# Local_LL_all: Log-likelihood, New Candidate and Directional Derivative for... In logcondens: Estimate a Log-Concave Probability Density from Iid Observations

## Description

Computes the value of the log-likelihood function

L(φ) = ∑_{i=1}^m w_i φ(x_i) - int_{x_1}^{x_m} exp(φ(t)) dt,

a new candidate for φ via the Newton method as well as the directional derivative of φ \to L(φ) into that direction.

## Usage

 1 Local_LL_all(x, w, phi) 

## Arguments

 x Vector of independent and identically distributed numbers, with strictly increasing entries. w Optional vector of nonnegative weights corresponding to x_m. phi Some vector φ of the same length as x and w.

## Value

 ll Value L(φ) of the log-likelihood function at φ. phi_new New candidate for φ via the Newton-method, using the complete Hessian matrix. dirderiv Directional derivative of φ \to L(φ) into the direction φ_{new}.

## Note

This function is not intended to be invoked by the end user.

## Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

logcondens documentation built on May 2, 2019, 6:11 a.m.