# cdfln3: Three-parameter lognormal distribution In lmom: L-Moments

## Description

Distribution function and quantile function of the three-parameter lognormal distribution.

## Usage

 ```1 2``` ```cdfln3(x, para = c(0, 0, 1)) qualn3(f, para = c(0, 0, 1)) ```

## Arguments

 `x` Vector of quantiles. `f` Vector of probabilities. `para` Numeric vector containing the parameters of the distribution, in the order zeta, mu, sigma (lower bound, mean on log scale, standard deviation on log scale).

## Details

The three-parameter lognormal distribution with lower bound zeta, mean on log scale mu, and standard deviation on log scale sigma has distribution function

F(x) = Phi(y),

x>0, where

y = (log(x-zeta) - mu) / sigma

and Phi(y) is the distribution function of the standard normal distribution.

## Value

`cdfln3` gives the distribution function; `qualn3` gives the quantile function.

## Note

The functions expect the distribution parameters in a vector, rather than as separate arguments as in the standard R distribution functions `pnorm`, `qnorm`, etc.

`cdfgno` for the generalized normal distribution, a more general form of the three-parameter lognormal distribution.

`qlnorm` for the standard R version of the two-parameter lognormal distribution.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# Random sample from three-parameter lognormal distribution # with parameters zeta=0, mu=1, sigma=0.5. qualn3(runif(100), c(0,1,0.5)) ## Functions for the three-parameter lognormal distribution can ## also be used with the two-parameter lognormal distribution # Generate a random sample from a standard lognormal distribution xx <- qualn3(runif(50)) # Fit 2-parameter LN distribution pelln3(samlmu(xx), bound=0) # Fit 2-parameter LN distribution "in log space", # i.e. fit normal distribution to log-transformed data pelnor(samlmu(log(xx))) ```

### Example output

```  [1] 2.1981496 2.6744751 1.7782023 5.7774691 3.0352066 3.7649139 6.6958241
[8] 1.2727841 3.6777735 2.6607394 2.3186818 3.6451312 3.3522716 5.1231877
[15] 1.9966579 4.3458603 3.9529507 2.8788097 2.2249698 2.9105198 1.2658233
[22] 3.1799066 1.0569375 1.4531747 3.7289422 4.2601300 1.2113673 1.5227061
[29] 2.6309719 3.2374093 3.0688309 2.5711899 2.9901954 1.8968627 1.5130249
[36] 4.0553580 1.7896613 2.6526040 2.9288711 4.7371379 3.4331731 1.1215958
[43] 3.0851889 2.0181858 3.8388099 3.6388748 3.3489397 2.1605604 2.4258114
[50] 1.5973666 1.4298143 2.3169269 1.8186165 2.0400001 1.8445986 3.0717770
[57] 0.9248795 4.7683585 3.9785726 2.2580340 3.2531440 2.9266187 3.0118770
[64] 2.2247095 3.7283662 3.0527434 3.2109587 3.2744570 3.7347119 2.4060219
[71] 8.5000684 2.2348444 3.4933171 2.0162284 4.0662488 2.5985229 1.5252285
[78] 2.4875903 1.7516536 3.3344703 3.4760317 4.0170002 3.3886455 4.1523201
[85] 3.5859599 2.9291180 3.0936896 2.0452494 3.3690879 3.3578843 3.0483681
[92] 2.9381442 3.6349152 2.9879866 3.7733980 1.8064662 3.8684495 1.6493543
[99] 1.9669844 2.2177204
zeta         mu      sigma
0.00000000 0.06061481 0.87792966
mu      sigma
0.06518059 0.92018991
```

lmom documentation built on Aug. 2, 2017, 9:03 a.m.