##### 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: PDF.CHISQ (x, df)
— Function: CDF.CHISQ (x, df)
— Function: SIG.CHISQ (x, df)
— Function: IDF.CHISQ (p, df)
— Function: RV.CHISQ (df)
— Function: NPDF.CHISQ (x, df, lambda)
— 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)
— Function: NPDF.F (x, df1, df2, lambda)
— Function: NCDF.F (x, df1, df2, lambda)

> 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.HALFNRM (x, a, b)
— Function: CDF.HALFNRM (x, a, b)
— Function: IDF.HALFNRM (p, a, b)
— Function: RV.HALFNRM (a, b)

> Half-normal distribution with location parameter a and shape parameter b. Constraints: b > 0, 0 < p < 1.

— Function: PDF.IGAUSS (x, a, b)
— Function: CDF.IGAUSS (x, a, b)
— Function: IDF.IGAUSS (p, a, b)
— Function: RV.IGAUSS (a, b)

> Inverse Gaussian distribution with parameters a and 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: CDF.SMOD (x, a, b)
— Function: IDF.SMOD (p, a, b)

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

— Function: CDF.SRANGE (x, a, b)
— Function: IDF.SRANGE (p, a, b)

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

— Function: PDF.T (x, df)
— Function: CDF.T (x, df)
— Function: IDF.T (p, df)
— Function: RV.T (df)
— Function: NPDF.T (x, df, lambda)
— Function: NCDF.T (x, df, lambda)

> 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.