Repository: damar-wicaksono/uqtestfuns (language: python)

Issue:
Add 10D Simple Test Function from Linkletter et al. (2006)
The ten-dimensional simple function from Linkletter et al. (2006)[^1] is a linear model defined as follows:

$$
\mathcal{M}(\boldsymbol{x}) = 0.2 x_1 + 0.2 x_2 + 0.2 x_3 + 0.2 x_4 + \epsilon
$$

where $\boldsymbol{x} = \{ x_1, x_2, x_3, x_4 \}$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^4$. $\epsilon$ is a random error generated from $\mathcal{N}(\mu = 0.0, \sigma^2=0.05)$. Although the model is defined to be of ten-dimensional, only four input variables are active.

In the paper, the response is standardized (with mean 0 and standard deviation 1.0), but we will skip this in the implementation of the function in UQTestFuns. The candidate name for this function is `LinkLetter2006Simple`.

The model is used as a test function in the context of sensitivity analysis.

[^1]: C. Linkletter, D. Bingham, N. Hengartner, D. Higdon, and K. Q. Ye, “Variable Selection for Gaussian Process Models in Computer Experiments,” Technometrics, vol. 48, no. 4, pp. 478–490, Nov. 2006, doi: [10.1198/004017006000000228](https://doi.org/10.1198/004017006000000228).


Discussion / hints:

Fix patch:
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 46c99ce..2e9c378 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,6 +9,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Added
 
+- The ten-dimensional linear function from Linkletter et al. (2006) featuring
+  only four active input variables out of ten; the function was used
+  in the context of metamodeling and sensitivity analysis.
 - The eight-dimensional function from Dette and Pepelyshev (2010) featuring
   curved and logarithm terms for metamodeling exercises.
 - The three-dimensional highly-curved function from Dette and Pepelyshev (2010)
diff --git a/docs/fundamentals/metamodeling.md b/docs/fundamentals/metamodeling.md
index c69fe16..9636a4f 100644
--- a/docs/fundamentals/metamodeling.md
+++ b/docs/fundamentals/metamodeling.md
@@ -18,51 +18,52 @@ kernelspec:
 The table below listed the available test functions typically used
 in the comparison of metamodeling approaches.
 
-|                                  Name                                   | Input Dimension |      Constructor       |
-|:-----------------------------------------------------------------------:|:---------------:|:----------------------:|
-|                  {ref}`Ackley <test-functions:ackley>`                  |        M        |       `Ackley()`       |
-|  {ref}`Alemazkoor & Meidani (2018) 2D <test-functions:alemazkoor-2d>`   |        2        |    `Alemazkoor2D()`    |
-| {ref}`Alemazkoor & Meidani (2018) 20D <test-functions:alemazkoor-20d>`  |       20        |   `Alemazkoor20D()`    |
-|                {ref}`Borehole <test-functions:borehole>`                |        8        |      `Borehole()`      |
-|        {ref}`Cheng and Sandu (2010) 2D <test-functions:cheng2d>`        |        2        |       `Cheng2D`        |
-|           {ref}`Coffee Cup Model <test-functions:coffee-cup>`           |        2        |     `CoffeeCup()`      |
-|      {ref}`Currin et al. (1988) Sine <test-functions:currin-sine>`      |        1        |     `CurrinSine()`     |
-|           {ref}`Damped Cosine <test-functions:damped-cosine>`           |        1        |    `DampedCosine()`    |
-|       {ref}`Damped Oscillator <test-functions:damped-oscillator>`       |        7        |  `DampedOscillator()`  |
-|      {ref}`Dette & Pepelyshev (2010) 8D <test-functions:dette-8d>`      |        3        |      `Dette8D()`       |
-|  {ref}`Dette & Pepelyshev (2010) Curved <test-functions:dette-curved>`  |        3        |    `DetteCurved()`     |
-| {ref}`Dette & Pepelyshev (2010) Exponential <test-functions:dette-exp>` |        3        |      `DetteExp()`      |
-|                   {ref}`Flood <test-functions:flood>`                   |        8        |       `Flood()`        |
-|        {ref}`Forrester et al. (2008) <test-functions:forrester>`        |        1        |   `Forrester2008()`    |
-|              {ref}`(1st) Franke <test-functions:franke-1>`              |        2        |      `Franke1()`       |
-|              {ref}`(2nd) Franke <test-functions:franke-2>`              |        2        |      `Franke2()`       |
-|              {ref}`(3rd) Franke <test-functions:franke-3>`              |        2        |      `Franke3()`       |
-|              {ref}`(4th) Franke <test-functions:franke-4>`              |        2        |      `Franke4()`       |
-|              {ref}`(5th) Franke <test-functions:franke-5>`              |        2        |      `Franke5()`       |
-|              {ref}`(6th) Franke <test-functions:franke-6>`              |        2        |      `Franke6()`       |
-|            {ref}`Friedman (6D) <test-functions:friedman-6d>`            |        6        |     `Friedman6D()`     |
-|           {ref}`Friedman (10D) <test-functions:friedman-10d>`           |       10        |    `Friedman10D()`     |
-|       {ref}`Genz (Corner Peak) <test-functions:genz-corner-peak>`       |        M        |   `GenzCornerPeak()`   |
-|     {ref}`Gramacy (2007) 1D Sine <test-functions:gramacy-1d-sine>`      |        1        |   `Gramacy1DSine()`    |
-|         {ref}`Higdon (2002) Sine <test-functions:higdon-sine>`          |        1        |     `HigdonSine()`     |
-|    {ref}`Holsclaw et al. (2013) Sine <test-functions:holsclaw-sine>`    |        1        |    `HolsclawSine()`    |
-|  {ref}`Lim et al. (2002) Non-Polynomial <test-functions:lim-non-poly>`  |        2        |     `LimNonPoly()`     |
-|      {ref}`Lim et al. (2002) Polynomial <test-functions:lim-poly>`      |        2        |      `LimPoly()`       |
-|               {ref}`McLain S1 <test-functions:mclain-s1>`               |        2        |      `McLainS1()`      |
-|               {ref}`McLain S2 <test-functions:mclain-s2>`               |        2        |      `McLainS2()`      |
-|               {ref}`McLain S3 <test-functions:mclain-s3>`               |        2        |      `McLainS3()`      |
-|               {ref}`McLain S4 <test-functions:mclain-s4>`               |        2        |      `McLainS4()`      |
-|               {ref}`McLain S5 <test-functions:mclain-s5>`               |        2        |      `McLainS5()`      |
-|      {ref}`Oakley & O'Hagan (2002) 1D <test-functions:oakley-1d>`       |        1        |      `Oakley1D()`      |
-|             {ref}`OTL Circuit <test-functions:otl-circuit>`             |     6 / 20      |     `OTLCircuit()`     |
-|            {ref}`Piston Simulation <test-functions:piston>`             |     7 / 20      |       `Piston()`       |
-|               {ref}`Robot Arm <test-functions:robot-arm>`               |        8        |      `RobotArm()`      |
-|           {ref}`Solar Cell Model <test-functions:solar-cell>`           |        5        |     `SolarCell()`      |
-|                  {ref}`Sulfur <test-functions:sulfur>`                  |        9        |       `Sulfur()`       |
-|     {ref}`Undamped Oscillator <test-functions:undamped-oscillator>`     |        6        | `UndampedOscillator()` |
-|       {ref}`Webster et al. (1996) 2D <test-functions:webster-2d>`       |        2        |     `Webster2D()`      |
-|          {ref}`Welch et al. (1992) <test-functions:welch1992>`          |       20        |     `Welch1992()`      |
-|             {ref}`Wing Weight <test-functions:wing-weight>`             |       10        |     `WingWeight()`     |
+|                                   Name                                    | Input Dimension |      Constructor       |
+|:-------------------------------------------------------------------------:|:---------------:|:----------------------:|
+|                   {ref}`Ackley <test-functions:ackley>`                   |        M        |       `Ackley()`       |
+|   {ref}`Alemazkoor & Meidani (2018) 2D <test-functions:alemazkoor-2d>`    |        2        |    `Alemazkoor2D()`    |
+|  {ref}`Alemazkoor & Meidani (2018) 20D <test-functions:alemazkoor-20d>`   |       20        |   `Alemazkoor20D()`    |
+|                 {ref}`Borehole <test-functions:borehole>`                 |        8        |      `Borehole()`      |
+|         {ref}`Cheng and Sandu (2010) 2D <test-functions:cheng2d>`         |        2        |       `Cheng2D`        |
+|            {ref}`Coffee Cup Model <test-functions:coffee-cup>`            |        2        |     `CoffeeCup()`      |
+|       {ref}`Currin et al. (1988) Sine <test-functions:currin-sine>`       |        1        |     `CurrinSine()`     |
+|            {ref}`Damped Cosine <test-functions:damped-cosine>`            |        1        |    `DampedCosine()`    |
+|        {ref}`Damped Oscillator <test-functions:damped-oscillator>`        |        7        |  `DampedOscillator()`  |
+|       {ref}`Dette & Pepelyshev (2010) 8D <test-functions:dette-8d>`       |        3        |      `Dette8D()`       |
+|   {ref}`Dette & Pepelyshev (2010) Curved <test-functions:dette-curved>`   |        3        |    `DetteCurved()`     |
+|  {ref}`Dette & Pepelyshev (2010) Exponential <test-functions:dette-exp>`  |        3        |      `DetteExp()`      |
+|                    {ref}`Flood <test-functions:flood>`                    |        8        |       `Flood()`        |
+|         {ref}`Forrester et al. (2008) <test-functions:forrester>`         |        1        |   `Forrester2008()`    |
+|               {ref}`(1st) Franke <test-functions:franke-1>`               |        2        |      `Franke1()`       |
+|               {ref}`(2nd) Franke <test-functions:franke-2>`               |        2        |      `Franke2()`       |
+|               {ref}`(3rd) Franke <test-functions:franke-3>`               |        2        |      `Franke3()`       |
+|               {ref}`(4th) Franke <test-functions:franke-4>`               |        2        |      `Franke4()`       |
+|               {ref}`(5th) Franke <test-functions:franke-5>`               |        2        |      `Franke5()`       |
+|               {ref}`(6th) Franke <test-functions:franke-6>`               |        2        |      `Franke6()`       |
+|             {ref}`Friedman (6D) <test-functions:friedman-6d>`             |        6        |     `Friedman6D()`     |
+|            {ref}`Friedman (10D) <test-functions:friedman-10d>`            |       10        |    `Friedman10D()`     |
+|        {ref}`Genz (Corner Peak) <test-functions:genz-corner-peak>`        |        M        |   `GenzCornerPeak()`   |
+|      {ref}`Gramacy (2007) 1D Sine <test-functions:gramacy-1d-sine>`       |        1        |   `Gramacy1DSine()`    |
+|          {ref}`Higdon (2002) Sine <test-functions:higdon-sine>`           |        1        |     `HigdonSine()`     |
+|     {ref}`Holsclaw et al. (2013) Sine <test-functions:holsclaw-sine>`     |        1        |    `HolsclawSine()`    |
+|   {ref}`Lim et al. (2002) Non-Polynomial <test-functions:lim-non-poly>`   |        2        |     `LimNonPoly()`     |
+|       {ref}`Lim et al. (2002) Polynomial <test-functions:lim-poly>`       |        2        |      `LimPoly()`       |
+| {ref}`Linkletter et al. (2006) Linear <test-functions:linkletter-linear>` |       10        |  `LinkletterLinear()`  |
+|                {ref}`McLain S1 <test-functions:mclain-s1>`                |        2        |      `McLainS1()`      |
+|                {ref}`McLain S2 <test-functions:mclain-s2>`                |        2        |      `McLainS2()`      |
+|                {ref}`McLain S3 <test-functions:mclain-s3>`                |        2        |      `McLainS3()`      |
+|                {ref}`McLain S4 <test-functions:mclain-s4>`                |        2        |      `McLainS4()`      |
+|                {ref}`McLain S5 <test-functions:mclain-s5>`                |        2        |      `McLainS5()`      |
+|       {ref}`Oakley & O'Hagan (2002) 1D <test-functions:oakley-1d>`        |        1        |      `Oakley1D()`      |
+|              {ref}`OTL Circuit <test-functions:otl-circuit>`              |     6 / 20      |     `OTLCircuit()`     |
+|             {ref}`Piston Simulation <test-functions:piston>`              |     7 / 20      |       `Piston()`       |
+|                {ref}`Robot Arm <test-functions:robot-arm>`                |        8        |      `RobotArm()`      |
+|            {ref}`Solar Cell Model <test-functions:solar-cell>`            |        5        |     `SolarCell()`      |
+|                   {ref}`Sulfur <test-functions:sulfur>`                   |        9        |       `Sulfur()`       |
+|      {ref}`Undamped Oscillator <test-functions:undamped-oscillator>`      |        6        | `UndampedOscillator()` |
+|        {ref}`Webster et al. (1996) 2D <test-functions:webster-2d>`        |        2        |     `Webster2D()`      |
+|           {ref}`Welch et al. (1992) <test-functions:welch1992>`           |       20        |     `Welch1992()`      |
+|              {ref}`Wing Weight <test-functions:wing-weight>`              |       10        |     `WingWeight()`     |
 
 In a Python terminal, you can list all the available functions relevant
 for metamodeling applications using ``list_functions()``
diff --git a/docs/fundamentals/sensitivity.md b/docs/fundamentals/sensitivity.md
index 7c67e2b..f96d9ba 100644
--- a/docs/fundamentals/sensitivity.md
+++ b/docs/fundamentals/sensitivity.md
@@ -18,32 +18,33 @@ kernelspec:
 The table below listed the available test functions typically used
 in the comparison of sensitivity analysis methods.
 
-|                               Name                               | Input Dimension |      Constructor       |
-|:----------------------------------------------------------------:|:---------------:|:----------------------:|
-|            {ref}`Borehole <test-functions:borehole>`             |        8        |      `Borehole()`      |
-|   {ref}`Bratley et al. (1992) A <test-functions:bratley1992a>`   |        M        |    `Bratley1992a()`    |
-|   {ref}`Bratley et al. (1992) B <test-functions:bratley1992b>`   |        M        |    `Bratley1992b()`    |
-|   {ref}`Bratley et al. (1992) C <test-functions:bratley1992c>`   |        M        |    `Bratley1992c()`    |
-|   {ref}`Bratley et al. (1992) D <test-functions:bratley1992d>`   |        M        |    `Bratley1992d()`    |
-|   {ref}`Damped Oscillator <test-functions:damped-oscillator>`    |        7        |  `DampedOscillator()`  |
-|               {ref}`Flood <test-functions:flood>`                |        8        |       `Flood()`        |
-|        {ref}`Friedman (6D) <test-functions:friedman-6d>`         |        6        |     `Friedman6D()`     |
-|   {ref}`Genz (Corner Peak) <test-functions:genz-corner-peak>`    |        M        |   `GenzCornerPeak()`   |
-| {ref}`Genz (Discontinuous) <test-functions:genz-discontinuous>`  |        M        | `GenzDiscontinuous()`  |
-|            {ref}`Ishigami <test-functions:ishigami>`             |        3        |      `Ishigami()`      |
-|          {ref}`Moon (2010) 3D <test-functions:moon3d>`           |        3        |       `Moon3D()`       |
-|     {ref}`Morris et al. (2006) <test-functions:morris2006>`      |        M        |     `Morris2006()`     |
-|         {ref}`OTL Circuit <test-functions:otl-circuit>`          |     6 / 20      |     `OTLCircuit()`     |
-|         {ref}`Piston Simulation <test-functions:piston>`         |     7 / 20      |       `Piston()`       |
-|   {ref}`Simple Portfolio Model <test-functions:portfolio-3d>`    |        3        |    `Portfolio3D()`     |
-|      {ref}`SaltelliLinear <test-functions:saltelli-linear>`      |        M        |   `SaltelliLinear()`   |
-|             {ref}`Sobol'-G <test-functions:sobol-g>`             |        M        |       `SobolG()`       |
-|          {ref}`Sobol'-G* <test-functions:sobol-g-star>`          |        M        |     `SobolGStar()`     |
-|       {ref}`Sobol'-Levitan <test-functions:sobol-levitan>`       |        M        |    `SobolLevitan()`    |
-|       {ref}`Solar Cell Model <test-functions:solar-cell>`        |        5        |     `SolarCell()`      |
-|              {ref}`Sulfur <test-functions:sulfur>`               |        9        |       `Sulfur()`       |
-|      {ref}`Welch et al. (1992) <test-functions:welch1992>`       |       20        |     `Welch1992()`      |
-|         {ref}`Wing Weight <test-functions:wing-weight>`          |       10        |     `WingWeight()`     |
+|                                    Name                                    | Input Dimension |      Constructor       |
+|:--------------------------------------------------------------------------:|:---------------:|:----------------------:|
+|                 {ref}`Borehole <test-functions:borehole>`                  |        8        |      `Borehole()`      |
+|        {ref}`Bratley et al. (1992) A <test-functions:bratley1992a>`        |        M        |    `Bratley1992a()`    |
+|        {ref}`Bratley et al. (1992) B <test-functions:bratley1992b>`        |        M        |    `Bratley1992b()`    |
+|        {ref}`Bratley et al. (1992) C <test-functions:bratley1992c>`        |        M        |    `Bratley1992c()`    |
+|        {ref}`Bratley et al. (1992) D <test-functions:bratley1992d>`        |        M        |    `Bratley1992d()`    |
+|        {ref}`Damped Oscillator <test-functions:damped-oscillator>`         |        7        |  `DampedOscillator()`  |
+|                    {ref}`Flood <test-functions:flood>`                     |        8        |       `Flood()`        |
+|             {ref}`Friedman (6D) <test-functions:friedman-6d>`              |        6        |     `Friedman6D()`     |
+|        {ref}`Genz (Corner Peak) <test-functions:genz-corner-peak>`         |        M        |   `GenzCornerPeak()`   |
+|      {ref}`Genz (Discontinuous) <test-functions:genz-discontinuous>`       |        M        | `GenzDiscontinuous()`  |
+|                 {ref}`Ishigami <test-functions:ishigami>`                  |        3        |      `Ishigami()`      |
+| {ref}`Linkletter et al. (2006) Linear <test-functions:linkletter-linear>`  |       10        |  `LinkletterLinear()`  |
+|               {ref}`Moon (2010) 3D <test-functions:moon3d>`                |        3        |       `Moon3D()`       |
+|          {ref}`Morris et al. (2006) <test-functions:morris2006>`           |        M        |     `Morris2006()`     |
+|              {ref}`OTL Circuit <test-functions:otl-circuit>`               |     6 / 20      |     `OTLCircuit()`     |
+|              {ref}`Piston Simulation <test-functions:piston>`              |     7 / 20      |       `Piston()`       |
+|        {ref}`Simple Portfolio Model <test-functions:portfolio-3d>`         |        3        |    `Portfolio3D()`     |
+|           {ref}`SaltelliLinear <test-functions:saltelli-linear>`           |        M        |   `SaltelliLinear()`   |
+|                  {ref}`Sobol'-G <test-functions:sobol-g>`                  |        M        |       `SobolG()`       |
+|               {ref}`Sobol'-G* <test-functions:sobol-g-star>`               |        M        |     `SobolGStar()`     |
+|            {ref}`Sobol'-Levitan <test-functions:sobol-levitan>`            |        M        |    `SobolLevitan()`    |
+|            {ref}`Solar Cell Model <test-functions:solar-cell>`             |        5        |     `SolarCell()`      |
+|                   {ref}`Sulfur <test-functions:sulfur>`                    |        9        |       `Sulfur()`       |
+|           {ref}`Welch et al. (1992) <test-functions:welch1992>`            |       20        |     `Welch1992()`      |
+|              {ref}`Wing Weight <test-functions:wing-weight>`               |       10        |     `WingWeight()`     |
 
 In a Python terminal, you can list all the available functions relevant
 for metamodeling applications using ``list_functions()``
diff --git a/docs/references.bib b/docs/references.bib
index aee4893..ad043d2 100644
--- a/docs/references.bib
+++ b/docs/references.bib
@@ -1043,4 +1043,15 @@ @Article{Dette2010
   doi     = {10.1198/tech.2010.09157},
 }
 
+@Article{Linkletter2006,
+  author  = {Linkletter, Crystal and Bingham, Derek and Hengartner, Nicholas and Higdon, David and Ye, Kenny Q.},
+  journal = {Technometrics},
+  title   = {Variable selection for {Gaussian} process models in computer experiments},
+  year    = {2006},
+  number  = {4},
+  pages   = {478--490},
+  volume  = {48},
+  doi     = {10.1198/004017006000000228},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}


Test patch:
diff --git a/docs/test-functions/available.md b/docs/test-functions/available.md
index c36d971..64da08c 100644
--- a/docs/test-functions/available.md
+++ b/docs/test-functions/available.md
@@ -66,6 +66,7 @@ regardless of their typical applications.
 |                      {ref}`Ishigami <test-functions:ishigami>`                      |        3        |          `Ishigami()`           |
 |        {ref}`Lim et al. (2002) Non-Polynomial <test-functions:lim-non-poly>`        |        2        |         `LimNonPoly()`          |
 |            {ref}`Lim et al. (2002) Polynomial <test-functions:lim-poly>`            |        2        |           `LimPoly()`           |
+|      {ref}`Linkletter et al. (2006) Linear <test-functions:linkletter-linear>`      |       10        |      `LinkletterLinear()`       |
 |                     {ref}`McLain S1 <test-functions:mclain-s1>`                     |        2        |          `McLainS1()`           |
 |                     {ref}`McLain S2 <test-functions:mclain-s2>`                     |        2        |          `McLainS2()`           |
 |                     {ref}`McLain S3 <test-functions:mclain-s3>`                     |        2        |          `McLainS3()`           |
diff --git a/docs/test-functions/linkletter-linear.md b/docs/test-functions/linkletter-linear.md
new file mode 100644
index 0000000..33ccb85
--- /dev/null
+++ b/docs/test-functions/linkletter-linear.md
@@ -0,0 +1,115 @@
+---
+jupytext:
+  formats: ipynb,md:myst
+  text_representation:
+    extension: .md
+    format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.14.1
+kernelspec:
+  display_name: Python 3 (ipykernel)
+  language: python
+  name: python3
+---
+
+(test-functions:linkletter-linear)=
+# Linear Function from Linkletter et al. (2006)
+
+```{code-cell} ipython3
+import numpy as np
+import matplotlib.pyplot as plt
+import uqtestfuns as uqtf
+```
+
+The linear function is a ten-dimensional, scalar-valued function.
+Only the first four input variables are active, while the rest is inert.
+The function was used in {cite}`Linkletter2006` to demonstrate a variable
+selection method (i.e., sensitivity analysis)
+in the context of Gaussian process metamodeling:
+
+```{note}
+Linkletter et al. {cite}`Linkletter2006` introduced four ten-dimensional
+analytical test functions with some of the input variables inert.
+They are used to demonstrate a variable selection method (i.e., screening)
+in the context of Gaussian process metamodeling:
+
+- {ref}`Linear <test-functions:linkletter-linear>` function features
+  a simple function with four active input variables (out of 10).
+  (_this function_)
+```
+
+
+## Test function instance
+
+To create a default instance of the test function:
+
+```{code-cell} ipython3
+my_testfun = uqtf.LinkletterLinear()
+```
+
+Check if it has been correctly instantiated:
+
+```{code-cell} ipython3
+print(my_testfun)
+```
+
+## Description
+
+The test function is defined as[^location]:
+
+$$
+\mathcal{M}(\boldsymbol{x}) = 0.2 (x_1 + x_2 + x_3 + x_4),
+$$
+
+where $\boldsymbol{x} = \left( x_1, \ldots x_{10} \right)$
+is the ten-dimensional vector of input variables further defined below.
+Notice that only four out of ten input variables are active.
+
+```{note}
+In the original paper, the function was added with an independent identically
+distributed (i.i.d) noise from $\mathcal{N}(0, \sigma)$
+with a standard deviation $\sigma = 0.05$.
+```
+
+## Probabilistic input
+
+The probabilistic input model for the test function is shown below.
+
+```{code-cell} ipython3
+:tags: [hide-input]
+
+print(my_testfun.prob_input)
+```
+
+## Reference results
+
+This section provides several reference results of typical UQ analyses involving
+the test function.
+
+### Sample histogram
+
+Shown below is the histogram of the output based on $100'000$ random points:
+
+```{code-cell} ipython3
+:tags: [hide-input]
+
+my_testfun.prob_input.reset_rng(42)
+xx_test = my_testfun.prob_input.get_sample(100000)
+yy_test = my_testfun(xx_test)
+
+plt.hist(yy_test, bins="auto", color="#8da0cb");
+plt.grid();
+plt.ylabel("Counts [-]");
+plt.xlabel("$\mathcal{M}(X)$");
+plt.gcf().tight_layout(pad=3.0)
+plt.gcf().set_dpi(150);
+```
+
+## References
+
+```{bibliography}
+:style: unsrtalpha
+:filter: docname in docnames
+```
+
+[^location]: see Eq. (5), Example 1, in {cite}`Linkletter2006`.
diff --git a/src/uqtestfuns/test_functions/__init__.py b/src/uqtestfuns/test_functions/__init__.py
index b17f8c4..f85cbc5 100644
--- a/src/uqtestfuns/test_functions/__init__.py
+++ b/src/uqtestfuns/test_functions/__init__.py
@@ -35,6 +35,7 @@
 from .hyper_sphere import HyperSphere
 from .ishigami import Ishigami
 from .lim import LimPoly, LimNonPoly
+from .linkletter import LinkletterLinear
 from .oakley2002 import Oakley1D
 from .otl_circuit import OTLCircuit
 from .mclain import McLainS1, McLainS2, McLainS3, McLainS4, McLainS5
@@ -104,6 +105,7 @@
     "Ishigami",
     "LimNonPoly",
     "LimPoly",
+    "LinkletterLinear",
     "Oakley1D",
     "OTLCircuit",
     "McLainS1",
diff --git a/src/uqtestfuns/test_functions/linkletter.py b/src/uqtestfuns/test_functions/linkletter.py
new file mode 100644
index 0000000..25e3724
--- /dev/null
+++ b/src/uqtestfuns/test_functions/linkletter.py
@@ -0,0 +1,76 @@
+"""
+Module with an implementation of the functions from Linkletter et al. (2006)
+
+The paper by Linkletter et al. (2006) [1] contains four analytical test
+functions used for sensitivity analysis in the context of variable selection
+in Gaussian process metamodeling.
+All functions are defined in ten dimensions but some of them are inactive.
+
+Available functions are:
+
+- Linear function with four active input variables (out of 10).
+
+References
+----------
+
+1. C. Linkletter, D. Bingham, N. Hengartner, D. Higdon, and K. Q. Ye,
+   “Variable Selection for Gaussian Process Models in Computer Experiments,”
+   Technometrics, vol. 48, no. 4, pp. 478–490, 2006.
+   DOI: 10.1198/004017006000000228.
+"""
+
+import numpy as np
+
+from uqtestfuns.core.custom_typing import ProbInputSpecs
+from uqtestfuns.core.uqtestfun_abc import UQTestFunFixDimABC
+
+__all__ = ["LinkletterLinear"]
+
+
+def evaluate_linear(xx: np.ndarray) -> np.ndarray:
+    """Evaluate the linear  function from Linkletter et al. (2006).
+
+    Parameters
+    ----------
+    xx : np.ndarray
+        M-Dimensional input values given by an N-by-10 array where
+        N is the number of input values.
+
+    Returns
+    -------
+    np.ndarray
+        The output of the test function evaluated on the input values.
+        The output is a 1-dimensional array of length N.
+    """
+    yy = 0.2 * np.sum(xx[:, :4], axis=1)
+
+    return yy
+
+
+class LinkletterLinear(UQTestFunFixDimABC):
+    """A concrete implementation of the linear function."""
+
+    _tags = ["metamodeling", "sensitivity"]
+    _description = "Linear function from Linkletter et al. (2006)"
+    _available_inputs: ProbInputSpecs = {
+        "Linkletter2006": {
+            "function_id": "LinkletterLinear",
+            "description": (
+                "Input specification for the linear test function Eq. (5)"
+                "from Linkletter et al. (2006)"
+            ),
+            "marginals": [
+                {
+                    "name": f"x_{i + 1}",
+                    "distribution": "uniform",
+                    "parameters": [0, 1],
+                    "description": None,
+                }
+                for i in range(10)
+            ],
+            "copulas": None,
+        },
+    }
+    _available_parameters = None
+
+    evaluate = staticmethod(evaluate_linear)  # type: ignore