The Andorville™ Distributions software is used to design and analyse probability distributions.
Probability distributions characterise the possible output values of a random process.
When the output can have a continuous range of values, the probability distribution can be represented by a probability density function (PDF).
When the output can only have a discrete set of values, the probability distribution can be represented by a probability mass function (PMF).
Cumulative distribution functions (CDFs) can also be used to represent continuous or discrete distributions.
The Andorville™ Distributions software can generate PDF, PMF and CDF data for a selection of continuous and discrete distributions.
The software contains tools to display charts of distributions, calculate statistical measures from a distribution,
generate random variable data and match the distribution parameters to a random variable data set.
The source code for the software can be downloaded from this GitHub page: ADVL_Distributions
If you have any questions or comments, contact me at
The software uses the Math.NET Numerics distributions library to calculate the PDF, PMF, CDF and inverse CDF values.
The table below shows the distributions supported.
| Distribution Name | Continuity | No. Parameters | Description |
|---|---|---|---|
| Bernoulli | Discrete | 1 | A discrete probability distribution of a random variable that takes the value of 1 with probability p and the value of 0 with probability q = 1 - p. |
| Beta | Continuous | 2 | A continuous probability distribution with two parameters. Defined on the interval 0 to 1 inclusive. Used to model a probability distribution of probabilities. |
| Beta Scaled | Continuous | 4 | A version of the Beta distribtion with an additional two parameters that extend the range of the distribution beyond the 0 to 1 range of the Beta distribution. |
| Binomial | Discrete | 2 | The discrete probability distribution of the number of successes in a sequence of independent experiments with binary outcomes. The two distribution parameter are n (number of experiments) and p (the probability of success). |
| Burr | Continuous | 3 | Three parameter continuous distribution with a flexible shape and controllable scale. |
| Cauchy | Continuous | 2 | The distribution of the x intercept of a ray emitted from a point. The mean and variance of this distribution do not exist. |
| Chi | Continuous | 1 | The distribution of the positive square root of the sum of squares of a set of independent random variables. |
| Chi Squared | Continuous | 1 | The sum of the squares of k independent standard normal random variables. |
| Continuous Uniform | Continuous | 2 | Distribution corresponding to an experiment with arbitrary outcomes between certain bounds. |
| Conway-Maxwell-Poisson | Discrete | 2 | A generalization of the Poisson, Geometric and Bernoulli distributions. |
| Discrete Uniform | Discrete | 2 | The probability distribution for a finite number of values equally likely to be observed. |
| Erlang | Continuous | 2 | The Erlang distribution is a generalization of the exponential distribution. |
| Exponential | Continuous | 1 | The distribution of the time between events that occur continuously and independently at a constant average rate (a Poisson point process). |
| Fisher-Snedecor | Continuous | 2 | Used for hypothesis testing with the comparison of variances between two samples. Also used to test if one model is statistically better than another. |
| Gamma | Continuous | 2 | A continuous, positive-only unimodal distribution. |
| Geometric | Discrete | 1 | The probability distribution of the number of Bernoulli trials needed to get one success. A Bernoulli trial has two possible outcomes, success or failure, with a constant probability of success. |
| Hypergeometric | Discrete | 3 | Distribution describing the probability of k successes in n draws, without replacement. |
| Inverse Gamma | Continuous | 2 | The reciprocal of the Gamma distribution. |
| Inverse Gaussian | Continuous | 2 | An exponential distribution with a single mode and a long tail. |
| Laplace | Continuous | 2 | The distribution of differences between two independent random variables with identical exponential distributions. Unimodal (one peak) and symmetrical. The peak is sharper than the normal distribution. |
| Log Normal | Continuous | 2 | The probability distribution of a random variable whose logarithm is normally distributed. A log normal distribution is the result of the product of of a large number of independent, identically distributed variables. |
| Negative Binomial | Discrete | 2 | The number of failures in a sequence of Bernoulli trials before a specified number of successes occurs. (The distribution is described as "negative" because the number of failures is counted instead of the number of successes.) |
| Normal | Continuous | 2 | The most common distribution function for independent, randomly generated variables. The distribution is symmetrical, with a bell shape and an equal mean and median located at the center of the distribution. |
| Pareto | Continuous | 2 | A power-law probability distribution. |
| Poisson | Discrete | 1 | The probability of a given number of events occurring in a fixed interval of time or space if the independent events occur with a known constant mean rate. |
| Rayleigh | Continuous | 1 | A continuous probability distribution for non-negative valued random variables. |
| Skewed Generalized Error | Continuous | 4 | A special case of the Skewed Generalized T distribution (where parameter q is set to + infinity). |
| Skewed Generalized T | Continuous | 5 | A highly flexible five parameter univariate distribution. |
| Stable | Continuous | 4 | A distribution where the linear combination of two independent random variables with this distribution also has the same distribution. Can be considered a generaization of the Normal distribution. |
| Student's T | Continuous | 3 | The distribution was published by William Gosset in 1908 under the pseudonym "Student". Similar to the Normal distribution but with greater chance of extreme values (fatter tails). |
| Triangular | Continuous | 3 | A continuous probability distribution with a lower limit, an upper limit and a mode within these limits. |
| Truncated Pareto | Continuous | 3 | A power-law probability distribution with upper and lower bounds. |
| Weibull | Continuous | 2 | The Weibull distribution is versatile because of the shape parameter. |
| Zipf | Discrete | 2 | A Zipf distribution is used to model data based on Zipf's law, where the nth common item occurs 1/n times as often as the most common item. |
Supported probability functions:
Probability Density Function (PDF)
Natural Log of Probability Density Function (Ln PDF)
Probability Mass Function (PMF)
Natural Log of Probability Mass Function (Ln PMF)
Cumulative Distribution Function (CDF)
Reverse Cumulative Distribution Function (Rev CDF)
Inverse Cumulative Distribution Function (Inv CDF)
Inverse Reverse Cumulative Distribution Function (Inv Rev CDF)
Charting
The software generates a table of sampled probability functions corresponding to specified probability distribution parameters.
This data is used to display charts of the distribution.
The chart can display multiple distributions.
Areas can be shaded on a PDF chart between specified random variable values.
The following points can be annotated on all probability functions:
mean, median, mode, standard deviation and any random variable value or probability value.
Distribution data and charts are updated immediately when the distribution paramters are adjusted.
This provides feedback on the effect of the adjustment.
Distribution Sample Generation
Single samples or sets of multiple samples can be generated from a specified probability distribution model.
Most Likely Parameter Estimation
The most likely distribution parameters can be estimated from a set of values sampled from a random process.