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

Density, distribution function, quantile function and random generation for the Topp-Leone distribution.

1 2 3 4 |

`x, q, p, n` |
Same as |

`shape` |
the (shape) parameter, which lies in |

`log` |
Logical.
If |

`lower.tail, log.p` |
Same meaning as in |

See `topple`

, the VGAM family function for
estimating the (shape) parameter *s* by maximum likelihood
estimation, for the formula of the probability density function.

`dtopple`

gives the density,
`ptopple`

gives the distribution function,
`qtopple`

gives the quantile function, and
`rtopple`

generates random deviates.

The Topp-Leone distribution is related to the triangle distribution.

T. W. Yee

Topp, C. W. and F. C. Leone (1955).
A family of J-shaped frequency functions.
*Journal of the American Statistical Association*,
**50**, 209–219.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## Not run: shape <- 0.7; x <- seq(0.02, 0.999, length = 300)
plot(x, dtopple(x, shape = shape), type = "l", col = "blue", las = 1,
main = "Blue is density, orange is cumulative distribution function",
sub = "Purple lines are the 10,20,...,90 percentiles", ylab = "")
abline(h = 0, col = "blue", lty = 2)
lines(x, ptopple(x, shape = shape), type = "l", col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qtopple(probs, shape = shape)
lines(Q, dtopple(Q, shape), col = "purple", lty = 3, type = "h")
lines(Q, ptopple(Q, shape), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(ptopple(Q, shape) - probs)) # Should be zero
## End(Not run)
``` |

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