Statistical Distribution Functions

PSPP can calculate several functions of standard statistical distributions. These functions are named systematically based on the function and the distribution. The table below describes the statistical distribution functions in general:

• PDF.DIST(X[, PARAM...])
  Probability density function for DIST. The domain of X depends on DIST. For continuous distributions, the result is the density of the probability function at X, and the range is nonnegative real numbers. For discrete distributions, the result is the probability of X.

• CDF.DIST(X[, PARAM...])
  Cumulative distribution function for DIST, that is, the probability that a random variate drawn from the distribution is less than X. The domain of X depends DIST. The result is a probability.

• SIG.DIST(X[, PARAM...)
  Tail probability function for DIST, that is, the probability that a random variate drawn from the distribution is greater than X. The domain of X depends DIST. The result is a probability. Only a few distributions include an SIG function.

• IDF.DIST(P[, PARAM...])
  Inverse distribution function for DIST, the value of X for which the CDF would yield P. The value of P is a probability. The range depends on DIST and is identical to the domain for the corresponding CDF.

• RV.DIST([PARAM...])
  Random variate function for DIST. The range depends on the distribution.

• NPDF.DIST(X[, PARAM...])
  Noncentral probability density function. The result is the density of the given noncentral distribution at X. The domain of X depends on DIST. The range is nonnegative real numbers. Only a few distributions include an NPDF function.

• NCDF.DIST(X[, PARAM...])
  Noncentral cumulative distribution function for DIST, that is, the probability that a random variate drawn from the given noncentral distribution is less than X. The domain of X depends DIST. The result is a probability. Only a few distributions include an NCDF function.

Continuous Distributions

The following continuous distributions are available:

• PDF.BETA(X)
CDF.BETA(X, A, B)
IDF.BETA(P, A, B)
RV.BETA(A, B)
NPDF.BETA(X, A, B, ꟛ)
NCDF.BETA(X, A, B, ꟛ)
  Beta distribution with shape parameters A and B. The noncentral distribution takes an additional parameter ꟛ. Constraints: A > 0, B > 0, ꟛ >= 0, 0 <= X <= 1, 0 <= P <= 1.

• PDF.BVNOR(X0, X1, ρ)
CDF.BVNOR(X0, X1, ρ)
  Bivariate normal distribution of two standard normal variables with correlation coefficient ρ. Two variates X0 and X1 must be provided. Constraints: 0 <= ρ <= 1, 0 <= P <= 1.

• PDF.CAUCHY(X, A, B)
CDF.CAUCHY(X, A, B)
IDF.CAUCHY(P, A, B)
RV.CAUCHY(A, B)
  Cauchy distribution with location parameter A and scale parameter B. Constraints: B > 0, 0 < P < 1.

• CDF.CHISQ(X, DF)
SIG.CHISQ(X, DF)
IDF.CHISQ(P, DF)
RV.CHISQ(DF)
NCDF.CHISQ(X, DF, ꟛ)
  Chi-squared distribution with DF degrees of freedom. The noncentral distribution takes an additional parameter ꟛ. Constraints: DF > 0, ꟛ > 0, X >= 0, 0 <= P < 1.

• PDF.EXP(X, A)
CDF.EXP(X, A)
IDF.EXP(P, A)
RV.EXP(A)
  Exponential distribution with scale parameter A. The inverse of A represents the rate of decay. Constraints: A > 0, X >= 0, 0 <= P < 1.

• PDF.XPOWER(X, A, B)
RV.XPOWER(A, B)
  Exponential power distribution with positive scale parameter A and nonnegative power parameter B. Constraints: A > 0, B >= 0, X >= 0, 0 <= P <= 1. This distribution is a PSPP extension.

• PDF.F(X, DF1, DF2)
CDF.F(X, DF1, DF2)
SIG.F(X, DF1, DF2)
IDF.F(P, DF1, DF2)
RV.F(DF1, DF2)
  F-distribution of two chi-squared deviates with DF1 and DF2 degrees of freedom. The noncentral distribution takes an additional parameter ꟛ. Constraints: DF1 > 0, DF2 > 0, ꟛ >= 0, X >= 0, 0 <= P < 1.

• PDF.GAMMA(X, A, B)
CDF.GAMMA(X, A, B)
IDF.GAMMA(P, A, B)
RV.GAMMA(A, B)
  Gamma distribution with shape parameter A and scale parameter B. Constraints: A > 0, B > 0, X >= 0, 0 <= P < 1.

• PDF.LANDAU(X)
RV.LANDAU()
  Landau distribution.

• PDF.LAPLACE(X, A, B)
CDF.LAPLACE(X, A, B)
IDF.LAPLACE(P, A, B)
RV.LAPLACE(A, B)
  Laplace distribution with location parameter A and scale parameter B. Constraints: B > 0, 0 < P < 1.

• RV.LEVY(C, ɑ)
  Levy symmetric alpha-stable distribution with scale C and exponent ɑ. Constraints: 0 < ɑ <= 2.

• RV.LVSKEW(C, ɑ, β)
  Levy skew alpha-stable distribution with scale C, exponent ɑ, and skewness parameter β. Constraints: 0 < ɑ <= 2, -1 <= β <= 1.

• PDF.LOGISTIC(X, A, B)
CDF.LOGISTIC(X, A, B)
IDF.LOGISTIC(P, A, B)
RV.LOGISTIC(A, B)
  Logistic distribution with location parameter A and scale parameter B. Constraints: B > 0, 0 < P < 1.

• PDF.LNORMAL(X, A, B)
CDF.LNORMAL(X, A, B)
IDF.LNORMAL(P, A, B)
RV.LNORMAL(A, B)
  Lognormal distribution with parameters A and B. Constraints: A > 0, B > 0, X >= 0, 0 <= P < 1.

• PDF.NORMAL(X, μ, σ)
CDF.NORMAL(X, μ, σ)
IDF.NORMAL(P, μ, σ)
RV.NORMAL(μ, σ)
  Normal distribution with mean μ and standard deviation σ. Constraints: B > 0, 0 < P < 1. Three additional functions are available as shorthand:

  • CDFNORM(X)
    Equivalent to CDF.NORMAL(X, 0, 1).

  • PROBIT(P)
    Equivalent to IDF.NORMAL(P, 0, 1).

  • NORMAL(σ)
    Equivalent to RV.NORMAL(0, σ).

• PDF.NTAIL(X, A, σ)
RV.NTAIL(A, σ)
  Normal tail distribution with lower limit A and standard deviation σ. This distribution is a PSPP extension. Constraints: A > 0, X > A, 0 < P < 1.

• PDF.PARETO(X, A, B)
CDF.PARETO(X, A, B)
IDF.PARETO(P, A, B)
RV.PARETO(A, B)
  Pareto distribution with threshold parameter A and shape parameter B. Constraints: A > 0, B > 0, X >= A, 0 <= P < 1.

• PDF.RAYLEIGH(X, σ)
CDF.RAYLEIGH(X, σ)
IDF.RAYLEIGH(P, σ)
RV.RAYLEIGH(σ)
  Rayleigh distribution with scale parameter σ. This distribution is a PSPP extension. Constraints: σ > 0, X > 0.

• PDF.RTAIL(X, A, σ)
RV.RTAIL(A, σ)
  Rayleigh tail distribution with lower limit A and scale parameter σ. This distribution is a PSPP extension. Constraints: A > 0, σ > 0, X > A.

• PDF.T(X, DF)
CDF.T(X, DF)
IDF.T(P, DF)
RV.T(DF)
  T-distribution with DF degrees of freedom. The noncentral distribution takes an additional parameter ꟛ. Constraints: DF > 0, 0 < P < 1.

• PDF.T1G(X, A, B)
CDF.T1G(X, A, B)
IDF.T1G(P, A, B)
  Type-1 Gumbel distribution with parameters A and B. This distribution is a PSPP extension. Constraints: 0 < P < 1.

• PDF.T2G(X, A, B)
CDF.T2G(X, A, B)
IDF.T2G(P, A, B)
  Type-2 Gumbel distribution with parameters A and B. This distribution is a PSPP extension. Constraints: X > 0, 0 < P < 1.

• PDF.UNIFORM(X, A, B)
CDF.UNIFORM(X, A, B)
IDF.UNIFORM(P, A, B)
RV.UNIFORM(A, B)
  Uniform distribution with parameters A and B. Constraints: A <= X <= B, 0 <= P <= 1. An additional function is available as shorthand:

  • UNIFORM(B)
    Equivalent to RV.UNIFORM(0, B).

• PDF.WEIBULL(X, A, B)
CDF.WEIBULL(X, A, B)
IDF.WEIBULL(P, A, B)
RV.WEIBULL(A, B)
  Weibull distribution with parameters A and B. Constraints: A > 0, B > 0, X >= 0, 0 <= P < 1.

Discrete Distributions

The following discrete distributions are available:

• PDF.BERNOULLI(X)
CDF.BERNOULLI(X, P)
RV.BERNOULLI(P)
  Bernoulli distribution with probability of success P. Constraints: X = 0 or 1, 0 <= P <= 1.

• PDF.BINOM(X, N, P)
CDF.BINOM(X, N, P)
RV.BINOM(N, P)
  Binomial distribution with N trials and probability of success P. Constraints: integer N > 0, 0 <= P <= 1, integer X <= N.

• PDF.GEOM(X, N, P)
CDF.GEOM(X, N, P)
RV.GEOM(N, P)
  Geometric distribution with probability of success P. Constraints: 0 <= P <= 1, integer X > 0.

• PDF.HYPER(X, A, B, C)
CDF.HYPER(X, A, B, C)
RV.HYPER(A, B, C)
  Hypergeometric distribution when B objects out of A are drawn and C of the available objects are distinctive. Constraints: integer A > 0, integer B <= A, integer C <= A, integer X >= 0.

• PDF.LOG(X, P)
RV.LOG(P)
  Logarithmic distribution with probability parameter P. Constraints: 0 <= P < 1, X >= 1.

• PDF.NEGBIN(X, N, P)
CDF.NEGBIN(X, N, P)
RV.NEGBIN(N, P)
  Negative binomial distribution with number of successes parameter N and probability of success parameter P. Constraints: integer N >= 0, 0 < P <= 1, integer X >= 1.

• PDF.POISSON(X, μ)
CDF.POISSON(X, μ)
RV.POISSON(μ)
  Poisson distribution with mean μ. Constraints: μ > 0, integer X >= 0.