# smsn.nl: Fit univariate NL-SMSN regression In nlsmsn: Fitting nonlinear models with scale mixture of skew-normal distributions.

## Description

Return EM algorithm output for NL-SMSN regression for both "Homoscedastic" and "Heteroscedastic" (univaritate case, p=1).

## Usage

 ```1 2 3``` ```smsn.nl(y, x = NULL, z = NULL, betas = NULL, sigma2 = NULL, shape = NULL, rho = NULL, nu = NULL, nlf = NULL, rho.func = 1, reg.type = "Homoscedastic", criteria = FALSE, family = "Skew.t", error = 1e-05, iter.max = 100) ```

## Arguments

 `y` the response vector `x` the independent covariates `z` the independent covariates for sigma2. "Heteroscedastic" model ONLY! `betas` regression coefficient(s) vector `sigma2` initial value for the scale parameter `shape` initial value for the skewness parameter `rho` initial value for "Heteroscedastic" coefficient rho. "Heteroscedastic" model ONLY! `nu` the parameter of the scale variable (vector or scalar) of the SMSN family (kurtosis parameter). For the "Skew.cn" must be a vector of length 2 and values in (0,1) `nlf` non linear function for the regression `rho.func` Choose the type of heteroscedasticity for sigma2. If rho.func == 1 ( f(z,rho) = exp(z*rho) ) and rho.func == 2 ( f(z,rho) = z^rho ). `reg.type` the type of possible regression: "Homoscedastic" or "Ho"; "Heteroscedastic" or "He". `criteria` if TRUE, loglik, AIC, BIC will be calculated `family` distribution famility to be used in fitting ("t", "Skew.t", "Skew.cn", "Skew.slash", "Skew.normal", "Normal") `error` the covergence maximum error `iter.max` maximum iterations of the EM algorithm

## Value

Estimated values of the location, scale, skewness, regression coefficients and "Heteroscedastic" coefficient (when reg.type = "He").

## Author(s)

Aldo Garay [email protected], Marcos Prates [email protected] and Victor Lachos [email protected]

## References

Aldo M. Garay, Victor H. Lachos, Carlos A. Abanto-Valle (2011). "Nonlinear regression models based on scale mixture of skew-normal distributions". Journal of the Korean Stastical Society, 40, 115-124.\

Victor H. Lachos, Dipankar Bandyopadhyay and Aldo M. Garay (2011). "Heteroscedastic nonlinear regression models based on scale mixture of skew-normal distributions". Statistics -and Probability Letters, 81, 1208-1217.

## Examples

 `1` ``` ##see examples in \code{\link{Oil}} and \code{\link{Ultrasonic}} ```

nlsmsn documentation built on May 30, 2017, 6:18 a.m.