Continuous Distribution

Functions

Description

Parameters and Domain

@PBETACDF( A, B, X)

Cumulative Beta

A = alpha > 0

B = beta > 0

X ∈ (0,1)

@PBETAINV( A, B, X)

Inverse Beta

A = alpha > 0

B = beta > 0

X ∈ [0,1]

@PBETAPDF( A, B, X)

Beta PDF

A = alpha > 0

B = beta > 0

X ∈ (0,1)

@PCACYCDF( L, S, X)

Cumulative Cauchy

L = location

S = scale > 0

X a real

@PCACYINV( L, S, X)

Inverse Cauchy

L = location

S = scale > 0

X ∈ [0,1]

@PCACYPDF( L, S, X)

Cauchy PDF

L = location

S = scale > 0

X a real

@PCHISCDF( DF, X)

Cumulative Chi-Square

DF = degrees of freedom = a positive integer

X ≥ 0

@PCHISINV( DF, X)

Inverse Chi-Square

DF = degrees of freedom = a positive integer

X ∈ [0,1]

@PCHISPDF( DF, X)

Chi-Square PDF

DF = degrees of freedom = a positive integer

X ≥ 0

@PEXPOCDF( L, X)

Cumulative Exponential

L = lambda > 0

X ≥ 0

@PEXPOINV( L, X)

Inverse Exponential

L = lambda > 0

X ∈ [0,1]

@PEXPOPDF( L, X)

Exponential PDF

L = lambda > 0

X ≥ 0

@PFDSTCDF( DF1, DF2, X)

Cumulative F-Distribution

DF1,DF2 = degrees of freedom = a positive integer

X ≥ 0

@PFDSTINV( DF1, DF2, X)

Inverse F-Distribution

DF1,DF2 = degrees of freedom = a positive integer

X ∈ [0,1]

@PFDSTPDF( DF1, DF2, X)

F-Distribution PDF

DF1,DF2 = degrees of freedom = a positive integer

X ≥ 0

@PGAMMCDF( SC, SH, X)

Cumulative Gamma

SC = scale > 0

SH = shape > 0

X ≥ 0

@PGAMMINV( SC, SH, X)

Inverse Gamma

SC = scale > 0

SH = shape > 0

X ∈ [0,1]

@PGAMMPDF( SC, SH, X)

Gamma PDF

SC = scale > 0

SH = shape > 0

X ≥ 0

@PGMBLCDF( L, S, X)

Cumulative Gumbel

L = location

S = scale > 0

X a real

@PGMBLINV( L, S, X)

Inverse Gumbel

L = location

S = scale > 0

X ∈ [0,1]

@PGMBLPDF( L, S, X)

Gumbel PDF

L = location

S = scale > 0

X a real

@PLAPLCDF( L, S, X)

Cumulative Laplace

L = location

S = scale > 0

X a real

@PLAPLINV( L, S, X)

Inverse Laplace

L = location

S = scale > 0

X ∈ [0,1]

@PLAPLPDF( L, S, X)

Laplace PDF

L = location

S = scale > 0

X a real

@PLGSTCDF( L, S, X)

Cumulative Logistic

L = location

S = scale > 0

X a real

@PLGSTINV( L, S, X)

Inverse Logistic

L = location

S = scale > 0

X ∈ [0,1]

@PLGSTPDF( L, S, X)

Logistic PDF

L = location

S = scale > 0

X a real

@PLOGNCDF( M, S, X)

Cumulative Lognormal

M = mu

S = sigma > 0

X > 0

@PLOGNINV( M, S, X)

Inverse Lognormal

M = mu

S = sigma > 0

X ∈ [0,1]

@PLOGNPDF( M, S, X)

Lognormal PDF

M = mu

S = sigma > 0

X > 0

@PNORMCDF( M, S, X)

Cumulative Normal

M = mu

S = sigma > 0

X a real

@PNORMINV( M, S, X)

Inverse Normal

M = mu

S = sigma > 0

X ∈ [0,1]

@PNORMPDF( M, S, X)

Normal PDF

M = mu

S = sigma > 0

X a real

@PPRTOCDF( SC, SH, X)

Cumulative Pareto

SC = scale > 0

SH = shape > 0

X ≥ SC

@PPRTOINV( SC, SH, X)

Inverse Pareto

SC = scale > 0

SH = shape > 0

X ∈ [0,1]

@PPRTOPDF( SC, SH, X)

Pareto PDF

SC = scale > 0

SH = shape > 0

X ≥ SC

@PSMSTCDF( A, X)

Cumulative Symmetric Stable

A = alpha ∈ [0.2,2]

X a real

@PSMSTINV( A, X)

Inverse Symmetric Stable

A = alpha ∈ [0.2,2]

X ∈ [0,1]

@PSMSTPDF( A, X)

Symmetric Stable PDF

A = alpha ∈ [0.2,2]

X a real

@PSTUTCDF( DF, X)

Cumulative Student's t

DF = degrees of freedom = a positive integer

X a real

@PSTUTINV( DF, X)

Inverse Student's t

DF = degrees of freedom = a positive integer

X ∈ [0,1]

@PSTUTPDF( DF, X)

Student's t PDF

DF = degrees of freedom = a positive integer

X a real

@PTRIACDF( L, U, M, X)

Cumulative Triangular

L = lower limit

U = upper limit

M = mode

X ∈ [L,U]

@PTRIAINV( L, U, M, X)

Inverse Triangular

L = lower limit

U = upper limit

M = mode

X ∈ [0,1]

@PTRIAPDF( L, U, M, X)

Triangular PDF

L = lower limit

U = upper limit

M = mode

X ∈ [L,U]

@PUNIFCDF( L, U, X)

Cumulative Uniform

L = lower limit

U = upper limit

X ∈ [L,U]

@PUNIFINV( L, U, X)

Inverse Uniform

L = lower limit

U = upper limit

X ∈ [0,1]

@PUNIFPDF( L, U, X)

Uniform PDF

L = lower limit

U = upper limit

X ∈ [L,U]

@PWEIBCDF( SC, SH, X)

Cumulative Weibull

SC = scale > 0

SH = shape > 0

X ≥ 0

@PWEIBINV( SC, SH, X)

Inverse Weibull

SC = scale > 0

SH = shape > 0

X ∈ [0,1]

@PWEIBPDF( SC, SH, X)

Weibull PDF

SC = scale > 0

SH = shape > 0

X ≥ 0

Discrete Distribution

Functions

Description

Parameters

@PBTBNCDF( N, A, B, X)

Cumulative Beta Binomial

N = trials ∈ {0,1,...}

A = alpha ∈ (0,+inf)

B = beta ∈ (0,+inf)

X ∈ {0,1,...,N}

@PBTBNINV( N, A, B, X)

Beta Binomial Inverse

N = trials ∈ {0,1,...}

A = alpha ∈ (0,+inf)

B = beta ∈ (0,+inf)

X ∈ [0,1]

@PBTBNPDF( N, A, B, X)

Beta Binomial PDF

N = trials ∈ {0,1,...}

A = alpha ∈ (0,+inf)

B = beta ∈ (0,+inf)

X ∈ {0,1,...,N}

@PBINOCDF( N, P, X)

Cumulative Binomial

N = trials ∈ {0,1,...}

P = probability of success ∈ [0,1]

X ∈ {0,1,...,N}

@PBINOINV( N, P, X)

Inverse Binomial

N = trials ∈ {0,1,...}

P = probability of success ∈ [0,1]

X ∈ [0,1]

@PBINOPDF( N, P, X)

Binomial PDF

N = trials ∈  {0,1,...}

P = probability of success ∈ [0,1]

X ∈ {0,1,...,N}

@PGEOMCDF( P, X)

Cumulative Geometric

P = probability of success ∈ (0,1]

X ∈ {0,1,...}

@PGEOMINV( P, X)

Inverse Geometric

P = probability of success ∈ (0,1]

X ∈ [0,1]

@PGEOMPDF( P, X)

Geometric PDF

P = probability of success∈ (0,1]

X ∈ {0,1,...}

@PHYPGCDF( N, D, K, X)

Cumulative Hypergeometric

N = population ∈ {0,1,...}

D = number defective ∈ {0,1,...,N}

K = sample size ∈ {0,1,...,N}

X ∈ {max(0,D+K-N),...,min(D,K)}

@PHYPGINV( N, D, K, X)

Inverse Hypergeometric

N = population ∈ {0,1,...}

D = number defective ∈ {0,1,...,N}

K = sample size ∈ {0,1,...,N}

X ∈ [0,1]

@PHYPGPDF( N, D, K, X)

Hypergeometric PDF

N = population ∈ {0,1,...}

D = number defective ∈ {0,1,...,N}

K = sample size ∈ {0,1,...,N}

X ∈ {max(0,D+K-N),...,min(D,K)}

@PLOGRCDF( P, X)

Cumulative Logarithmic

P = p-factor ∈ (0,1)

X ∈ {0,1,...,N}

@PLOGRINV( P, X)

Inverse Logarithmic

P = p-factor ∈ (0,1)

X ∈ [0,1]

@PLOGRPDF(  P, X)

Logarithmic PDF

P = p-factor ∈ (0,1)

X ∈ {0,1,...,N}

@PNEGBCDF( R, P, X)

Cumulative Negative Binomial

R = number of failures ∈ (0,+inf)

P = probability of success ∈ (0,1)

X ∈ {0,1,...}

@PNEGBINV( R, P, X)

Inverse Negative Binomial

R = number of failures ∈ (0,+inf)

P = probability of success ∈ (0,1)

X ∈ [0,1]

@PNEGBPDF( R, P, X)

Negative Binomial PDF

R = number of failures ∈ (0,+inf)

P = probability of success ∈ (0,1)

X ∈ {0,1,...}

@PPOISCDF( L, X)

Cumulative Poisson

L = lambda ∈ (0,+inf)

X ∈ {0,1,...,N}

@PPOISINV( L, X)

Inverse Poisson

L = lambda ∈ (0,+inf)

X ∈ [0,1]

@PPOISPDF( L, X)

Poisson PDF

L = lambda ∈ (0,+inf)

X ∈ {0,1,...,N}