#### 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.