Spreadsheet input has been replaced by Carlo — it works on the same principle but is redesigned from the ground up.
Transition from Dagger's format with just one change: add the header UseCarlo to the column containing the distribution families (e.g. Normal, Uniform, ...).
Carlo will try to guess the output variables(s) you are interested in — if the result isn't what you expected (an error, or too many / too few variables), you can explicitly specify the output(s) with the keyword Output.

Why you'll love Carlo:
• More flexible input format
• Interactive — histograms update as you edit the spreadsheet
(Bonus: this lets you collaborate in real time)
• ≈1000x faster — sensitivity analysis runs in an instant
• Overhauled UI with dozens of new features
• No need to manually type in result cell coordinate
• Supports multiple result variables
!

This greatly increases the runtime if you have many inputs with uncertainty.

If you:

1. Take an existing spreadsheet (works with Google Sheets, OneDrive, or a direct URL to any `.xlsx` file)
2. Add columns to specify probability distributions for (some) variables using a simple format

Then:

1. Your calculation is run as a Monte Carlo simulation
2. The results are displayed on this website.

### Input format

Each of the cells the result depends on corresponds to a variable (or 'node') in our calculation. For each variable, you can optionally supply a name and/or a probability distribution. This information must be given in the cells to the left and right of the variable cell.

#### Probability Distribution

Input probability distributions must be specified in the columns to the right.

The first cell to the right contains a string for the distribution family. This should be left blank for a deterministic variable. Options are:

Family Quantiles Notes
`Normal` `mean` `std` 2
`LogNormal` `mu` `sigma` 2 Be careful, `mu` and `sigma` are not the mean and standard deviation of the distribution.
`Uniform` `a` `b` 2 `a` need not be less than `b`
`PERT` `min` `mode` `max` `[lambda]` Like the triangular, but a smoother shape (Wikipedia)

The optional parameter `lambda` (default: 4) controls the weight given to the mode. Values of `lambda < 4` have the effect of flattening the density curve.
`Beta` `alpha` `beta` 2
`LogUniform` `a` `b` 2 `a` need not be less than `b`
`Bernoulli` `p`
`Discrete` `x_1` `p_1` `x_2` `p_2` ... Generic discrete distribution over any finite set of values
`TwoPieceUniform` `min` `sep` `max` `[psep]` A piecewise uniform distribution with two pieces: a left piece from `min` to `sep`, and a right piece from `sep` to `max`.

By default, each piece has 0.5 probability mass. If the optional parameter `psep` is supplied, it controls the probability of the left piece, i.e. the value of the CDF at `sep`.

The family is not case-sensitive.

A distribution's parameters can be specified in one of two ways: explicitly as parameters, or via quantiles.

##### A. Via quantiles

To the right of the distribution family, the next 1 or more columns specify the quantiles. The expected format is as follows:

• For each quantile column, the column header (row 1) must be a string composed of the character `p` followed by 1 or 2 digits representing integer percentiles between 0 and 100. For example: `p5`, `p05`, or `p42`.
• If quantiles are supplied, an `n`-parameter distribution must have exactly `n` quantiles. The CDF will pass through these quantiles exactly.
##### B. Via parameters

To the right of the quantiles (if any) the next 1 or more columns specify the distribution parameters directly. No column headers are expected (since the parameters in question are different for each distribution family). The parameters are interpreted based on their order (i.e. as positional arguments).

#### Name

The name of a variable is in the column to the left

1. The calculations may be in any worksheet of the file, not just the result worksheet.
2. Within a worksheet, the calculations must be arranged all in one column. Columns can vary across worksheets.
3. For any variables that follow a probability distribution (either supplied as an input or computed by the simulation), the value taken by the cell in the spreadsheet is ignored: only the formulae are used. The cell value is only considered for deterministic inputs that do not follow a probability distribution.

### Supported files

The URL field accepts any URL to a publicly accessible `.xlsx` file.

For your convenience, if a Google Sheets or OneDrive (Microsoft 365) URL is provided, we attempt to understand the URL and download the `.xlsx` file from the provider (so you don't need to link to where the `.xlsx` file is actually hosted).

Remember, if you create a new spreadsheet on Google Sheets or OneDrive, you need change sharing permissions so that Dagger can view it (to at least "anyone with the link can view").

### Features

• Probability distribution of each variable
• View histogram, quantiles, moments