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The **Tine distribution** (sometimes called symmetric triangular distribution) made an entry in the Index to the Distributions of Mathematical Statistics [1] as:

The Annals of Mathematical Statistics [2] contains an expanded definition:

Rinne [3] defines Tine’s distribution as the distribution of two independent and identically distributed uniform variables (i.e., the convolution of two uniform distributions):

*X*_{1}, *X*_{2} iid∼ *UN*(*a, b*) ⇒ *X* = *X*_{1} + *X*_{2} ∼ *TS*(2 *a* + *b*, *b*).

He notes it is also called Simpson’s distribution, after Thomas Simpson (1710-1761) who is thought to be the first to suggest the distribution.

## References

[1] Schmidt, R. Statistical Analysis of One-Dimensional Distributions. Annals of Mathematical Statistics. 5:33.

[2] Haight, F. (1958). Index to the Distributions of Mathematical Statistics. National Bureau of Standards Report.

[3] Rinne, H. Location–Scale Distributions Linear Estimation and Probability Plotting Using MATLAB. Online: http://geb.uni-giessen.de/geb/volltexte/2010/7607/pdf/RinneHorst_LocationScale_2010.pdf