#### 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.