- probability density(mass) function (pdf,pmf) 
   - cumulative distribution function (cdf)
   - inverse
   - graph of pdf/pmf and cdf
   - random number generator (rng)

Probability Distribution Functions 

type threshold non
Beta continuous   X X
Cauchy continuous     X
Chi2 continuous   X X
Exponential continuous X    X 
F continuous   X X
Gamma continuous X X X
Gumbel continuous     X
Laplace continuous      X 
Logistic continuous     X
LogLogistic continuous X    X 
LogNormal continuous X   X
Normal continuous     X
t continuous   X X
triangular continuous     X
Uniform continuous      X 
Weibull continuous X    X 
geometric discrete      
binomial discrete      
negative binomial discrete      
poisson discrete      
hypergeometric discrete      
neg. hypergeometric discrete      
Gamma-Poisson mixed      
Beta-Binomial mixed      
Beta-NegativeBinomial mixed      

Random Number Generator

   - MT19937   (see Links)
   - WELL512a (see Links)
   - WELL1024a (see Links)
   - WELL19937a (see Links)
   - WELL44497a (see Links)
   - Law, A. M. and Kelton, W. D., Simulation Modeling and Analysis, McGraw-Hill pp. 430
   - Brian Wichman, David Hill, Algorithm AS 183 (Excel's RAND-Function)
   - Pierre L'Ecuyer,Communications of the ACM, Volume 31, No. 6, June 1988, pp. 742-751
   - VBA's RND-function


   - show formular of distribution function in user form
   - input parameter value via keyboard or from worksheet (click onto cell in worksheet containing the value then double click textfield in userform)    
   - output results to message box or worksheet
   - input/output a range of percentile (or cum. probability) values from/to worksheet    

   - generate graphs of pdf/pmf (left vertical axis) and cdf (right vertical axis). The colored area under the pdf is generated by laying a shape over the chart.
     Changing the min/max axis causes a missfit of shape and chart. The sub to generate the shape can be found on Jon Peltier's website. See Links. 

   - define a SEED (starting value) for the rng. If a seed is defined the same set of random numbers will be generated each time the procedure is executed. If SEED is empty
     a new set of random numbers will be generated.
   - generate integer values 1,2,3,...,n in a random order


   - Threshold (δ): lower limit for skewed (tail to the right) distributions. Can take negative values. Allows to shift distribution "away" from 0.
   - Non Centrality Parameter (θ): additional parameter to change shape of distribution
   - Order Statistics: determines pdf/cdf/inverse of the r-th smallest of n random variables all following the predefined distribution

   - Inverse transform sampling is used to generate random numbers following a predefined distribution
   - For the non central t-distribution accuracy tends to be poor if the percentile is negative


Input userform with formulars, result to messagebox

Input range of values from worksheet and Output results to worksheet

pdf/cdf of beta distribution with predefined parameter values



pmf/cdf of beta binomial distribution with predefined parameter values 

Random Numbers generated with WELL512a that follow a Weibull distribution with predefined parameter values

Random Integers generated with MT19937