# Coefficients of non-negative penalized generalized linear models for a given lambda for Poisson family

### Description

The function computes regression coefficients for a penalized generalized linear models subject to non-negativity constraints for a given lambda value for response variable following Poisson distribution.

### Usage

1 2 | ```
nnlasso.poisson.lambda(n,p,sumy,beta0.old,beta1.old,
x,y,dxkx0,tau,lambda1,tol,maxiter,xbeta.old,mu1,eps,SE)
``` |

### Arguments

`n` |
Number of observations |

`p` |
Number of predictors |

`sumy` |
Sum of y values |

`beta0.old` |
Initial value of intercept |

`beta1.old` |
A vector of initial values of slope coefficients |

`x` |
A n by p1 matrix of predictors |

`y` |
A vector of n observations |

`dxkx0` |
In case of a model with intercept, first diagonal of X'X |

`tau` |
Elastic net paramter. Default is 1 |

`lambda1` |
The value of lambda |

`tol` |
Tolerance criterion. Default is 10^-6 |

`maxiter` |
Maximum number of iterations. Default is 10000 |

`xbeta.old` |
A n by 1 vector of xbeta values |

`mu1` |
The value of mu at beta.old |

`eps` |
A small value below which a coefficient would be considered as zero. Default is eps=1e-6 |

`SE` |
Logical. If SE=TRUE, standard errors of the coefficients will be produced. Default is SE=FALSE |

### Details

This function is internal and used by nnlasso.poisson function. User need not call this function.

### Value

A list with following components

`beta0.new` |
Intercept estimate |

`beta1.new` |
Slope coefficient estimates |

`conv` |
"yes" means converged and "no" means did not converge |

`iter` |
Number of iterations to estimate the coefficients |

`ofv.new` |
Objective function value at solution |

`xbeta.new` |
xbeta values at solution |

`mu1` |
Value of mu at solution |

`vcov` |
Variance-covariance matrix of the coefficient estimates |

### Author(s)

Baidya Nath Mandal and Jun Ma

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