Zoabeta | R Documentation |

Density, distribution function, and random generation for the zero/one-inflated beta distribution.

dzoabeta(x, shape1, shape2, pobs0 = 0, pobs1 = 0, log = FALSE, tol = .Machine$double.eps) pzoabeta(q, shape1, shape2, pobs0 = 0, pobs1 = 0, lower.tail = TRUE, log.p = FALSE, tol = .Machine$double.eps) qzoabeta(p, shape1, shape2, pobs0 = 0, pobs1 = 0, lower.tail = TRUE, log.p = FALSE, tol = .Machine$double.eps) rzoabeta(n, shape1, shape2, pobs0 = 0, pobs1 = 0, tol = .Machine$double.eps)

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

`pobs0, pobs1` |
vector of probabilities that 0 and 1 are observed
( |

`shape1, shape2` |
Same as |

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

`tol` |
Numeric, tolerance for testing equality with 0 and 1. |

This distribution is a mixture of a discrete distribution
with a continuous distribution.
The cumulative distribution function of *Y* is

*
F(y) =(1 - omega_0 - omega_1) B(y) + omega_0 * I[0 <= y] +
omega_1 * I[1 <= y]*

where *B(y)* is the cumulative distribution function
of the beta distribution with the same shape parameters
(`pbeta`

),
*omega_0* is the inflated probability at 0 and
*omega_1* is the inflated probability at 1.
The default values of *omega_j* mean that these
functions behave like the ordinary `Beta`

when only the essential arguments are inputted.

`dzoabeta`

gives the density,
`pzoabeta`

gives the distribution function,
`qzoabeta`

gives the quantile, and
`rzoabeta`

generates random deviates.

Xiangjie Xue and T. W. Yee

`zoabetaR`

,
`beta`

,
`betaR`

,
`Betabinom`

.

## Not run: N <- 1000; y <- rzoabeta(N, 2, 3, 0.2, 0.2) hist(y, probability = TRUE, border = "blue", las = 1, main = "Blue = 0- and 1-altered; orange = ordinary beta") sum(y == 0) / N # Proportion of 0s sum(y == 1) / N # Proportion of 1s Ngrid <- 1000 lines(seq(0, 1, length = Ngrid), dbeta(seq(0, 1, length = Ngrid), 2, 3), col = "orange") lines(seq(0, 1, length = Ngrid), col = "blue", dzoabeta(seq(0, 1, length = Ngrid), 2 , 3, 0.2, 0.2)) ## End(Not run)

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