How it works
Four steps, in the order the page asks for them.
What the calculator provides
The thirteen distributions
Grouped the way the workspace groups them. Each one gives the density or mass function, the cumulative function, and the quantile behind a probability you specify.
Continuous distributions
- Normal
- Mean and standard deviation, with the chart range set in multiples of sigma.
- Uniform
- A minimum and a maximum, with constant density between them.
- Exponential
- A single rate parameter, for waiting times between events.
- Log-Normal
- Location and scale on the log scale, for right-skewed quantities.
- Weibull
- Shape and scale, the usual choice for time-to-failure work.
- Beta
- Alpha and beta on the unit interval, for proportions and rates.
Discrete distributions
- Binomial
- Trials and success probability, with exact, cumulative and interval queries.
- Poisson
- A rate parameter, for counts in a fixed window.
- Geometric
- A success probability, for the number of trials until the first success.
- Hypergeometric
- Population size, success states and sample size, for sampling without replacement.
Test distributions
- Chi-Square
- Degrees of freedom, for goodness-of-fit and contingency tests.
- F
- Numerator and denominator degrees of freedom, for variance ratios and ANOVA.
- t
- Degrees of freedom, for means and regression coefficients from small samples.
How the questions are phrased
The same three or four questions, on every distribution.
- Continuous distributions answer the probability below a value, the probability between two values, and the value that sits at a probability you specify.
- Discrete distributions add the probability of an exact count, and draw the mass function as spikes with a step cumulative function rather than smooth curves.
- Asking for the value behind a probability is what produces a critical value, which is why the chi-square, F and t calculators sit in their own group.
- Random samples are drawn from the distribution as parameterised, summarised with a histogram and statistics, and can be copied one value per row for pasting into a worksheet.
Common questions
Which distributions are included?
Normal, uniform, exponential, log-normal, Weibull and beta among the continuous ones; binomial, Poisson, geometric and hypergeometric among the discrete ones; and chi-square, F and t for hypothesis testing.
Can I get a critical value rather than a probability?
Yes. Choose the option to find the value for a given probability, and the calculator inverts the cumulative function for you. That is how you obtain a t, chi-square or F critical value at a chosen alpha.
Does it show the distribution, not just the number?
Yes. Each calculator draws the density and cumulative functions, separately or combined, and shades the region the probability refers to.
Can I generate random data from a distribution?
Yes. Any of the thirteen can generate a random sample, shown as a table with a histogram and summary statistics, and copied one value per row so it pastes into Excel as a column.