Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0001 360664 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0869 1210752 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0869 1210752 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.3664 4109376 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.3678 4136880 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.3687 4154592 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.3687 4171600 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.3696 4179336 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.3696 4179336 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.4108 4419040 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.4125 4436440 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.4130 4457368 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.6711 9555312 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.6713 9555760 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.6713 9555760 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.6715 9564008 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.6718 9565704 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.6725 9598984 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.6725 9599384 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.6726 9599464 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274

Biased Estimators

An estimatorfora statistical parameterissaid to be biased if

Bias is often impossible toavoid in practice and must be taken into account when statisicalcalculations are performed.

Example: To estimate thenumber,ofnesting birds, scientists catch 100, tag them and release them. Thefraction of birds with tags isLater,they catch another 100 and count the number with tags. Supposeofthese birds have tags, so the probability of a randomly picked birdfrom this sample having a tag is

Equating these two fractionsgivessothatandIn fact isa random variable since it will vary between samples, soisan estimate forWe write

The expected value forisbut it is possible thatsothat usingthis estimator. In fact,isobviously at mostsothat the estimatorisbiased.

More subtle examples of biasare give by considering the mode and median as estimators for themean.

Suppose we have 100 people.80 of the people are labelled with a 1 and 20 are labelled with a 0(probably signifying, like me, that their net wealth is zero).

The mode is 1 but the meanis 0.8 times 1 + 0.2 times 0 = 0.8

The bias of an estimatorfora parameteris

The bias of the mode as anestimator for the mean is 1-0.8=0.2

The 100 people are lined upin numerical order. First in line are those twenty people labelledwith a zero, and then the 80 people labelled with a 1.

The median is obviously 1,but the mean is 0.8, as before.

The bias of the median as anestimate for the mean is 1-0.8=0.2

Add comment

Security code
Refresh