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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
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