loglik_function

A numeric vector which consists of lifetime data. Lifetime
data could be every characteristic influencing the reliability of a product,
e.g. operating time (days/months in service), mileage (km, miles), load
cycles.

A vector of binary data (0 or 1) indicating whether unit i
is a right censored observation (= 0) or a failure (= 1).

status

Optional vector of case weights. The length of <code>wts</code> must be the
same as the number of observations in <code>x</code>.

A (named) numeric vector of (log-)location-scale parameters
in the order of location (\(\mu\)) and scale (\(\sigma\)). If a
three-parametric model is selected, the threshold parameter (\(\gamma\))
has to be the third element.

dist_params

Supposed distribution of the random variable.

distribution

This function computes the log-likelihood value with respect to a given set
of parameters. For two-parametric models the location and scale parameters
are required. If a three-parametric lifetime distribution is needed an
additional threshold parameter has to be provided. In terms of
Maximum Likelihood Estimation this function can be optimized (<code><a href="/link/optim?package=weibulltools&version=2.0.0" data-mini-rdoc="weibulltools::optim">optim</a></code>)
to estimate the parameters and variance-covariance matrix of the parameters.

Provides statistical methods and visualizations that are often
used in reliability engineering. Comprises a compact and easily
accessible set of methods and visualization tools that make the
examination and adjustment as well as the analysis and interpretation
of field data (and bench tests) as simple as possible.
Non-parametric estimators like Median Ranks,
Kaplan-Meier (Abernethy, 2006, <ISBN:978-0-9653062-3-2>),
Johnson (Johnson, 1964, <ISBN:978-0444403223>), and Nelson-Aalen
for failure probability estimation within samples that contain
failures as well as censored data are included.
The package supports methods like Maximum Likelihood and Rank Regression,
(Genschel and Meeker, 2010, <DOI:10.1080/08982112.2010.503447>)
for the estimation of multiple parametric lifetime distributions,
as well as the computation of confidence intervals of quantiles and
probabilities using the delta method related to Fisher's confidence
intervals (Meeker and Escobar, 1998, <ISBN:9780471673279>) and the
beta-binomial confidence bounds.
If desired, mixture model analysis can be done with segmented regression
and the EM algorithm.
Besides the well-known Weibull analysis, the package also contains
Monte Carlo methods for the correction and completion of imprecisely
recorded or unknown lifetime characteristics.
(Verband der Automobilindustrie e.V. (VDA), 2016, <ISSN:0943-9412>).
Plots are created statically ('ggplot2') or interactively ('plotly') and
can be customized with functions of the respective visualization package.
The graphical technique of probability plotting as well as the addition
of regression lines and confidence bounds to existing plots are
supported.

Hensel Tim-Gunnar

weibulltools

Statistical Methods for Life Data Analysis

Tim-Gunnar Hensel

David Barkemeyer

loglik_function function

<dl><dt>x</dt>
<dd>A numeric vector which consists of lifetime data. Lifetime
data could be every characteristic influencing the reliability of a product,
e.g. operating time (days/months in service), mileage (km, miles), load
cycles.</dd>
<dt>status</dt>
<dd>A vector of binary data (0 or 1) indicating whether unit i
is a right censored observation (= 0) or a failure (= 1).</dd>
<dt>wts</dt>
<dd>Optional vector of case weights. The length of <code>wts</code> must be the
same as the number of observations in <code>x</code>.</dd>
<dt>dist_params</dt>
<dd>A (named) numeric vector of (log-)location-scale parameters
in the order of location (\(\mu\)) and scale (\(\sigma\)). If a
three-parametric model is selected, the threshold parameter (\(\gamma\))
has to be the third element.</dd>
<dt>distribution</dt>
<dd>Supposed distribution of the random variable.</dd></dl>

Arguments

This function computes the log-likelihood value with respect to a given set
of parameters. For two-parametric models the location and scale parameters
are required. If a three-parametric lifetime distribution is needed an
additional threshold parameter has to be provided. In terms of
Maximum Likelihood Estimation this function can be optimized (<code><a href='https://rdrr.io/r/stats/optim.html'>optim</a></code>)
to estimate the parameters and variance-covariance matrix of the parameters.

Log-Likelihood Function for Parametric Lifetime Distributions — loglik_function

<dl>

<dt>x</dt>
<dd>A numeric vector which consists of lifetime data. Lifetime
data could be every characteristic influencing the reliability of a product,
e.g. operating time (days/months in service), mileage (km, miles), load
cycles.</dd>


<dt>status</dt>
<dd>A vector of binary data (0 or 1) indicating whether unit i
is a right censored observation (= 0) or a failure (= 1).</dd>


<dt>wts</dt>
<dd>Optional vector of case weights. The length of <code>wts</code> must be the
same as the number of observations in <code>x</code>.</dd>


<dt>dist_params</dt>
<dd>A (named) numeric vector of (log-)location-scale parameters
in the order of location (\(\mu\)) and scale (\(\sigma\)). If a
three-parametric model is selected, the threshold parameter (\(\gamma\))
has to be the third element.</dd>


<dt>distribution</dt>
<dd>Supposed distribution of the random variable.</dd>

</dl>

loglik_function: Log-Likelihood Function for Parametric Lifetime Distributions

Description

Usage

Value

Arguments

References

Examples