Generally Altered, Inflated and Truncated and Deflated Zeta Distribution

Density, distribution function, quantile function and random generation for the generally altered, inflated, truncated and deflated 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.

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.

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.

Warning

See Gaitdpois about the dangers of too much inflation and/or deflation on GAITD PMFs, and the difficulties detecting such.

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.

Author

T. W. Yee.

Note

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

See also

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

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 <- dgaitdzeta(xgrid, shape, truncate = tvec,
   max.support = max.support, pobs.mix = pobs.a,
   a.mix = avec, pstr.mix = pstr.i, i.mix = ivec))
#>  [1] 0.0000000000 0.4674039610 0.2647391363 0.0548663339 0.0313094476
#>  [6] 0.0202628664 0.0839192325 0.0105135942 0.0081033932 0.0064404987
#> [11] 0.0114769540 0.0043548846 0.0036752675 0.0031441471 0.0160807675
#> [16] 0.0000000000 0.0020972897 0.0018634468 0.0016669056 0.0015001092
#> [21] 0.0013573252 0.0012341410 0.0011271148 0.0010335300 0.0009512189
#> [26] 0.0008784345 0.0000000000 0.0000000000 0.0000000000 0.0000000000
if (FALSE) plot(xgrid, ddd, type = "n", ylab = "Probability",
              xlab = "x", main = "GAIT PMF---Zeta Parent")
mylwd <- 0.5
abline(v = avec, col = 'blue', lwd = mylwd)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
abline(v = ivec, col = 'purple', lwd = mylwd)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
abline(v = tvec, col = 'tan', lwd = mylwd)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
abline(v = max.support, col = 'magenta', lwd = mylwd)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
abline(h = c(pobs.a, pstr.i, 0:1), col = 'gray', lty = "dashed")
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
lines(xgrid, dzeta(xgrid, shape), col='gray', lty="dashed")  # f_{\pi}
#> Error in plot.xy(xy.coords(x, y), type = type, ...): plot.new has not been called yet
lines(xgrid, ddd, type = "h", col = "pink", lwd = 3)  # GAIT PMF
#> Error in plot.xy(xy.coords(x, y), type = type, ...): plot.new has not been called yet
points(xgrid[ddd == 0], ddd[ddd == 0], pch = 16, col = 'tan', cex = 2)
#> Error in plot.xy(xy.coords(x, y), type = type, ...): plot.new has not been called yet
 # \dontrun{}