Generally–Altered, –Inflated and –Truncated Logarithmic Distribution

Description

Density, distribution function, quantile function and random generation for the generally–altered, –inflated and –truncated 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. Altogether it can be abbreviated as GAAIIT–Log(shape.p)–Log(shape.a)–MLM–Log(shape.i)–MLM, and it is also known as the GAIT-Log PNP combo.

Usage

dgaitlog(x, shape.p, alter.mix = NULL, alter.mlm = NULL,
         inflate.mix = NULL, inflate.mlm = NULL, truncate = NULL,
         max.support = Inf, pobs.mix.a = 0, pobs.mlm.a = 0,
         pstr.mix.i = 0, pstr.mlm.i = 0, shape.a = shape.p,
         shape.i = shape.p, byrow.arg = FALSE, deflation = FALSE,
         log.arg = FALSE)
pgaitlog(q, shape.p, alter.mix = NULL, alter.mlm = NULL,
         inflate.mix = NULL, inflate.mlm = NULL, truncate = NULL,
         max.support = Inf, pobs.mix.a = 0, pobs.mlm.a = 0,
         pstr.mix.i = 0, pstr.mlm.i = 0, shape.a = shape.p,
         shape.i = shape.p, byrow.arg = FALSE)
qgaitlog(p, shape.p, alter.mix = NULL, alter.mlm = NULL,
         inflate.mix = NULL, inflate.mlm = NULL, truncate = NULL,
         max.support = Inf, pobs.mix.a = 0, pobs.mlm.a = 0,
         pstr.mix.i = 0, pstr.mlm.i = 0, shape.a = shape.p,
         shape.i = shape.p, byrow.arg = FALSE)
rgaitlog(n, shape.p, alter.mix = NULL, alter.mlm = NULL,
         inflate.mix = NULL, inflate.mlm = NULL, truncate = NULL,
         max.support = Inf, pobs.mix.a = 0, pobs.mlm.a = 0,
         pstr.mix.i = 0, pstr.mlm.i = 0, shape.a = shape.p,
         shape.i = shape.p, byrow.arg = FALSE)

Arguments

Details

These functions allow any combination of 3 operator types: truncation, alteration and inflation. See Gaitpois for generic information. These functions do what Oalog, Oilog, Otlog collectively did plus much more.

In the notation of Yee and Ma (2020) these functions allow for the special cases: (i) GAIT–Log(shape.p)–Log(shape.a, alter.mix, pobs.mix.a)–Log(shape.i, inflate.mix, pstr.mix.i); (ii) GAIT–Log(shape.p)–MLM(alter.mlm, pobs.mlm.a)–MLM(inflate.mlm, pstr.mlm.i). Model (i) is totally parametric while model (ii) is the most nonparametric possible.

Value

dgaitlog gives the density, pgaitlog gives the distribution function, qgaitlog gives the quantile function, and rgaitlog generates random deviates. The default values of the arguments correspond to ordinary dlog, plog, qlog, rlog respectively.

Note

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

Author(s)

T. W. Yee.

See Also

Gaitpois, multinomial, gaitlog.mix, Oalog, Oilog, Otlog.

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 <- dgaitlog(xgrid, shape, truncate = tvec,
   max.support = max.support, pobs.mix.a = pobs.a,
   alter.mix = avec, pstr.mix.i = pstr.i, inflate.mix = ivec))
## Not run: plot(xgrid, ddd, type = "n", ylab = "Probability", xlab = "x",
              main = "GAIT PMF---Logarithmic Parent")
mylwd <- 0.5
abline(v = avec, col = 'green', lwd = mylwd)
abline(v = ivec, col = 'red', 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, dlog(xgrid, shape), col = 'gray', lty = "dashed")  # f_{\pi}
lines(xgrid, ddd, type = "h", col = "blue", lwd = 3)  # GAIT PMF
points(xgrid[ddd == 0], ddd[ddd == 0], pch = 16)  
## End(Not run)