loglik_function

loglik_function.wt_reliability_data

This function computes the log-likelihood value with respect to a given set
of parameters. In terms of Maximum Likelihood Estimation this function can
be optimized (<a href="/link/optim?package=weibulltools&version=2.1.0" data-mini-rdoc="weibulltools::optim">optim</a>) 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 <code>tibble</code> with class <code>wt_reliability_data</code> returned by reliability_data.</dd>
<dt>...</dt>
<dd>Further arguments passed to or from other methods. Currently not used.</dd>
<dt>wts</dt>
<dd>Optional vector of case weights. The length of <code>wts</code> must be equal
to the number of observations in <code>x</code>.</dd>
<dt>dist_params</dt>
<dd>A vector of parameters. An overview of the
distribution-specific parameters can be found in section 'Distributions'.</dd>
<dt>distribution</dt>
<dd>Supposed distribution of the random variable.</dd></dl>

Arguments

The following table summarizes the available distributions and their parameters<ul>
<li>location parameter \(\mu\),</li>
<li>scale parameter \(\sigma\) or \(\theta\) and</li>
<li>threshold parameter \(\gamma\).</li>
</ul>The order within <code>dist_params</code> is given in the table header.<table class="table">
<tr><td><code>distribution</code></td><td><code>dist_params[1]</code></td><td><code>dist_params[2]</code></td><td><code>dist_params[3]</code></td></tr>
<tr><td><code>"sev"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"weibull"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"weibull3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"normal"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"lognormal"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"lognormal3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"logistic"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"loglogistic"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"loglogistic3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"exponential"</code></td><td>\(\theta\)</td><td>-</td><td>-</td></tr>
<tr><td><code>"exponential2"</code></td><td>\(\theta\)</td><td>\(\gamma\)</td><td>-</td></tr>
</table>

Distributions

This function computes the log-likelihood value with respect to a given set
of parameters. In terms of Maximum Likelihood Estimation this function can
be optimized (<a href='https://rdrr.io/r/stats/optim.html'>optim</a>) 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 <code>tibble</code> with class <code>wt_reliability_data</code> returned by reliability_data.</dd>


<dt>...</dt>
<dd>Further arguments passed to or from other methods. Currently not used.</dd>


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


<dt>dist_params</dt>
<dd>A vector of parameters. An overview of the
distribution-specific parameters can be found in section 'Distributions'.</dd>


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

</dl>

The following table summarizes the available distributions and their parameters<ul>
<li>location parameter \(\mu\),</li>
<li>scale parameter \(\sigma\) or \(\theta\) and</li>
<li>threshold parameter \(\gamma\).</li>
</ul>

The order within <code>dist_params</code> is given in the table header.<table class='table'>
<tr><td><code>distribution</code></td><td><code>dist_params[1]</code></td><td><code>dist_params[2]</code></td><td><code>dist_params[3]</code></td></tr>
<tr><td><code>"sev"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"weibull"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"weibull3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"normal"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"lognormal"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"lognormal3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"logistic"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"loglogistic"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"loglogistic3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"exponential"</code></td><td>\(\theta\)</td><td>-</td><td>-</td></tr>
<tr><td><code>"exponential2"</code></td><td>\(\theta\)</td><td>\(\gamma\)</td><td>-</td></tr>
</table>

loglik_function: Log-Likelihood Function for Parametric Lifetime Distributions

Description

Usage

Value

Arguments

Distributions

References

Examples

`distribution`	`dist_params[1]`	`dist_params[2]`	`dist_params[3]`
`"sev"`	\(\mu\)	\(\sigma\)	-
`"weibull"`	\(\mu\)	\(\sigma\)	-
`"weibull3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"normal"`	\(\mu\)	\(\sigma\)	-
`"lognormal"`	\(\mu\)	\(\sigma\)	-
`"lognormal3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"logistic"`	\(\mu\)	\(\sigma\)	-
`"loglogistic"`	\(\mu\)	\(\sigma\)	-
`"loglogistic3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"exponential"`	\(\theta\)	-	-
`"exponential2"`	\(\theta\)	\(\gamma\)	-