Generally Altered, Inflated, Truncated and Deflated Logarithmic Distribution

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

dgaitdlog(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)
pgaitdlog(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)
qgaitdlog(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)
rgaitdlog(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 dlog.

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

Same meaning as shape for dlog, i.e., for an ordinary logarithmic 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 logarithmic distribution are analogous to the Poisson, hence most details have been put in Gaitdpois. These functions do what Oalog, Oilog, Otlog 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

dgaitdlog gives the density, pgaitdlog gives the distribution function, qgaitdlog gives the quantile function, and rgaitdlog generates random deviates. The default values of the arguments correspond to ordinary dlog, plog, qlog, rlog respectively.

Author

T. W. Yee.

Note

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

See also

gaitdlog, Gaitdpois, dgaitdplot, Gaitdzeta, multinomial, Oalog, Oilog, Otlog.

Examples

ivec <- c(2, 10); avec <- ivec + 1; shape <- 0.995; xgrid <- 0:15
max.support <- 15; pobs.a <- 0.10; pstr.i <- 0.15
dvec <- 1; pdip.mlm <- 0.05
(ddd <- dgaitdlog(xgrid, shape,
   max.support = max.support, pobs.mix = pobs.a,
   pdip.mlm = pdip.mlm, d.mlm = dvec,
   a.mix = avec, pstr.mix = pstr.i, i.mix = ivec))
#>  [1] 0.00000000 0.23125894 0.26575062 0.07923885 0.06926528 0.05513516
#>  [7] 0.04571624 0.03898942 0.03394516 0.03002261 0.05106095 0.02076115
#> [13] 0.02218089 0.02037230 0.01882255 0.01747987
if (FALSE)  dgaitdplot(shape, ylab = "Probability", xlab = "x",
   max.support = max.support, pobs.mix = 0,
   pobs.mlm = 0, a.mlm = avec, all.lwd = 3,
   pdip.mlm = pdip.mlm, d.mlm = dvec, fam = "log",
   pstr.mix = pstr.i, i.mix = ivec, deflation = TRUE,
   main = "GAITD Combo PMF---Logarithmic Parent")    # \dontrun{}