# 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

 ```1 2 3 4``` ```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.

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

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## 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.