Predictive Analytics Using Statistics and Big Data: Concepts and Modeling

On Mean Estimation Using a Generalized Class of Chain Type Estimator under Successive Sampling

Author(s): Shashi Bhushan, Nishi Rastogi and Shailja Pandey

Pp: 31-46 (16)

DOI: 10.2174/9789811490491120010006

* (Excluding Mailing and Handling)

Abstract

The present paper comprises a significantly generalized class of chain type estimators to estimate the population means on the current occasion under the framework of successive sampling based on auxiliary information on both the occasion. The proposed generalized class constitutes two renowned chain type classes proposed by Singh and Vishwakarma [1, 2]. As its particular case, an improvement over their notion, with some eased regularity conditions, is proposed by us, which consists of chain type regression estimators additionally to chain type ratio estimators. The construction of the proposed class is fruitful in the sense of constructing the chain type classes of estimators in the realm of successive sampling. In terms of efficiency, we provide a comparative study of the proposed class oversample mean estimator, Cochran's estimator [3], Sukhatme et al. estimator [4] and Singh’s estimator [5]. A numerical illustration is demonstrated in support of the proposed class.


Keywords: Auxiliary information, Generalized class of chain type estimator, Optimum replacement policy, Successive sampling.

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      • 14. app/Models/UserAccess/UserAccess.php:784
      • 15. middleware::check_user_access:114
      • 16. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
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      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ChapterController.php:1478
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      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      660μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 2930 and `b`.`banner_from_date` <= 1740515967 and `b`.`banner_to_date` >= 1740515967 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.07msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 2930
      • 3: 1740515967
      • 4: 1740515967
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='9e7cb15141df03bff284347c2c6d66e8'
      330μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    4Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        xOXwtRTLfOEs6dvZ0IBr6N76jXJ2pN1gFwJ1u06D
        uc_cart_id
        9e7cb15141df03bff284347c2c6d66e8
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/14414" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/14414
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6IllnOThSMDJPTk55bksxdGhkZ1ozRWc9PSIsInZhbHVlIjoiU1orNHVTUVdtTVdJeE1hY1BERUY1ckpjZUJsU3F3LytMYkxqcjhxV01pcz0iLCJtYWMiOiJmYjZlNTcxOGViODcwOWRiOWNkNzk3YWMwN2Q5ODlkMzhkYzNhZDNiYzNiNWJlNmNhOWUyZjU4N2RhMzE1MTEwIiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6IllnOThSMDJPTk55bksxdGhkZ1ozRWc9PSIsInZhbHVlIjoiU1orNHVTUVdtTVdJeE1hY1BERUY1ckpjZUJsU3F3LytMYkxqcjhxV01pcz0iLCJtYWMiOiJmYjZlNTcxOGViODcw" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 25 Feb 2025 20:39:27 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjVTN2gyNnBhb0puUndOa1FIVG9FSUE9PSIsInZhbHVlIjoicENWSGVWMks2WUluSDQyWlZpWlVZaDdtTnBSaDN2NzVoRFBHMkg3SzExUk5Vb0FoUWFNWkZsdHpIalVTN1VNdDB5OGlqajFqRVlqNzRQOXVsUWsyUlJwcWhQbDJKVzA1bk9aM1ZhVGMxdlpNMElybEpBSkNFK3Q3blpKT2crYkciLCJtYWMiOiIxNjhhZmQwNDEzMzgxN2ExYzQ3NGQ3MGQxOTlkM2VjODE5MDFkMWYwZWE0NThhZDExMDIxNmI4NTk2ZjIyZjM0IiwidGFnIjoiIn0%3D; expires=Fri, 28 Feb 2025 08:39:27 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6IjVTN2gyNnBhb0puUndOa1FIVG9FSUE9PSIsInZhbHVlIjoicENWSGVWMks2WUluSDQyWlZpWlVZaDdtTnBSaDN2NzVoRFBHMkg3SzExUk5Vb0FoUWFNWkZsdHpIalVTN1VNdDB5OGlqa" 1 => "alphaeurekaselectnet_session=eyJpdiI6Ik01Y0xONHZVL3E4RFdUdXRFcCtuV3c9PSIsInZhbHVlIjoibHFiZWNmc1lNeWh1M1FCc0ZqK0JOM0ZPTzZLTElpaWxtZDBxcEkrcHdLZTZZQ2liRUJjVm9RODBzeDZVelhseFl4N3FLMnFQMEdTcnR2bUZWbnhiT3N2aUJTMnNidm9GZW45SW56WGNMTGFpQ3VLeFFpcU5FMDJJVXhpcW1hekEiLCJtYWMiOiJhZTA2MWM0ZGE3ZWZiNzYyZTkwN2YwMGI0MTM0M2Q1OGYyMmJkNDZmZjZkNjUwZjJjZTEzOTFlYmJmOTkwMWYzIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6Ik01Y0xONHZVL3E4RFdUdXRFcCtuV3c9PSIsInZhbHVlIjoibHFiZWNmc1lNeWh1M1FCc0ZqK0JOM0ZPTzZLTElpaWxtZDBxcEkrcHdLZTZZQ2liRUJjVm9RODB" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjVTN2gyNnBhb0puUndOa1FIVG9FSUE9PSIsInZhbHVlIjoicENWSGVWMks2WUluSDQyWlZpWlVZaDdtTnBSaDN2NzVoRFBHMkg3SzExUk5Vb0FoUWFNWkZsdHpIalVTN1VNdDB5OGlqajFqRVlqNzRQOXVsUWsyUlJwcWhQbDJKVzA1bk9aM1ZhVGMxdlpNMElybEpBSkNFK3Q3blpKT2crYkciLCJtYWMiOiIxNjhhZmQwNDEzMzgxN2ExYzQ3NGQ3MGQxOTlkM2VjODE5MDFkMWYwZWE0NThhZDExMDIxNmI4NTk2ZjIyZjM0IiwidGFnIjoiIn0%3D; expires=Fri, 28-Feb-2025 08:39:27 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6IjVTN2gyNnBhb0puUndOa1FIVG9FSUE9PSIsInZhbHVlIjoicENWSGVWMks2WUluSDQyWlZpWlVZaDdtTnBSaDN2NzVoRFBHMkg3SzExUk5Vb0FoUWFNWkZsdHpIalVTN1VNdDB5OGlqa" 1 => "alphaeurekaselectnet_session=eyJpdiI6Ik01Y0xONHZVL3E4RFdUdXRFcCtuV3c9PSIsInZhbHVlIjoibHFiZWNmc1lNeWh1M1FCc0ZqK0JOM0ZPTzZLTElpaWxtZDBxcEkrcHdLZTZZQ2liRUJjVm9RODBzeDZVelhseFl4N3FLMnFQMEdTcnR2bUZWbnhiT3N2aUJTMnNidm9GZW45SW56WGNMTGFpQ3VLeFFpcU5FMDJJVXhpcW1hekEiLCJtYWMiOiJhZTA2MWM0ZGE3ZWZiNzYyZTkwN2YwMGI0MTM0M2Q1OGYyMmJkNDZmZjZkNjUwZjJjZTEzOTFlYmJmOTkwMWYzIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6Ik01Y0xONHZVL3E4RFdUdXRFcCtuV3c9PSIsInZhbHVlIjoibHFiZWNmc1lNeWh1M1FCc0ZqK0JOM0ZPTzZLTElpaWxtZDBxcEkrcHdLZTZZQ2liRUJjVm9RODB" ] ]
        session_attributes
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        array:5 [ "_token" => "xOXwtRTLfOEs6dvZ0IBr6N76jXJ2pN1gFwJ1u06D" "uc_cart_id" => "9e7cb15141df03bff284347c2c6d66e8" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/14414" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 20:39:27GET/chapter/14414112186