P 29. ZETA: ALPHA 30. ZIPF: ALPHA, N

Date created: 9/21/2011
Last updated: 9/21/2011