Dataplot Distributions      4/2005
 
Dataplot supports a number of probability functions:

   1) pdf = probability density function
   2) cdf = cumulative distribution function
   3) ppf = percent point function (= inverse cdf)
   4) sf  = sparsity function (= derivative of ppf)
   5) haz = hazard function
   6) cha = cumulative hazard function

   Note that the survival function can be computed as the
   CDF(1-X) and the inverse survival function can be computed
   as PPF(1-P).  For this reason, distinct functions are not provided
   for the survival and inverse survival functions.

Random number generation is available for most, but not all,
of the supported distributions.

The following capabilities are available when the PPF function
is available:

   1) probability plots
   2) ppcc plots (for distributions with either one or two
      shape parameters)

The following capabilities are available (for univariate
distributions)when the CDF function is available (Kolmogorov-Smirnov
tests are not supported for discrete distributions):

   1) chi-square goodness of fit tests
   2) Kolmogorov-Smirnov goodness of fit tests

The following are available for a subset of the distributions:

   1) The Anderson-Darling goodness of fit test (a refinement of the
      Kolmogorov-Smirnov test that is more powerful) is supported
      for:

         normal, lognormal, exponential, Weibull,
         extreme value type 1, logistic, double exponential,
         generalized pareto, uniform (0,1), Cauchy,
         extreme value type 2

   2) There are a number of numerical parameter estimation
      methods for probability distributions.  For the following
      distributions, one or more of the following numeric
      estimation methods is supported: maximum likelihood,
      method of momements, L-moments, and elemental percentiles.

      Continuous Distributions
         normal, lognormal, exponential, double exponential,
         Weibull, Pareto, gamma, inverse gaussian,
         extreme value type 1, power, logistic, uniform, beta,
         Johnson SU, Johnson SB, two-sided power,
         fatigue life, geometric extreme exponential,
         folded normal, Cauchy, generalized Pareto,
         Rayleigh, Maxwell, asymmetric double exponential,
         extreme value type 2, generalized extreme value,
         generalized logistic type 5, mixture of normals,
         slash, log beta, four parameter beta

      Discrete Distributions
         binomial, Poisson, geometric, logarithmic series,
         beta-binomial, beta-geometric,
         negative binomial, hypergeometric, Hermite, Yule,
         Borel-Tanner, Lagrange-Poisson, zeta,
         lost games, generalized lost games, Polya-Aeppli,
         generalized logarithmic series, geeta,
         quasi binomial type I, consul,
         generalized negative binomial

   Enter HELP ANDERSON DARLING GOODNESS OF FIT or
   HELP MAXIMUM LIKELIHOOD for details.

To use one of these functions in Dataplot, enter something like:

     PLOT GAMPDF(X,2) FOR X = .01 .01 4

NOTES:

   1) 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 parameters.  Optional location and scale parameters are
      available for many of the distributions and are referred to as LOC
      and SCALE in the table.

      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.

      For example, the Normal functions 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)

      The distribution identifier is included in the table.

   2) 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

   3) 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.

   4) The multivariate distributions are supported via the MATRIX
      subcommands under LET.  For example,

        LET M = MULTIVARIATE NORMAL RANDOM NUMBERS MU SIGMA

      with the variable MU denoting a variable containing the means
      and the matrix SIGMA containing the variance-covariance matrix,
      respectively.

                                                           cha
       Name            Rand  Prob  ppcc  cdf   pdf   ppf   haz  sf   Parameters
________________________________________________________________________________

Symmetric, continuous distributions
 1. Uniform        UNI YES   YES   N/A   YES   YES   YES   YES YES  LOWER, UPPER
 2. Normal         NOR YES   YES   N/A   YES   YES   YES   YES YES  LOC, SCALE
    (= Gaussian)
 3. Logistic       LOG YES   YES   N/A   YES   YES   YES   YES YES  LOC, SCALE
 4. Double         DEX YES   YES   N/A   YES   YES   YES   NO  YES  LOC, SCALE
    Exponential
 5. Double Weibull DWE YES   YES   YES   YES   YES   YES   NO  NO   GAMMA, LOC,
                                                                    SCALE
 6. Double Gamma   DGA YES   YES   YES   YES   YES   YES   NO  NO   GAMMA, LOC,
                                                                    SCALE
 7. Cauchy         CAU YES   YES   N/A   YES   YES   YES   NO  YES  LOC, SCALE
 8. Tukey Lambda   LAM YES   YES   YES   YES   YES   YES   NO  YES  LAMBDA
                                                                    LOC, SCALE
 9. T                T YES   YES   YES   YES   YES   YES   NO  NO   NU
                                                                    LOC, SCALE
10. Semi-Circular  SEM YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
11. Von Misese     VON YES   YES   YES   YES   YES   YES   NO  NO   B, LOC
12. Cosine         COS YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
13. Anglit         ANG YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
14. Hyperbolic     HSE YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
    Secant
15. Error          ERR YES   YES   YES   YES   YES   YES   NO  NO   ALPHA,
    (Exponential Power                                              LOC, SCALE
    Subbotin,
    Generalized Error)

Skewed, continuous distributions
 1. Lognormal      LGN YES   YES   YES   YES   YES   YES   YES NO   SD, LOC,
                                                                    SCALE
 2. Power          PLN YES   YES   YES   YES   YES   YES   YES NO   P, SD
    Lognormal                                                       LOC
 3. Power Normal   PNR YES   YES   YES   YES   YES   YES   YES NO   P,
                                                                    LOC, SCALE
 4. Half Normal    HFN YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
 5. Folded Normal  FNR YES   YES   YES   YES   YES   YES   NO  NO   U, SD
 6. Truncated      TNR YES   YES   N/A   YES   YES   YES   NO  NO   A,B,U,SD
    Normal
 7. Skewed Normal  SN  YES   YES   YES   YES   YES   YES   NO  NO   LAMBDA, 
                                                                    LOC, SCALE
 8. Log Skewed     LSN YES   YES   YES   YES   YES   YES   NO  NO   LAMBDA, SD,
    Normal                                                          LOC, SCALE
 9. Chi-Squared    CHS YES   YES   YES   YES   YES   YES   NO  NO   NU, LOC
                                                                    SCALE
10. Chi            CHI YES   YES   YES   YES   YES   YES   NO  NO   NU, LOC
                                                                    SCALE
11. Non-Central    NCC YES   YES   YES   YES   YES   YES   NO  NO   NU, LAMBDA
    Chi-Square
12. F                F YES   YES   YES   YES   YES   YES   NO  NO   NU1, NU2
                                                                    LOC, SCALE
13. Non-Central F  NCF YES   YES   N/A   YES   YES   YES   NO  NO   NU1, NU2,
                                                                    LAMBDA
14. Doubly         DNF YES   YES   N/A   YES   YES   YES   NO  NO   NU1, NU2
    Non-Central F                                                   LAMBDA1,
                                                                    LAMBDA2
15. Folded T       FT  YES   YES   YES   YES   YES   YES   NO  NO   NU,
                                                                    LOC, SCALE
16. Skewed T       ST  YES   YES   YES   YES   YES   YES   NO  NO   NU, LAMBDA, 
                                                                    LOC, SCALE
17. Log Skewed T   LST YES   YES   N/A   YES   YES   YES   NO  NO   NU, LAMBDA, SD,
                                                                    LOC, SCALE
18. Non-Central T  NCT YES   YES   YES   YES   YES   YES   NO  NO   NU, LAMBDA
19. Doubly         DNT YES   YES   N/A   YES   YES   YES   NO  NO   NU, LAMBDA1,
    Non-Central T                                                   LAMBDA2
20. Beta           BET YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, BETA
                                                                    LOWER, UPPER
21. Non-Central    NCB NO    YES   N/A   YES   NO    YES   NO  NO   ALPHA, BETA,
    Beta                                                            LAMBDA
22. Inverted Beta  IB  YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, BETA
                                                                    LOC, SCALE
23. Power Function POW YES   YES   YES   YES   YES   YES   NO  NO   C, LOC, SCALE
24. Reflected      RPO YES   YES   YES   YES   YES   YES   NO  NO   C, LOC, SCALE
    Power Function
25. Arcsin         ARC YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
26. Gamma          GAM YES   YES   YES   YES   YES   YES   YES NO   GAMMA
                                                                    LOC, SCALE
27. Generalized    GGD YES   YES   YES   YES   YES   YES   YES NO   GAMMA, C
    Gamma                                                           LOC, SCALE
28. Inverted Gamma IGA YES   YES   YES   YES   YES   YES   YES NO   GAMMA
                                                                    LOC, SCALE
29. Log-Gamma      LGA YES   YES   YES   YES   YES   YES   NO  NO   GAMMA
                                                                    LOC, SCALE
30. Exponential    EXP YES   YES   N/A   YES   YES   YES   YES YES  LOC, SCALE
31. Truncated      TNE YES   YES   N/A   YES   YES   YES   NO  NO   X0, M, SD
    Exponential
32. Power          PEX YES   YES   YES   YES   YES   YES   YES NO   BETA
    Exponential                                                     LOC, SCALE
33. Generalized    GEX YES   YES   N/A   YES   YES   YES   NO  NO   LAMBDA1,
    Exponential                                                     LAMBDA2, S
34. Geometric      GEE YES   YES   YES   YES   YES   YES   YES NO   GAMMA
    Extreme Exponential                                             LOC, SCALE
35. Weibull--MIN   WEI YES   YES   YES   YES   YES   YES   YES NO   GAMMA
                                                                    LOC, SCALE
36. Weibull--MAX   WEI YES   YES   YES   YES   YES   YES   YES NO   GAMMA
                                                                    LOC, SCALE
37. Exponentiated  EWE YES   YES   YES   YES   YES   YES   YES NO   GAMMA, THETA
    Weibull                                                         LOC, SCALE
38. Inverted       IWE YES   YES   YES   YES   YES   YES   YES NO   GAMMA
    Weibull                                                         LOC, SCALE
39. EV1 (Gumbel)   EV1 YES   YES   N/A   YES   YES   YES   YES NO   LOC, SCALE
    --MIN
40. EV1 (Gumbel)   EV1 YES   YES   N/A   YES   YES   YES   YES NO   LOC, SCALE
    --MAX
41. EV2 (Frechet)  EV2 YES   YES   YES   YES   YES   YES   YES NO   GAMMA
    --MIN                                                           LOC, SCALE
42. EV2 (Frechet)  EV2 YES   YES   YES   YES   YES   YES   YES NO   GAMMA
    --MAX                                                           LOC, SCALE
43. Generalized    GEV YES   YES   YES   YES   YES   YES   NO  NO   GAMMA
    Extreme Value                                                   LOC, SCALE
44. Gompertz       GOM YES   YES   YES   YES   YES   YES   NO  NO   C, B
                                                                    LOC, SCALE
45. Gompertz-      MAK YES   YES   N/A   YES   YES   YES   NO  NO   XI, LAMBDA,
    Makeham                                                         THETA, LOC, SCALE
46. Pareto         PAR YES   YES   YES   YES   YES   YES   YES NO   GAMMA, LOC
    (of First Kind)
47. Pareto         PA2 YES   YES   YES   YES   YES   YES   NO  NO   GAMMA,
    (of Second Kind)                                                LOC, SCALE
48. Generalized    GEP YES   YES   YES   YES   YES   YES   YES NO   GAMMA, SCALE
    Pareto
49. Alpha          ALP YES   YES   YES   YES   YES   YES   YES NO   ALPHA,
                                                                    LOC, SCALE
50. Inverse         IG YES   YES   YES   YES   YES   YES   YES NO   GAMMA
    Gaussian                                                        LOC, SCALE
51. Wald           WAL YES   YES   YES   YES   YES   YES   YES NO   GAMMA, LOC
52. Reciprocal     RIG YES   YES   YES   YES   YES   YES   YES NO   GAMMA
    Inverse Gaussian                                                LOC, SCALE
    (= Random Walk)
53. Generalized    GIG YES   YES   N/A   YES   YES   YES   NO  NO   CHI, LAMBDA,
    Inverse                                                         THETA,
    Gaussian                                                        LOC, SCALE
54. Failure Time    FL YES   YES   YES   YES   YES   YES   YES NO   GAMMA
                                                                    LOC, SCALE
55. Log-Logistic   LLG YES   YES   YES   YES   YES   YES   NO  NO   DELTA
                                                                    LOC, SCALE
56. Half-Logistic  HFL YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
57. Generalized    HFL YES   YES   YES   YES   YES   YES   NO  NO   GAMMA
    Half-Logistic                                                   LOC, SCALE
58. Generalized    GLO YES   YES   YES   YES   YES   YES   NO  NO   ALPHA
    Logistic                                                        LOC, SCALE
59. Generalized    GL2 YES   YES   YES   YES   YES   YES   NO  NO   GAMMA
    Logistic (Type 2)                                               LOC, SCALE
60. Generalized    GL3 YES   YES   YES   YES   YES   YES   NO  NO   GAMMA
    Logistic (Type 3)                                               LOC, SCALE
61. Generalized    GL5 YES   YES   YES   YES   YES   YES   NO  NO   GAMMA
    Logistic (Type 5)                                               LOC, SCALE
62. Generalized    GL4 YES   YES   YES   YES   YES   YES   NO  NO   P, Q,
    Logistic (Type 4)                                               LOC, SCALE
63. Half-Cauchy    HFC YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
64. Wrapped-Up     WCA YES   YES   YES   YES   YES   YES   NO  NO   P, LOC
    Cauchy
65. Folded Cauchy  FCA YES   YES   YES   YES   YES   YES   NO  NO   M, SD
66. Mielke's       KAP YES   YES   N/A   YES   YES   YES   NO  NO   K, BETA,
    Beta-Kappa                                                      THETA
                                                                    LOC, SCALE
67. Bradford       BRA YES   YES   YES   YES   YES   YES   NO  NO   BETA
                                                                    LOC, SCALE
68. Reciprocal     REC YES   YES   YES   YES   YES   YES   NO  NO   B
                                                                    LOC, SCALE
69. Log Double     LDE YES   YES   YES   YES   YES   YES   NO  NO   ALPHA
    Exponential                                                     LOC, SCALE
70. Skew Double    SDE YES   YES   YES   YES   YES   YES   NO  NO   LAMBDA
    Exponential                                                     LOC, SCALE
71. Asymmetric     ADE YES   YES   YES   YES   YES   YES   NO  NO   LAMBDA
    Double Exponential                                              LOC, SCALE
72. Generalized    GAL YES   YES   YES   YES   YES   YES   NO  NO   KAPPA, TAU,
    Asymmetric Laplace                                              LOC, SCALE
73. Asymmetric     ALD YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, BETA,
    Log Laplace                                                     LOC, SCALE
74. Johnson SB     JSB YES   YES   YES   YES   YES   YES   NO  NO   ALPHA1, ALPHA2,
                                                                    LOC, SCALE
75. Johnson SU     JSU YES   YES   YES   YES   YES   YES   NO  NO   ALPHA1, ALPHA2,
                                                                    LOC, SCALE
76. Two-Sided      TSP YES   YES   YES   YES   YES   YES   NO  NO   THETA, N,
    Power                                                           LOC, SCALE
77. Landau         LAN YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
78. Slash          SLA YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
79. G-and-H        GH  YES   YES   YES   YES   YES   YES   NO  NO   G, H,
                                                                    LOC, SCALE
80. Generalized    GLD YES   YES   YES   YES   YES   YES   NO  NO   LAMBDA3, LAMBDA4,
    Tukey-Lambda                                                    LOC, SCALE
81. Maxwell        MAX YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
82. Rayleigh       RAY YES   YES   N/A   YES   YES   YES   NO  NO   LOC, SCALE
83. Bessel I       BEI YES   YES   N/A   YES   YES   YES   NO  NO   SIGMA1SQ,
    Function                                                        SIGMA2SQ, NU,
                                                                    LOC, SCALE
84. Beta-Normal    BNO YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, BETA,
85. Triangular     TRI YES   YES   YES   YES   YES   YES   NO  NO   C,
                                                                    LOWER, UPPER
86. Slope          SLO YES   YES   YES   YES   YES   YES   NO  NO   ALPHA,
                                                                    LOWER, UPPER
87. Two-Sided      TSS YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, THETA,
    Slope                                                           LOWER, UPPER

88. Ogive          OGI YES   YES   YES   YES   YES   YES   NO  NO   N,
                                                                    LOWER, UPPER
89. Two-Sided      TSO YES   YES   YES   YES   YES   YES   NO  NO   N, THETA,,
    Ogive                                                           LOWER, UPPER
90. Burr Type 2    BU2 YES   YES   YES   YES   YES   YES   NO  NO   R,
                                                                    LOC, SCALE
91. Burr Type 3    BU3 YES   YES   YES   YES   YES   YES   NO  NO   R, K,
                                                                    LOC, SCALE
92. Burr Type 4    BU4 YES   YES   YES   YES   YES   YES   NO  NO   R, C,
                                                                    LOWLIM, UPPLIM, SCALE
93. Burr Type 5    BU5 YES   YES   YES   YES   YES   YES   NO  NO   R, K,
                                                                    LOC, SCALE
94. Burr Type 6    BU6 YES   YES   YES   YES   YES   YES   NO  NO   R, K,
                                                                    LOC, SCALE
95. Burr Type 7    BU7 YES   YES   YES   YES   YES   YES   NO  NO   R,
                                                                    LOC, SCALE
96. Burr Type 8    BU8 YES   YES   YES   YES   YES   YES   NO  NO   R,
                                                                    LOC, SCALE
97. Burr Type 9    BU9 YES   YES   YES   YES   YES   YES   NO  NO   R, K,
                                                                    LOC, SCALE
98. Burr Type 10   B10 YES   YES   YES   YES   YES   YES   NO  NO   R,
                                                                    LOC, SCALE
99. Burr Type 11   B11 YES   YES   YES   YES   YES   YES   NO  NO   R,
                                                                    LOC, SCALE
100. Burr Type 12   B12 YES   YES   YES   YES   YES   YES   NO  NO   C, K,
                                                                    LOC, SCALE
101. Doubly Pareto  DPU YES   YES   YES   YES   YES   YES   NO  NO  M, N,
     Uniform                                                        ALPHA, BETA
102. Kumaraswamy    KUM YES   YES   YES   YES   YES   YES   NO  NO  ALPHA, BETA
                                                                    LOWER, UPPER
103. Uneven         UTS YES   YES   NO    YES   YES   YES   NO  NO  A, B, D,
     Two-Sided Power                                                NU1, NU3, ALPHA
104. Muth           MUT YES   YES   YES   YES   YES   YES   NO  NO  BETA,
                                                                    LOC, SCALE
105. Exponential-   LEX YES   YES   YES   YES   YES   YES   NO  NO  BETA,
     Logistic                                                       LOC, SCALE
106. Wakeby         WAK YES   YES   YES   YES   YES   YES   NO  NO  BETA, GAMMA, DELTA,
                                                                    LOC, SCALE

Mixtures
 1. Mixture of   NORMX YES   YES   N/A   YES   YES   YES   NO  NO   P, U1, SD1,
    2 Normals                                                       U2, SD2
 2. Bi-Weibull     BWE YES   YES   N/A   YES   YES   YES   YES NO   SCALE1, GAMMA1
                                                                    LOC2, SCALE2, GAMMA2

Bivariate/Multivariate
 1. Bivariate      BVN NO    N/A   N/A   YES   YES   N/A   NO  N/A  P
    Normal
 2. Multivariate   N/A YES   N/A   N/A   YES   NO    N/A   NO  N/A  MU, SIGMA,
    Normal                                                          N
 3. Multivariate   N/A YES   N/A   N/A   YES   NO    N/A   NO  N/A  MU, SIGMA
    T                                                               NU, N
                                                                    N
 4. Wishart        N/A YES   N/A   N/A   NO    NO    N/A   NO  N/A  MU, SIGMA
                                                                    N
 5. Multinomial    N/A YES   N/A   N/A   NO    NO    N/A   NO  N/A  P, NEVENTS,
                                                                    NCAT, N
 6. Dirichelet     N/A YES   N/A   N/A   NO    YES   N/A   NO  N/A  ALPHA, N
 7. Independent    N/A YES   N/A   N/A   NO    NO    N/A   NO  N/A  LOWLIM, UPPLIM,
    Uniform                                                         N
 8. Dependent      N/A YES   N/A   N/A   NO    NO    N/A   NO  N/A  LOWLIM, UPPLIM,
    Uniform                                                         N

Discrete
 1. Beta-Binomial  BBN YES   YES   YES   YES   YES   YES   NO  NO   ALPHA,
                                                                    BETA, N
 2. Beta-Geometric BGE YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, BETA
 3. Beta-Negative  BNB YES   YES   NO    YES   YES   YES   NO  NO   ALPHA, BETA
    Binomial                                                        K
    (reparameterized generalized Waring)
 4. Binomial       BIN YES   YES   YES   YES   YES   YES   NO  NO   N, P
 5. Borel-Tanner   BTA YES   YES   YES   YES   YES   YES   NO  NO   LAMBDA, K
 6. Consul         CON YES   YES   YES   YES   YES   YES   NO  NO   THETA (or MU),
    (generalized geometric)                                         BETA
 7. Discrete       DIS YES   YES   NO    YES   YES   YES   NO  NO   N
    Uniform
 8. Discrete       DIW YES   YES   YES   YES   YES   YES   NO  NO   Q, BETA
    Weibull
 9. Geeta          GET YES   YES   YES   YES   YES   YES   NO  NO   THETA (or MU),
                                                                    BETA
10. Generalized    GLS YES   YES   YES   YES   YES   YES   NO  NO   THETA, BETA
    Logarithmic Series
11. Generalized    GLG YES   YES   YES   YES   YES   YES   NO  NO   P, J, A
    Lost Games
12. Generalized    GNB YES   YES   NO    YES   YES   YES   NO  NO   THETA, BETA,
                                                                    M
    Negative Binomial
13. Geometric      GEO YES   YES   YES   YES   YES   YES   NO  NO   P
14. Hermite        HER YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, BETA
15. Hypergeometric HYP YES   YES   NO    YES   YES   YES   NO  NO   L, K, N, M
16. Katz           KAT YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, BETA
17. Lagrange-      LPO YES   YES   YES   YES   YES   YES   NO  NO   LAMBDA,
    Poisson (Consul's generalized Poisson)                          THETA
18. Leads in Coin  LCT YES   YES   NO    YES   YES   YES   NO  NO   N
    Tossing (Discrete Arcsine)
19. Logarithmic    DLG YES   YES   YES   YES   YES   YES   NO  NO   THETA
    Series
20. Lost Games     LOS YES   YES   YES   YES   YES   YES   NO  NO   P, R
21. Classical      MAT YES   YES   NO    YES   YES   YES   NO  NO   K
    Matching
22. Negative        NB YES   YES   YES   YES   YES   YES   NO  NO   N, P
    Binomial
23. Poisson        POI YES   YES   YES   YES   YES   YES   NO  NO   LAMBDA
24. Polya-Aeppli   PAP YES   YES   YES   YES   YES   YES   NO  NO   THETA, P
25. Quasi Binomial QBI YES   YES   YES   YES   YES   YES   NO  NO   P, PHI
    Type I
26. Truncated      GNT YES   YES   NO    YES   YES   YES   NO  NO   THETA, BETA,
    Generalized                                                     B, N
    Negative Binomial
                                                                    M
27. Waring         WAR YES   YES   YES   YES   YES   YES   NO  NO   C, A
    (reparameterized beta-geometric)
28. Yule           YUL YES   NO    NO    YES   YES   YES   NO  NO   P
29. Zeta           ZET YES   YES   YES   YES   YES   YES   NO  NO   ALPHA
30. Zipf           ZIP YES   YES   YES   YES   YES   YES   NO  NO   ALPHA, N
_________________________________________________________________________________


Rand     = Random numbers
Prob     = Probability plot
ppcc     = Probability plot correlation coefficient plot
cdf      = Cumulative distribution function
pdf      = Probability density function (or probability mass for discrete)
ppf      = Percent point (or inverse cdf) function
sf       = Sparsity function 
haz      = Hazard function 
cha      = Cumulative hazard function 
