#### 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.VBNOR (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.