7.7.10.1 Continuous Distributions

The following continuous distributions are available:

Function: __PDF.BETA ( x) Function: __CDF.BETA ( x, a, b) Function: __IDF.BETA ( p, a, b) Function: __RV.BETA ( a, b) Function: __NPDF.BETA ( x, a, b, lambda) Function: __NCDF.BETA ( x, a, b, lambda)

Beta distribution with shape parameters a and b. The noncentral distribution takes an additional parameter lambda. Constraints: a > 0, b > 0, lambda >= 0, 0 <= x <= 1, 0 <= p <= 1.

Function: __PDF.BVNOR ( x0, x1, rho) Function: __CDF.BVNOR ( x0, x1, rho)

Bivariate normal distribution of two standard normal variables with correlation coefficient rho. Two variates x0 and x1 must be provided. Constraints: 0 <= rho <= 1, 0 <= p <= 1.

Function: __PDF.CAUCHY ( x, a, b) Function: __CDF.CAUCHY ( x, a, b) Function: __IDF.CAUCHY ( p, a, b) Function: __RV.CAUCHY ( a, b)

Cauchy distribution with location parameter a and scale parameter b. Constraints: b > 0, 0 < p < 1.

Function: __CDF.CHISQ ( x, df) Function: __SIG.CHISQ ( x, df) Function: __IDF.CHISQ ( p, df) Function: __RV.CHISQ ( df) Function: __NCDF.CHISQ ( x, df, lambda)

Chi-squared distribution with df degrees of freedom. The noncentral distribution takes an additional parameter lambda. Constraints: df > 0, lambda > 0, x >= 0, 0 <= p < 1.

Function: __PDF.EXP ( x, a) Function: __CDF.EXP ( x, a) Function: __IDF.EXP ( p, a) Function: __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.

Function: __PDF.XPOWER ( x, a, b) Function: __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.

Function: __PDF.F ( x, df1, df2) Function: __CDF.F ( x, df1, df2) Function: __SIG.F ( x, df1, df2) Function: __IDF.F ( p, df1, df2) Function: __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 lambda. Constraints: df1 > 0, df2 > 0, lambda >= 0, x >= 0, 0 <= p < 1.

Function: __PDF.GAMMA ( x, a, b) Function: __CDF.GAMMA ( x, a, b) Function: __IDF.GAMMA ( p, a, b) Function: __RV.GAMMA ( a, b)

Gamma distribution with shape parameter a and scale parameter b. Constraints: a > 0, b > 0, x >= 0, 0 <= p < 1.

Function: __PDF.LANDAU ( x) Function: __RV.LANDAU ()

Landau distribution.

Function: __PDF.LAPLACE ( x, a, b) Function: __CDF.LAPLACE ( x, a, b) Function: __IDF.LAPLACE ( p, a, b) Function: __RV.LAPLACE ( a, b)

Laplace distribution with location parameter a and scale parameter b. Constraints: b > 0, 0 < p < 1.

Function: __RV.LEVY ( c, alpha)

Levy symmetric alpha-stable distribution with scale c and exponent alpha. Constraints: 0 < alpha <= 2.

Function: __RV.LVSKEW ( c, alpha, beta)

Levy skew alpha-stable distribution with scale c, exponent alpha, and skewness parameter beta. Constraints: 0 < alpha <= 2, -1 <= beta <= 1.

Function: __PDF.LOGISTIC ( x, a, b) Function: __CDF.LOGISTIC ( x, a, b) Function: __IDF.LOGISTIC ( p, a, b) Function: __RV.LOGISTIC ( a, b)

Logistic distribution with location parameter a and scale parameter b. Constraints: b > 0, 0 < p < 1.

Function: __PDF.LNORMAL ( x, a, b) Function: __CDF.LNORMAL ( x, a, b) Function: __IDF.LNORMAL ( p, a, b) Function: __RV.LNORMAL ( a, b)

Lognormal distribution with parameters a and b. Constraints: a > 0, b > 0, x >= 0, 0 <= p < 1.

Function: __PDF.NORMAL ( x, mu, sigma) Function: __CDF.NORMAL ( x, mu, sigma) Function: __IDF.NORMAL ( p, mu, sigma) Function: __RV.NORMAL ( mu, sigma)

Normal distribution with mean mu and standard deviation sigma. Constraints: b > 0, 0 < p < 1. Three additional functions are available as shorthand:

Function: __CDFNORM ( x)

Equivalent to CDF.NORMAL(x, 0, 1).

Function: __PROBIT ( p)

Equivalent to IDF.NORMAL(p, 0, 1).

Function: __NORMAL ( sigma)

Equivalent to RV.NORMAL(0, sigma).

Function: __PDF.NTAIL ( x, a, sigma) Function: __RV.NTAIL ( a, sigma)

Normal tail distribution with lower limit a and standard deviation sigma. This distribution is a PSPP extension. Constraints: a > 0, x > a, 0 < p < 1.

Function: __PDF.PARETO ( x, a, b) Function: __CDF.PARETO ( x, a, b) Function: __IDF.PARETO ( p, a, b) Function: __RV.PARETO ( a, b)

Pareto distribution with threshold parameter a and shape parameter b. Constraints: a > 0, b > 0, x >= a, 0 <= p < 1.

Function: __PDF.RAYLEIGH ( x, sigma) Function: __CDF.RAYLEIGH ( x, sigma) Function: __IDF.RAYLEIGH ( p, sigma) Function: __RV.RAYLEIGH ( sigma)

Rayleigh distribution with scale parameter sigma. This distribution is a PSPP extension. Constraints: sigma > 0, x > 0.

Function: __PDF.RTAIL ( x, a, sigma) Function: __RV.RTAIL ( a, sigma)

Rayleigh tail distribution with lower limit a and scale parameter sigma. This distribution is a PSPP extension. Constraints: a > 0, sigma > 0, x > a.

Function: __PDF.T ( x, df) Function: __CDF.T ( x, df) Function: __IDF.T ( p, df) Function: __RV.T ( df)

T-distribution with df degrees of freedom. The noncentral distribution takes an additional parameter lambda. Constraints: df > 0, 0 < p < 1.

Function: __PDF.T1G ( x, a, b) Function: __CDF.T1G ( x, a, b) Function: __IDF.T1G ( p, a, b)

Type-1 Gumbel distribution with parameters a and b. This distribution is a PSPP extension. Constraints: 0 < p < 1.

Function: __PDF.T2G ( x, a, b) Function: __CDF.T2G ( x, a, b) Function: __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.

Function: __PDF.UNIFORM ( x, a, b) Function: __CDF.UNIFORM ( x, a, b) Function: __IDF.UNIFORM ( p, a, b) Function: __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:

Function: __UNIFORM ( b)

Equivalent to RV.UNIFORM(0, b).

Function: __PDF.WEIBULL ( x, a, b) Function: __CDF.WEIBULL ( x, a, b) Function: __IDF.WEIBULL ( p, a, b) Function: __RV.WEIBULL ( a, b)

Weibull distribution with parameters a and b. Constraints: a > 0, b > 0, x >= 0, 0 <= p < 1.