In the descriptions of the distributions described throughout the website, we have provided formulas for the distribution mean and variance. Real Statistics provides the following functions to carry out these calculations.
Worksheet Functions
Real Statistics Functions: The Real Statistics Resource Pack contains the following functions.
MEAN_DIST(dist, param1, param2, param3) = the mean of the distribution dist based on the listed parameters.
VAR_DIST(dist, param1, param2, param3) = the variance of the distribution dist based on the listed parameters.
Here, dist is a text string that specifies a distribution. The distributions that are currently supported are shown in Figure 1, as well as the values for the parameters.
| Distribution | dist | param1 | param2 | param3 |
| Normal | norm | μ | σ | |
| Log normal | lognorm | μ | σ | |
| Chi-square | chisq | df | ||
| t | t | df | ||
| F | f | df1 | df2 | |
| Binomial | binom | n | p | |
| Poisson | poisson | μ | ||
| Skellam | skellam | μ1 | μ2 | |
| Beta | beta | α | β | |
| Gamma | gamma | α | β | |
| Uniform | uniform | α | β | |
| PERT | pert | a | b | c |
| Triangular | triang | a | b | c |
| Weibull | weibull | β | α | |
| Exponential | expon | λ | ||
| Geometric | geom | p | ||
| Hypergeometric | hypgeom | n | k | m |
| Negative Binomial | negbinom | k | p | |
| Gumbel | gumbel | μ | β | |
| Logistic | logistic | μ | β | |
| Laplace | laplace | μ | β | |
| Pareto | pareto | α | m | |
| Inverse Chi-square | ichisq | df | ||
| Inverse Gamma | igamma | α | β |
Figure 1 – MEAN_DIST and VAR_DIST parameters
Examples
For example, the formula =MEAN_DIST(“beta”,3,4) returns the mean of a beta distribution with alpha parameter 3 and beta parameter 4. The text string is the one used by Excel or Real Statistics to return the cdf/pdf of the distribution (e.g. “chisq” for chi-square, “triang” for triangular, etc.). The order of the parameters is the same as that found in the Excel or Real Statistics function that returns the cdf/pdf.
References
Wikipedia (2020) List of probability distributions
https://en.wikipedia.org/wiki/List_of_probability_distributions
Hastings, N., Peacock, B. (2011) Statistical distributions. 4th Ed, Wiley
https://www.wiley.com/en-us/Statistical+Distributions%2C+4th+Edition-p-9780470390634