Description Usage Arguments Details Value Author(s) See Also Examples

Density, distribution function, quantile function and random generation for the triangular distribution with range 'min' to 'max' and mode equal to 'mode'.

1 2 3 4 5 6 7 8 9 10 | ```
dtri(x, min=-sqrt(6), max=sqrt(6), mode = (min + max)/2,
log = FALSE)
ptri(q, min=-sqrt(6), max=sqrt(6), mode = (min + max)/2,
lower.tail = TRUE, log.p = FALSE)
qtri(p, min=-sqrt(6), max=sqrt(6), mode = (min + max)/2,
lower.tail = TRUE, log.p = FALSE)
rtri(n, min=-sqrt(6), max=sqrt(6), mode = (min + max)/2)
``` |

`x, q` |
Vector of quantiles. |

`p` |
Vector of quantiles. |

`n` |
Number of observations. If 'length(n) > 1', the length is taken to be the number required. |

`min` |
Vector of lower limits of distribution. |

`max` |
Vector of upper limits of distribution. |

`mode` |
Vector of modes |

`lower.tail` |
logical; if TRUE (default), probabilities are P[X <= x]; otherwise, P[X > x]. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

The triangular distribution has density

*f(x)=2*(x-min) / ((max-min)*(mode-min)) (min < x <= mode)*

*f(x)=2*(max-x) / ((max-min)*(max-mode)) (mode < x < max)*

and 0 elsewhere.

The mean is

*(min + mode + max)/3*

and the variance is

*\frac{1}{18}(min^2 + mode^2 + max^2 - min*mode - min*max - mode*max)*

The default values of `min`

, `max`

and `mode`

give a distribution with
mean 0 and unit variance.

If `min>max`

, `min`

amd `max`

will be silently interchanged. If
mode is not within `[min, max]`

, the functions return `NA`

, with a warning.

`rtri`

calls `runif(n, 0, 1)`

to generate probabilities which are passed to
`qtri`

.

A vector of densities, probabilities, quantiles or random deviates.
`dtri`

gives the density, `ptri`

gives the distribution function,
`qtri`

gives the quantile function, and `rtri`

generates random deviates.

S. L. R. Ellison s.ellison@lgc.co.uk

1 2 3 4 5 6 7 8 9 10 |

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