# SSnegExp: Negative exponential functions In OnofriAndreaPG/aomisc: Statistical methods for the agricultural sciences

 negExp R Documentation

## Negative exponential functions

### Description

These functions provide the negative exponential model (negExp.fun) with the related self-starters for the `nls` function (NLS.negExp) `drm` function in the 'drc' package (DRC.negExp) and the exponential cumulative distribution function (negExpDist.fun), with self-starters for both 'nls' (NLS.negExpDist) and 'drc' (DRC.negExpDist).

### Usage

``````  negExp.fun(predictor, a, c)
negExpDist.fun(predictor, c)
NLS.negExp(predictor, a, c)
DRC.negExp(fixed = c(NA, NA), names = c("a", "c"))
NLS.negExpDist(predictor, c)
DRC.negExpDist(fixed = NA, names = c("c"))
``````

### Arguments

 `predictor` a numeric vector of values at which to evaluate the model. `a` a numeric parameter representing the higher asymptote `c` a numeric parameter that is proportional to the relative rate of increase of the fitted function `fixed` numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. `names` a vector of character strings giving the names of the parameters. The default is reasonable.

### Details

The negative exponential model is given by the following function:

` f(x) = \textrm{a} \{1 - \exp [- \exp( c x )] \} `

while the exponential CDF is obtained by setting a = 1:

` f(x) = 1 - \exp [- \exp( c x )] `

The ‘drc’ package contains also the function AR.2(), where c is replaced by e = 1/c. The ‘nlme’ package also contains an alternative parameterisation named 'SSasympOrig()', where c is replaced by ϕ3 = log(c).

### Value

negExp.fun and negExpDist.fun return a numeric value, while the self-starters return a list containing the nonlinear function, the self starter function and the parameter names.

Andrea Onofri

### References

Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc. Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/

### Examples

``````X <- c(1, 3, 5, 7, 9, 11, 13, 20)
Y <- c(4.5, 12.0, 16.1, 16.4, 18.9, 19.5, 19.3, 19.6)
model <- drm(Y ~ X, fct = DRC.negExp())
summary(model)
``````

OnofriAndreaPG/aomisc documentation built on Feb. 26, 2024, 8:21 p.m.