# Triangular10 50 90

## Triangular_10_50_90(p10, p50, p90)

This defines a trianglar distribution given percentiles p10 ≤ p50 ≤ p90.

There are a couple downsides of defining a triangular distribution using percentiles, rather than using «min»-«mode»-«max» as is done with the built-in Triangular distribution function. First, the percentiles do not always uniquely specify the triangular distribution. When p10 and p90 are on opposite sides of the mode, there are often two possible triangular distributions with the indicated fractiles, and when p10 and p90 are on the same side of the mode, there is a fully unconstrained degree of freedom, leading to an infinite number of triangular distributions matching the fractiles. In these cases, this function will select one of the possible consistent distributions.

In addition to non-uniqueness, there are some combinations of p10 ≤ p50 ≤ p90 that have no triangular distribution with the indicated percentiles. This may occur when p50-p10 << p90-p50 or p50-p10 >> p90-p50 (where << means much less than). In this case, an error results. You can suppress this error by setting the optional «noErr» parameter to false, e.g.:

Triangular_10_50_90(a, b, c, noErr: true)

in which case a triangular distribution not precisely matching the indicated p10, p50 and p90 percentiles (but usually fairly close) is returned.

## Library

Distribution Variations library (Distribution Variations.ana)

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## See Also

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