Spreadsheet Formulas - Distributions and Their Functions
Statistica provides a predefined broad selection of distribution functions, their integrals and inverse distribution functions that can be used in spreadsheet formulas like all other functions.
Below is a list of all available distributions (parameters are given in parentheses).
| Distribution | Density or Probability Function | Distribution Function | Inverse Distribution Function | |
| Beta | Beta Distribution of x, where nu and omega are shape parameters, respectively. | beta (x,υ,ω) | ibeta (x,υ,ω) | vbeta (x,υ,ω) |
| Binom | Binomial Distribution of x, where p is the probability of success at each trial and n is the number of trials. | binom (x,p,n) | ibinom (x,p,n) | |
| Cauchy | Cauchy Distribution of x, where eta and theta are the location (median) and scale parameters, respectively. | cauchy (x,η,θ) | icauchy (x,η,θ) | vcauchy (x,η,θ) |
| Chi2 | Chi-square Distribution of x, where nu is the degrees of freedom. | chi2 (x,υ) | ichi2 (x,υ) | vchi2 (x,υ) |
| Expon | Exponential Distribution of x, where lambda is the scale parameter. | expon (x,λ) | iexpon (x,λ) | vexpon (x,λ) |
| Extreme | Extreme value (Gumbel) Distribution of x, where a and b are the location and scale parameters, respectively. | extreme (x,a,b) | iextreme (x,a,b) | vextreme (x,a,b) |
| F | F Distribution of x, where nu and omega are the degrees of freedom. | F (x,υ,ω) | iF (x,υ,ω) | vF (x,υ,ω) |
| Gamma | Gamma Distribution of x, where c is the shape parameter. | gamma (x,c) | igamma (x,c) | vgamma (x,c) |
| Geom | Geometric Distribution of x, where p is the probability of occurrence. | geom (x,p) | igeom (x,p) | |
| GEV | Generalized Extreme Value distribution | GEV(x, location, scale, shape) | ||
| GPD | Generalized Pareto distribution | GPD(x, threshold, scale, shape) | ||
| Hypergeometric | Hypergeometric distribution, where M is the number of items, N is the total population size, and n is the sample size | Hypergeometric(x,M,N,n) | ||
| IBeta | Integral of Beta distribution of x, where nu and omega are shape parameters, respectively. | IBeta(x, nu, omega) | ||
| IBinom | Integral of Binomial distribution of x, where p is the probability of success at each trial and n is the number of trials. | IBinom(x, p, n) | ||
| ICauchy | Integral of Cauchy distribution of x, where eta and theta are the location (median) and scale parameters, respectively. | ICauchy(x, eta, theta) | ||
| IChi2 | Integral of Chi-square distribution of x, where nu is the degrees of freedom. | IChi2(x, nu) | ||
| IExpon | Integral of Exponential distribution of x, where lambda is the scale parameter. | IExpon(x, lambda) | ||
| IExtreme | Integral of Extreme value (Gumbel) distribution of x, where a and b are the location and scale parameters, respectively. | IExtreme(x, a, b) | ||
| IF | Integral of F distribution of x, where nu and omega are the degrees of freedom. | IF(x, nu, omega) | ||
| IGamma | Integral of Gamma distribution of x, where c is the shape parameter. | IGamma(x, c) | ||
| IGeom | Integral of Geometric distribution of x, where p is the probability of occurrence. | IGeom(x, p) | ||
| IGEV | Integral of Generalized Extreme Value distribution | IGEV(x, location, scale, shape) | ||
| IGPD | Integral of Generalized Pareto distribution | IGPD(x, threshold, scale, shape) | ||
| IHypergeometric | hypergeometric cumulative distribution, where M is the number of items, N is the total population size, and n is the sample size | IHypergeometric(x,M,N,n) | ||
| iJohnson( | Johnson Distribution computes the integral of the Johnson distribution (curve) defined by parameters JohnsonType, Gamma, Delta, Lambda, and Xi, for the Johnson variate value x. | |||
| iJohnsonFromMoments( | Johnson From Moments computes the integral of the Johnson distribution (curve) defined by moments Mean, StandardDeviation, Skewness, and Kurtosis, for the Johnson variate value x. Note that this can be computationally expensive, because the actual parameters for the respective best-fitting Johnson curve has to be computed from the moments, every time this function is invoked. | |||
| ILaplace( | Laplace Distribution
Integral of Laplace distribution of x, where a and b are the mean and scale parameter, respectively. |
laplace (x,a,b) | ilaplace (x,a,b) | vlaplace (x,a,b) |
| ILogis( | Logistic Distribution
Integral of Logistic distribution of x, where a and b are the mean and scale parameter, respectively. |
logis (x,a,b) | ilogis (x,a,b) | vlogis (x,a,b) |
| ILognorm( | Lognormal Distribution
Integral of Log-normal distribution of x, where mu and sigma are the scale and shape parameters, respectively. |
lognorm (x,μ,σ) | ilognorm (x,μ,σ) | vlognorm (x,μ,σ) |
| INoncentralChi2( | INoncentralChi2 | INoncentralChi2(x,df,ncp) | ||
| INoncentralF( | Noncentral Chi-square cumulative distribution function with degrees of freedom and noncentrality parameter df and ncp respectively | |||
| INoncentralT( | Noncentral Student's t Distribution
Noncentral t cumulative density function |
NoncentralT(x,df, ncp) | INoncentralT(x,df, ncp) | VNoncentralT(prob, df, ncp) |
| INormal( | Normal Distribution
Integral of Normal distribution of x, where mu and sigma are the mean and standard deviation, respectively. |
normal (x,μ,σ) | inormal (x,μ,σ) | vnormal (x,μ,σ) |
| Integral of Pareto distribution of x, where c is the shape parameter. | Pareto Distribution
Integral of Pareto distribution of x, where c is the shape parameter. |
pareto (x,c) | ipareto (x,c) | vpareto (x,c) |
| IPoisson | Poisson Distribution
Integral of Poisson distribution of x, where lambda is the expected value of x (the mean). |
poisson (x,λ) | ipoisson (x,λ) | |
| IRayl | Rayleigh Distribution
Integral of Rayleigh distribution of x, where b is the scale parameter. |
rayleigh (x,b) | irayleigh (x,b) | vrayleigh (x,b) |
| IStudent | Student's t Distribution
Integral of Student's t distribution of x, with df degrees of freedom. |
student (x,df) | istudent (x,df) | vstudent (x,df) |
| ITweedie | Tweedie cumulative density function | ITweedie(y, power, mu, phi) | ||
| IWeibull | Weibull Distribution | weibull (x,b,c,θ) | iweibull (x,b,c,θ) | vweibull (x,b,c,θ) |
| Johnson | Computes the density of the Johnson distribution (curve) defined by parameters JohnsonType, Gamma, Delta, Lambda, and Xi, for the Johnson variate value x | Johnson( x, JohnsonType, Gamma, Delta, Lambda, Xi) | ||
| JohnsonFromMoments | Computes the density of the Johnson distribution (curve) defined by moments Mean, StandardDeviation, Skewness, and Kurtosis, for the Johnson variate value x. Note that this can be computationally expensive, because the actual parameters for the respective best-fitting Johnson curve will have to be computed from the moments, every time this function is invoked. | JohnsonFromMoments( x, Mean, StandardDeviation, Skewness, Kurtosis) | ||
| Laplace | Laplace distribution of x, where a and b are the mean and scale parameter, respectively. | Laplace(x, a, b) | ||
| Logis | Logistic distribution of x, where a and b are the mean and scale parameter, respectively. | Logis(x, a, b) | ||
| Lognorm | Log-normal distribution of x, where mu and sigma are the scale and shape parameters, respectively. | Lognorm(x, mu, sigma) | ||
| NoncentralChi2 | Noncentral Chi-square probability density function with degrees of freedom and noncentrality parameter df and ncp respectively | NoncentralChi2(x,df,ncp) | ||
| NoncentralF | Noncentral f probability density function with degrees of freedom and noncentrality parameter df1, df2, and ncp respectively | NoncentralF(x,df1,df2,ncp) | ||
| NoncentralT | Noncentral t probability density function | NoncentralT(y, df, ncp) | ||
| Normal | Normal distribution of x, where mu and sigma are the mean and standard deviation, respectively. | Normal(x, mu, sigma) | ||
| Pareto | Pareto distribution of x, where c is the shape parameter. | Pareto(x, c) | ||
| Poisson | Poisson distribution of x, where lambda is the shape parameter. | Poisson(x, lambda) | ||
| QC_C4 | Quality Control Function C4 of x | QC_C4(x) | ||
| QC_D2 | Quality Control Function D2 of x | QC_D2(x) | ||
| QC_D3 | Quality Control Function D3 of x | QC_D3(x) | ||
| Rayl | Rayleigh distribution of x, where b is the scale parameter. | Rayl(x, b) | ||
| RndChi2 | Chi-square random number generator | RndChi2(df) | ||
| RndExp | Exponential random number generator | RndExp(lambda) | ||
| RndGamma | Gamma random number generator | RndGamma(shape,scale) | ||
| RndHypergeometric | hypergeometric random number generator, where M is the number of items, N is the total population size, and n is the sample size | RndHypergeometric(x,M,N,n) | ||
| RndNoncentralT | Noncentral t random number generator | RndNoncentralT(df, ncp) | ||
| RndTweedie | Tweedie random number generator | RndTweedie(power, mu, phi) | ||
| Student | Student's t distribution of x, with df degrees of freedom. | Student(x, df) | ||
| Tweedie | Tweedie probability density function | Tweedie(y, power, mu, phi) | ||
| VBeta | Inverse function for Beta distribution of x, where nu and omega are shape parameters, respectively. | VBeta(x, nu, omega) | ||
| VBinom | Binomial inverse cumulative distribution, where pi is the probability of success at each trial and n is the number of trials. | VBinom(p, pi, n) | ||
| VCauchy | Inverse function for Cauchy distribution of x, where eta and theta are the location (median) and scale parameters, respectively. | VCauchy(x, eta, theta) | ||
| VChi2 | Inverse function for Chi-square distribution of x, where nu is the degrees of freedom. | VChi2(x, nu) | ||
| VExpon | Inverse function for Exponential distribution of x, where lambda is the scale parameter. | VExpon(x, lambda) | ||
| VExtreme | Inverse function for Extreme value (Gumbel) distribution of x, where a and b are the location and scale parameters, respectively. | VExtreme(x, a, b) | ||
| VF | Inverse function for F distribution of x, where nu and omega are the degrees of freedom. | VF(x, nu, omega) | ||
| VGamma | Inverse function for Gamma distribution of x, where c is the shape parameter. | VGamma(x, c) | ||
| VGEV | Inverse function of Generalized Extreme Value distribution | VGEV(x, location, scale, shape) | ||
| VGPD | Inverse function of Generalized Pareto distribution | VGPD(x, threshold, scale, shape) | ||
| VHypergeometric | hypergeometric inverse cumulative distribution, where M is the number of items, N is the total population size, and n is the sample size | VHypergeometric(x,M,N,n) | ||
| vJohnson | Computes the inverse integral (Johnson variate value) of the Johnson distribution (curve) defined by parameters JohnsonType, Gamma, Delta, Lambda, and Xi, for the probability value p. | vJohnson( p, JohnsonType, Gamma, Delta, Lambda, Xi) | ||
| vJohnsonFromMoments | Computes the inverse integral (Johnson variate value) of the Johnson distribution (curve) defined by moments Mean, StandardDeviation, Skewness, and Kurtosis, for the probability value p. Note that this can be computationally expensive, because the actual parameters for the respective best-fitting Johnson curve will have to be computed from the moments, every time this function is invoked. | vJohnsonFromMoments( p, Mean, StandardDeviation, Skewness, Kurtosis) | ||
| VLaplace | Inverse function for Laplace distribution of x, where a and b are the mean and scale parameter, respectively. | VLaplace(x, a, b) | ||
| VLogis | Inverse function for Logistic distribution of x, where a and b are the mean and scale parameter, respectively. | VLogis(x, a, b) | ||
| VLognorm | Inverse function for Log-normal distribution of x, where mu and sigma are the scale and shape parameters, respectively. | VLognorm(x, mu, sigma) | ||
| VNoncentralChi2 | Noncentral Chi-square inverse cumulative distribution function or quantile function with degrees of freedom and noncentrality parameter df and ncp respectively | VNoncentralChi2(p,df,ncp) | ||
| VNoncentralF | Noncentral f inverse cumulative distribution function or quantile function with degrees of freedom and noncentrality parameter df1, df2, and ncp respectively | VNoncentralF(p,df1,df2,ncp) | ||
| VNoncentralT | Noncentral T inverse cumulative distribution | VNoncentralT(y, df, ncp) | ||
| VNormal | Inverse function for Normal distribution of x, where mu and sigma are the mean and standard deviation, respectively. | VNormal(x, mu, sigma) | ||
| VPareto | Inverse function for Pareto distribution of x, where c is the shape parameter. | VPareto(x, c) | ||
| VPoisson | Poisson inverse cumulative distribution, where lambda is the shape parameter. | VPoisson(x, lambda) | ||
| VRayl | Inverse function for Rayleigh distribution of x, where b is the scale parameter. | VRayl(x, b) | ||
| VStudent | Inverse function for Student's t distribution of x, with df degrees of freedom. | VStudent(x, df) | ||
| VTweedie | Tweedie inverse cumulative distribution function | VTweedie(p, power, mu, phi) | ||
| VWeibull | Inverse function for Weibull distribution of x, where b, c and theta are the scale, shape, and threshold (location) parameters, respectively. | VWeibull(x, b, c, theta) | ||
| Weibull | Weibull distribution of x, where b, c and theta are the scale, shape, and threshold (location) parameters, respectively. | Weibull(x, b, c, theta) |
See also: Spreadsheet Formulas - Overview, Spreadsheet Formulas - Syntax Summary, Spreadsheet Formulas - Examples, Spreadsheet Formulas - Predefined Functions.
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