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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.