VGAM (version 1.1-9)

Gaitdlog: Generally Altered, Inflated, Truncated and Deflated Logarithmic Distribution

Description

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.

Usage

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)

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.

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.

Warning

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

Author

T. W. Yee.

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.

See Also

gaitdlog, Gaitdpois, 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))
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")