Loggamma: The log-gamma(LG) distribution

In reliaR: Package for some probability distributions.

Description

Density, distribution function, quantile function and random generation for the log-gamma(LG) distribution with parameters alpha and lambda.

Usage

dlog.gamma(x, alpha, lambda, log = FALSE)
plog.gamma(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qlog.gamma(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rlog.gamma(n, alpha, lambda)

Arguments

x,q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
alpha	parameter.
lambda	parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].

Details

The log-gamma(LG) distribution has density

f(x; α, λ) = α λ exp(λ x) exp{-α exp(λ x)}; (α, λ) > 0, x > 0

where α and λ are the parameters, respectively.

Value

dlog.gamma gives the density, plog.gamma gives the distribution function, qlog.gamma gives the quantile function, and rlog.gamma generates random deviates.

References

Klugman, S., Panjer, H. and Willmot, G. (2004). Loss Models: From Data to Decisions, 2nd ed., New York, Wiley.

Lawless, J. F., (2003). Statistical Models and Methods for Lifetime Data, 2nd ed., John Wiley and Sons, New York.

See Also

.Random.seed about random number; slog.gamma for ExpExt survival / hazard etc. functions

Examples

## Load data sets
data(conductors)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(conductors)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 0.0088741, lambda.est = 0.6059935
dlog.gamma(conductors, 0.0088741, 0.6059935, log = FALSE)
plog.gamma(conductors, 0.0088741, 0.6059935, lower.tail = TRUE, log.p = FALSE)
qlog.gamma(0.25, 0.0088741, 0.6059935, lower.tail=TRUE, log.p = FALSE)
rlog.gamma(30, 0.0088741, 0.6059935)

Example output

 [1] 0.17769326 0.12656282 0.22044603 0.19966524 0.17464348 0.11533119
 [7] 0.21840077 0.07986723 0.18700118 0.03130737 0.19439387 0.15329166
[13] 0.00345913 0.11124544 0.19976176 0.06416459 0.17637359 0.05916786
[19] 0.21861499 0.21945599 0.17929110 0.17729228 0.12232793 0.15081279
[25] 0.13452461 0.18775767 0.19853713 0.08468278 0.16746782 0.20287112
[31] 0.20999625 0.13452596 0.22200391 0.19534757 0.16646823 0.07962176
[37] 0.19927790 0.13050059 0.09303768 0.21932159 0.21700602 0.14763472
[43] 0.04376336 0.21947817 0.07295049 0.22159913 0.17741964 0.22241786
[49] 0.21125945 0.21604330 0.19805439 0.12513253 0.11401216 0.22210243
[55] 0.17597076 0.17371703 0.14986993 0.01856427 0.14120754
 [1] 0.37400917 0.91546467 0.57582406 0.45168180 0.36467211 0.21538454
 [7] 0.70376030 0.14246281 0.82010852 0.05309823 0.80179525 0.30513845
[13] 0.99919943 0.20654862 0.45208123 0.11245805 0.36993739 0.10315081
[19] 0.55738027 0.56526580 0.37900697 0.37276672 0.23082993 0.29875228
[25] 0.25881722 0.40690757 0.79020225 0.95490815 0.34363109 0.46536894
[31] 0.75010715 0.90619544 0.66518404 0.43449710 0.34079263 0.14198434
[37] 0.45008603 0.91096600 0.16861955 0.56394946 0.54409268 0.29069425
[43] 0.98203160 0.56548526 0.12909857 0.67161647 0.84052529 0.60684097
[49] 0.50681008 0.53694719 0.44511933 0.23714004 0.21251776 0.66340762
[55] 0.36870418 0.36188522 0.29634682 0.99401495 0.27480859
[1] 5.740522
 [1]  0.4439167  9.5519168  8.4003302  7.9678701  8.4181952  8.3795368
 [7]  7.4035645  9.0401984  7.3371837  5.7535683  8.1927983  5.4216908
[13]  6.6675220  8.0613461  7.4483014  6.6841777  8.4953158  8.7186131
[19]  9.8001621  6.1594553 10.2221670  8.1643837  7.5467394  9.5617286
[25]  8.9187228  0.3014123  7.2197568  7.8597558  8.0736232  8.3030515

reliaR documentation built on May 1, 2019, 9:51 p.m.