VGAM (version 1.1-6)

Gaitdzeta: 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.

Usage

dgaitdzeta(x, shape.p, a.mix = NULL, a.mlm = NULL,
          i.mix = NULL, i.mlm = NULL,
          d.mix = NULL, d.mlm = NULL, truncate = NULL,
          max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
          pstr.mix = 0, pstr.mlm = 0,
          pdip.mix = 0, pdip.mlm = 0,
          byrow.aid = FALSE,
          shape.a = shape.p, shape.i = shape.p, shape.d = shape.p,
          log = FALSE)
pgaitdzeta(q, shape.p, a.mix = NULL, a.mlm = NULL,
          i.mix = NULL, i.mlm = NULL,
          d.mix = NULL, d.mlm = NULL, truncate = NULL,
          max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
          pstr.mix = 0, pstr.mlm = 0,
          pdip.mix = 0, pdip.mlm = 0,
          byrow.aid = FALSE,
          shape.a = shape.p, shape.i = shape.p, shape.d = shape.p,
          lower.tail = TRUE)
qgaitdzeta(p, shape.p, a.mix = NULL, a.mlm = NULL,
          i.mix = NULL, i.mlm = NULL,
          d.mix = NULL, d.mlm = NULL, truncate = NULL,
          max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
          pstr.mix = 0, pstr.mlm = 0,
          pdip.mix = 0, pdip.mlm = 0,
          byrow.aid = FALSE,
          shape.a = shape.p, shape.i = shape.p, shape.d = shape.p)
rgaitdzeta(n, shape.p, a.mix = NULL, a.mlm = NULL,
          i.mix = NULL, i.mlm = NULL,
          d.mix = NULL, d.mlm = NULL, truncate = NULL,
          max.support = Inf, pobs.mix = 0, pobs.mlm = 0,
          pstr.mix = 0, pstr.mlm = 0,
          pdip.mix = 0, pdip.mlm = 0,
          byrow.aid = FALSE,
          shape.a = shape.p, shape.i = shape.p, shape.d = shape.p)

Arguments

x, q, p, n, log, lower.tail

Same meaning as in dzeta.

shape.p, shape.a, shape.i, shape.d

Same meaning as shape for dzeta, i.e., for an ordinary zeta distribution. See Gaitdpois for generic information.

truncate, max.support

See Gaitdpois for generic information.

a.mix, i.mix, d.mix

See Gaitdpois for generic information.

a.mlm, i.mlm, d.mlm

See Gaitdpois for generic information.

pobs.mlm, pstr.mlm, pdip.mlm, byrow.aid

See Gaitdpois for generic information.

pobs.mix, pstr.mix, pdip.mix

See Gaitdpois for generic information.

Value

dgaitdzeta gives the density, pgaitdzeta gives the distribution function, qgaitdzeta gives the quantile function, and rgaitdzeta generates random deviates. The default values of the arguments correspond to ordinary dzeta, pzeta, qzeta, rzeta respectively.

Details

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

See Also

gaitdzeta, Gaitdpois, multinomial, Oazeta, Oizeta, Otzeta.

Examples

# NOT RUN {
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 <- dgaitdzeta(xgrid, shape, truncate = tvec,
   max.support = max.support, pobs.mix = pobs.a,
   a.mix = avec, pstr.mix = pstr.i, i.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)  
# }