VGAM: gaitzetaUC – R documentation

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gaitzetaUC

Generally–Altered, –Inflated and –Truncated Zeta Distribution

Description

Density, distribution function, quantile function and random generation for the generally–altered, –inflated and –truncated zeta distribution. Both parametric and nonparametric variants are supported; these are based on finite mixtures of the parent with itself and the multinomial logit model (MLM) respectively. Altogether it can be abbreviated as GAAIIT–Zeta(shape.p)–Zeta(shape.a)–MLM–Zeta(shape.i)–MLM, and it is also known as the GAIT-Zeta PNP combo.

Usage

dgaitzeta(x, shape.p, alt.mix = NULL, alt.mlm = NULL,
          inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
          max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
          pstr.mix = 0, pstr.mlm = 0, byrow.ai = FALSE,
          shape.a = shape.p, shape.i = shape.p,
          deflation = FALSE, log = FALSE)
pgaitzeta(q, shape.p, alt.mix = NULL, alt.mlm = NULL,
          inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
          max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
          pstr.mix = 0, pstr.mlm = 0, byrow.ai = FALSE,
          shape.a = shape.p, shape.i = shape.p, lower.tail = TRUE)
qgaitzeta(p, shape.p, alt.mix = NULL, alt.mlm = NULL,
          inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
          max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
          pstr.mix = 0, pstr.mlm = 0, byrow.ai = FALSE,
          shape.a = shape.p, shape.i = shape.p)
rgaitzeta(n, shape.p, alt.mix = NULL, alt.mlm = NULL,
          inf.mix = NULL, inf.mlm = NULL, truncate = NULL,
          max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
          pstr.mix = 0, pstr.mlm = 0, byrow.ai = FALSE,
          shape.a = shape.p, shape.i = shape.p)

Arguments

`x, q, p, n, log, lower.tail`	Same meaning as in `dzeta`.
`shape.p, shape.a, shape.i`	Same meaning as `shape` for `dzeta`, i.e., for an ordinary zeta distribution. See `Gaitpois` for generic information.
`truncate, max.support`	See `Gaitpois` for generic information.
`alt.mix, inf.mix`	See `Gaitpois` for generic information.
`alt.mlm, inf.mlm`	See `Gaitpois` for generic information.
`pobs.mlm, pstr.mlm, byrow.ai`	See `Gaitpois` for generic information.
`pobs.mix, pstr.mix`	See `Gaitpois` for generic information.
`deflation`	See `Gaitpois` for generic information.

Details

These functions for the zeta distribution are analogous to the Poisson, hence most details have been put in Gaitpois. These functions do what Oazeta, Oizeta, Otzeta collectively did plus much more.

Value

dgaitzeta gives the density, pgaitzeta gives the distribution function, qgaitzeta gives the quantile function, and rgaitzeta generates random deviates. The default values of the arguments correspond to ordinary dzeta, pzeta, qzeta, rzeta respectively.

Note

See Gaitpois for general information also relevant to this parent distribution.

Author(s)

T. W. Yee.

Examples

ivec <- c(2, 10); avec <- ivec + 4; shape <- 0.95; xgrid <- 0:29
tvec <- 15; max.support <- 25; pobs.a <- 0.10; pstr.i <- 0.15
(ddd <- dgaitzeta(xgrid, shape, truncate = tvec,
   max.support = max.support, pobs.mix = pobs.a,
   alt.mix = avec, pstr.mix = pstr.i, inf.mix = ivec))
## Not run: plot(xgrid, ddd, type = "n", ylab = "Probability", xlab = "x",
              main = "GAIT PMF---Zeta Parent")
mylwd <- 0.5
abline(v = avec, col = 'blue', lwd = mylwd)
abline(v = ivec, col = 'purple', lwd = mylwd)
abline(v = tvec, col = 'tan', lwd = mylwd)
abline(v = max.support, col = 'magenta', lwd = mylwd)
abline(h = c(pobs.a, pstr.i, 0:1), col = 'gray', lty = "dashed")
lines(xgrid, dzeta(xgrid, shape), col = 'gray', lty = "dashed")  # f_{\pi}
lines(xgrid, ddd, type = "h", col = "pink", lwd = 3)  # GAIT PMF
points(xgrid[ddd == 0], ddd[ddd == 0], pch = 16, col = 'tan', cex = 2)  
## End(Not run)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13