{"id":29185,"date":"2023-09-13T15:52:32","date_gmt":"2023-09-13T08:52:32","guid":{"rendered":"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi"},"modified":"2023-09-13T15:52:32","modified_gmt":"2023-09-13T08:52:32","slug":"tham-so-la-gi","status":"publish","type":"post","link":"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi","title":{"rendered":"T\u00ecm hi\u1ec3u v\u1ec1 tham s\u1ed1 v\u00e0 vai tr\u00f2 trong ph\u01b0\u01a1ng tr\u00ecnh"},"content":{"rendered":"<p>&#8220;Tham s\u1ed1 l\u00e0 m\u1ed9t thu\u1eadt ng\u1eef quan tr\u1ecdng trong l\u0129nh v\u1ef1c khoa h\u1ecdc v\u00e0 c\u00f4ng ngh\u1ec7. \u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 bi\u1ec3u th\u1ecb c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o c\u1ee7a m\u1ed9t h\u00e0m, tham s\u1ed1 gi\u00fap \u0111i\u1ec1u ch\u1ec9nh ho\u1ea1t \u0111\u1ed9ng v\u00e0 t\u00f9y ch\u1ec9nh c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh. H\u00e3y c\u00f9ng kh\u00e1m ph\u00e1 kh\u00e1i ni\u1ec7m tham s\u1ed1 v\u00e0 vai tr\u00f2 quan tr\u1ecdng c\u1ee7a n\u00f3 trong c\u00e1c l\u0129nh v\u1ef1c kh\u00e1c nhau!&#8221;<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_40 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-6ad10c0c64f3a\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-6ad10c0c64f3a\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#1_Khai_niem_ve_tham_so_parameter_trong_phuong_trinh\" title=\"1. Kh\u00e1i ni\u1ec7m v\u1ec1 tham s\u1ed1 (parameter) trong ph\u01b0\u01a1ng tr\u00ecnh\">1. Kh\u00e1i ni\u1ec7m v\u1ec1 tham s\u1ed1 (parameter) trong ph\u01b0\u01a1ng tr\u00ecnh<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Quyen_luc_cua_cac_tham_so\" title=\"Quy\u1ec1n l\u1ef1c c\u1ee7a c\u00e1c tham s\u1ed1\">Quy\u1ec1n l\u1ef1c c\u1ee7a c\u00e1c tham s\u1ed1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Vi_du_ve_tham_so_trong_phuong_trinh_tieu_dung\" title=\"V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng\">V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#2_Vi_du_ve_tham_so_trong_phuong_trinh_tieu_dung\" title=\"2. V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng\">2. V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Tham_so_trong_phuong_trinh_tieu_dung\" title=\"Tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng\">Tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Vi_du_ve_tham_so_trong_phuong_trinh_tieu_dung-2\" title=\"V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng\">V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#3_Su_khac_nhau_giua_tham_so_va_doi_so_trong_toan_hoc\" title=\"3. S\u1ef1 kh\u00e1c nhau gi\u1eefa tham s\u1ed1 v\u00e0 \u0111\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc\">3. S\u1ef1 kh\u00e1c nhau gi\u1eefa tham s\u1ed1 v\u00e0 \u0111\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Su_khac_nhau_giua_tham_so_va_doi_so_trong_toan_hoc\" title=\"S\u1ef1 kh\u00e1c nhau gi\u1eefa tham s\u1ed1 v\u00e0 \u0111\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc\">S\u1ef1 kh\u00e1c nhau gi\u1eefa tham s\u1ed1 v\u00e0 \u0111\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Tham_so_trong_toan_hoc\" title=\"Tham s\u1ed1 trong to\u00e1n h\u1ecdc\">Tham s\u1ed1 trong to\u00e1n h\u1ecdc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Doi_so_trong_toan_hoc\" title=\"\u0110\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc\">\u0110\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#4_Tham_so_va_cac_phan_bo_xac_suat_trong_ly_thuyet_xac_suat\" title=\"4. Tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t\">4. Tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Tham_so_va_cac_phan_bo_xac_suat_trong_ly_thuyet_xac_suat\" title=\"Tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t\">Tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Vi_du_ve_tham_so_va_cac_phan_bo_xac_suat\" title=\"V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t\">V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#5_Uoc_luong_cac_tham_so_dua_tren_du_lieu_quan_sat_duoc\" title=\"5. \u01af\u1edbc l\u01b0\u1ee3ng c\u00e1c tham s\u1ed1 d\u1ef1a tr\u00ean d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c\">5. \u01af\u1edbc l\u01b0\u1ee3ng c\u00e1c tham s\u1ed1 d\u1ef1a tr\u00ean d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#51_Phuong_phap_uoc_luong_hop_ly_toi_da_Maximum_Likelihood_Estimation_-_MLE\" title=\"5.1 Ph\u01b0\u01a1ng ph\u00e1p \u01b0\u1edbc l\u01b0\u1ee3ng h\u1ee3p l\u00fd t\u1ed1i \u0111a (Maximum Likelihood Estimation &#8211; MLE)\">5.1 Ph\u01b0\u01a1ng ph\u00e1p \u01b0\u1edbc l\u01b0\u1ee3ng h\u1ee3p l\u00fd t\u1ed1i \u0111a (Maximum Likelihood Estimation &#8211; MLE)<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Uu_diem\" title=\"\u01afu \u0111i\u1ec3m:\">\u01afu \u0111i\u1ec3m:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Nhuoc_diem\" title=\"Nh\u01b0\u1ee3c \u0111i\u1ec3m:\">Nh\u01b0\u1ee3c \u0111i\u1ec3m:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#6_Thong_ke_phi_tham_so_va_thong_ke_co_tham_so\" title=\"6. Th\u1ed1ng k\u00ea phi tham s\u1ed1 v\u00e0 th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1\">6. Th\u1ed1ng k\u00ea phi tham s\u1ed1 v\u00e0 th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#61_Thong_ke_phi_tham_so\" title=\"6.1 Th\u1ed1ng k\u00ea phi tham s\u1ed1\">6.1 Th\u1ed1ng k\u00ea phi tham s\u1ed1<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Phuong_phap_thong_ke_phi_tham_so\" title=\"Ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea phi tham s\u1ed1:\">Ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea phi tham s\u1ed1:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#62_Thong_ke_co_tham_so\" title=\"6.2 Th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1\">6.2 Th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tham-so-la-gi\/#Phuong_phap_thong_ke_co_tham_so\" title=\"Ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1:\">Ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1:<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"1_Khai_niem_ve_tham_so_parameter_trong_phuong_trinh\"><\/span>1. Kh\u00e1i ni\u1ec7m v\u1ec1 tham s\u1ed1 (parameter) trong ph\u01b0\u01a1ng tr\u00ecnh<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"1. Kh\u00e1i ni\u1ec7m v\u1ec1 tham s\u1ed1 (parameter) trong ph\u01b0\u01a1ng tr\u00ecnh\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/tim_hieu_ve_tham_so_va_vai_tro_trong_phuong_trinh.jpeg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"1. Kh\u00e1i ni\u1ec7m v\u1ec1 tham s\u1ed1 (parameter) trong ph\u01b0\u01a1ng tr\u00ecnh\"\/><\/p>\n<p>Tham s\u1ed1 l\u00e0 m\u1ed9t gi\u00e1 tr\u1ecb c\u1ed1 \u0111\u1ecbnh trong m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 bi\u1ec3u di\u1ec5n c\u00e1c y\u1ebfu t\u1ed1 kh\u00f4ng thay \u0111\u1ed5i trong ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng. Tham s\u1ed1 c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1, m\u1ed9t bi\u1ebfn ho\u1eb7c m\u1ed9t vector.<\/p>\n<p>V\u00ed d\u1ee5, trong ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng y = mx + b, tham s\u1ed1 m l\u00e0 \u0111\u1ed9 d\u1ed1c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 b l\u00e0 \u0111i\u1ec3m giao v\u1edbi tr\u1ee5c y. Trong v\u00ed d\u1ee5 n\u00e0y, m v\u00e0 b l\u00e0 c\u00e1c tham s\u1ed1 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Quyen_luc_cua_cac_tham_so\"><\/span>Quy\u1ec1n l\u1ef1c c\u1ee7a c\u00e1c tham s\u1ed1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>C\u00e1c tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 quy\u1ec1n l\u1ef1c \u0111\u1ec3 ki\u1ec3m so\u00e1t v\u00e0 \u0111i\u1ec1u ch\u1ec9nh k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng. Khi ch\u00fang ta thay \u0111\u1ed5i gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c tham s\u1ed1, ch\u00fang ta c\u00f3 kh\u1ea3 n\u0103ng t\u00e1c \u0111\u1ed9ng v\u00e0o k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh. \u0110i\u1ec1u n\u00e0y cho ph\u00e9p ch\u00fang ta \u0111i\u1ec1u ch\u1ec9nh v\u00e0 t\u00f9y ch\u1ec9nh c\u00e1c m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc \u0111\u1ec3 ph\u00f9 h\u1ee3p v\u1edbi d\u1eef li\u1ec7u ho\u1eb7c y\u00eau c\u1ea7u c\u1ee5 th\u1ec3.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Vi_du_ve_tham_so_trong_phuong_trinh_tieu_dung\"><\/span>V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong l\u0129nh v\u1ef1c kinh t\u1ebf, m\u1ed9t v\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 h\u1ec7 s\u1ed1 \u0111\u00e0n h\u1ed3i thu nh\u1eadp. \u0110\u00e2y l\u00e0 m\u1ed9t tham s\u1ed1 trong m\u00f4 h\u00ecnh ti\u00eau d\u00f9ng, bi\u1ec3u di\u1ec5n s\u1ef1 thay \u0111\u1ed5i c\u1ee7a ti\u00eau th\u1ee5 h\u00e0ng h\u00f3a v\u00e0 d\u1ecbch v\u1ee5 khi thu nh\u1eadp t\u0103ng ho\u1eb7c gi\u1ea3m. H\u1ec7 s\u1ed1 n\u00e0y cho bi\u1ebft t\u1ef7 l\u1ec7 t\u0103ng (ho\u1eb7c gi\u1ea3m) c\u1ee7a ti\u00eau th\u1ee5 h\u00e0ng h\u00f3a v\u00e0 d\u1ecbch v\u1ee5 so v\u1edbi s\u1ef1 thay \u0111\u1ed5i c\u1ee7a thu nh\u1eadp.<\/p>\n<p>V\u00ed d\u1ee5 kh\u00e1c l\u00e0 h\u1ec7 s\u1ed1 gi\u00e1 c\u1ea3. \u0110\u00e2y l\u00e0 m\u1ed9t tham s\u1ed1 trong m\u00f4 h\u00ecnh ti\u00eau d\u00f9ng, bi\u1ec3u di\u1ec5n s\u1ef1 \u1ea3nh h\u01b0\u1edfng c\u1ee7a gi\u00e1 c\u1ea3 l\u00ean vi\u1ec7c ti\u00eau th\u1ee5 h\u00e0ng h\u00f3a v\u00e0 d\u1ecbch v\u1ee5. H\u1ec7 s\u1ed1 n\u00e0y cho bi\u1ebft t\u1ef7 l\u1ec7 t\u0103ng (ho\u1eb7c gi\u1ea3m) c\u1ee7a ti\u00eau th\u1ee5 h\u00e0ng h\u00f3a v\u00e0 d\u1ecbch v\u1ee5 so v\u1edbi s\u1ef1 thay \u0111\u1ed5i c\u1ee7a gi\u00e1 c\u1ea3.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"2_Vi_du_ve_tham_so_trong_phuong_trinh_tieu_dung\"><\/span>2. V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Tham_so_trong_phuong_trinh_tieu_dung\"><\/span>Tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong l\u0129nh v\u1ef1c kinh t\u1ebf, ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 quan tr\u1ecdng \u0111\u1ec3 nghi\u00ean c\u1ee9u h\u00e0nh vi ti\u00eau d\u00f9ng c\u1ee7a ng\u01b0\u1eddi d\u00e2n. Trong ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y, c\u00e1c tham s\u1ed1 \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c x\u00e1c \u0111\u1ecbnh m\u1ee9c \u0111\u1ed9 \u1ea3nh h\u01b0\u1edfng c\u1ee7a c\u00e1c y\u1ebfu t\u1ed1 kh\u00e1c nhau \u0111\u1ebfn h\u00e0nh vi ti\u00eau d\u00f9ng. V\u00ed d\u1ee5, gi\u1ea3 s\u1eed ch\u00fang ta c\u00f3 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng \u0111\u01a1n gi\u1ea3n: C = a + bY, trong \u0111\u00f3 C l\u00e0 chi ti\u00eau ti\u00eau th\u1ee5, Y l\u00e0 thu nh\u1eadp v\u00e0 a, b l\u00e0 c\u00e1c tham s\u1ed1.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du_ve_tham_so_trong_phuong_trinh_tieu_dung-2\"><\/span>V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Gi\u1ea3 s\u1eed r\u1eb1ng ch\u00fang ta mu\u1ed1n nghi\u00ean c\u1ee9u m\u1ed1i quan h\u1ec7 gi\u1eefa thu nh\u1eadp v\u00e0 chi ti\u00eau c\u1ee7a ng\u01b0\u1eddi d\u00e2n. Ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng tr\u00ecnh C = a + bY \u0111\u1ec3 m\u00f4 h\u00ecnh ho\u00e1 m\u1ed1i quan h\u1ec7 n\u00e0y. Trong v\u00ed d\u1ee5 n\u00e0y, a v\u00e0 b \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 c\u00e1c tham s\u1ed1 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<p>V\u00ed d\u1ee5: N\u1ebfu ch\u00fang ta t\u00ecm ra r\u1eb1ng a = 100 v\u00e0 b = 0.8, \u0111i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 m\u1ed7i \u0111\u01a1n v\u1ecb t\u0103ng c\u1ee7a thu nh\u1eadp s\u1ebd d\u1eabn \u0111\u1ebfn vi\u1ec7c t\u0103ng chi ti\u00eau kho\u1ea3ng 0.8 \u0111\u01a1n v\u1ecb. \u0110i\u1ec1u n\u00e0y cho th\u1ea5y m\u1ee9c \u0111\u1ed9 \u1ea3nh h\u01b0\u1edfng c\u1ee7a thu nh\u1eadp \u0111\u1ebfn chi ti\u00eau v\u00e0 l\u00e0 m\u1ed9t v\u00ed d\u1ee5 v\u1ec1 c\u00e1ch c\u00e1c tham s\u1ed1 trong ph\u01b0\u01a1ng tr\u00ecnh ti\u00eau d\u00f9ng c\u00f3 th\u1ec3 gi\u00fap ch\u00fang ta hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"3_Su_khac_nhau_giua_tham_so_va_doi_so_trong_toan_hoc\"><\/span>3. S\u1ef1 kh\u00e1c nhau gi\u1eefa tham s\u1ed1 v\u00e0 \u0111\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Su_khac_nhau_giua_tham_so_va_doi_so_trong_toan_hoc\"><\/span>S\u1ef1 kh\u00e1c nhau gi\u1eefa tham s\u1ed1 v\u00e0 \u0111\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong to\u00e1n h\u1ecdc, c\u1ea3 tham s\u1ed1 v\u00e0 \u0111\u1ed1i s\u1ed1 \u0111\u1ec1u l\u00e0 c\u00e1c th\u00e0nh ph\u1ea7n quan tr\u1ecdng trong c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 bi\u1ec3u th\u1ee9c. Tuy nhi\u00ean, ch\u00fang c\u00f3 s\u1ef1 kh\u00e1c nhau v\u1ec1 \u00fd ngh\u0129a v\u00e0 vai tr\u00f2.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tham_so_trong_toan_hoc\"><\/span>Tham s\u1ed1 trong to\u00e1n h\u1ecdc<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Tham s\u1ed1 l\u00e0 m\u1ed9t gi\u00e1 tr\u1ecb c\u1ed1 \u0111\u1ecbnh \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh t\u00ednh ch\u1ea5t ho\u1eb7c m\u00f4 h\u00ecnh c\u1ee7a m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh hay bi\u1ec3u th\u1ee9c. Th\u00f4ng qua vi\u1ec7c \u0111i\u1ec1u ch\u1ec9nh gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c tham s\u1ed1, ch\u00fang ta c\u00f3 th\u1ec3 ki\u1ec3m so\u00e1t ho\u1eb7c \u0111i\u1ec1u ch\u1ec9nh k\u1ebft qu\u1ea3 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c bi\u1ec3u th\u1ee9c \u0111\u00f3. V\u00ed d\u1ee5, trong ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng y = mx + c, m v\u00e0 c l\u00e0 c\u00e1c tham s\u1ed1. Thay \u0111\u1ed5i gi\u00e1 tr\u1ecb c\u1ee7a m v\u00e0 c s\u1ebd d\u1eabn \u0111\u1ebfn vi\u1ec7c thay \u0111\u1ed5i h\u00ecnh d\u1ea1ng v\u00e0 v\u1ecb tr\u00ed c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Doi_so_trong_toan_hoc\"><\/span>\u0110\u1ed1i s\u1ed1 trong to\u00e1n h\u1ecdc<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u0110\u1ed1i s\u1ed1 l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n k\u1ebft qu\u1ea3 c\u1ee7a m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh hay bi\u1ec3u th\u1ee9c. \u0110\u1ed1i s\u1ed1 c\u00f3 th\u1ec3 l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee5 th\u1ec3 ho\u1eb7c bi\u1ebfn. Ch\u00fang ta c\u00f3 th\u1ec3 thay \u0111\u1ed5i gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c \u0111\u1ed1i s\u1ed1 \u0111\u1ec3 t\u00ecm ra k\u1ebft qu\u1ea3 mong mu\u1ed1n t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh hay bi\u1ec3u th\u1ee9c. V\u00ed d\u1ee5, trong ph\u01b0\u01a1ng tr\u00ecnh y = f(x), x l\u00e0 m\u1ed9t \u0111\u1ed1i s\u1ed1 v\u00e0 ch\u00fang ta c\u00f3 th\u1ec3 g\u00e1n cho x b\u1ea5t k\u1ef3 gi\u00e1 tr\u1ecb n\u00e0o \u0111\u1ec3 t\u00ednh to\u00e1n gi\u00e1 tr\u1ecb t\u01b0\u01a1ng \u1ee9ng c\u1ee7a y.<\/p>\n<p>D\u1ec5 nh\u1ea7m l\u1eabn: Trong m\u1ed9t s\u1ed1 ng\u1eef c\u1ea3nh, thu\u1eadt ng\u1eef &#8220;tham s\u1ed1&#8221; v\u00e0 &#8220;\u0111\u1ed1i s\u1ed1&#8221; c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng ho\u00e1n \u0111\u1ed5i \u00fd ngh\u0129a. Tuy nhi\u00ean, trong to\u00e1n h\u1ecdc ch\u00ednh x\u00e1c, ch\u00fang c\u00f3 \u00fd ngh\u0129a kh\u00e1c nhau nh\u01b0 \u0111\u00e3 \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 \u1edf tr\u00ean.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"4_Tham_so_va_cac_phan_bo_xac_suat_trong_ly_thuyet_xac_suat\"><\/span>4. Tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"4. Tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t\" src=\"https:\/\/media.store123doc.com\/images\/document\/2014_11\/17\/larger_erd1416198123.jpg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"4. Tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t\"\/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tham_so_va_cac_phan_bo_xac_suat_trong_ly_thuyet_xac_suat\"><\/span>Tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t, c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 m\u00f4 h\u00ecnh ho\u00e1 s\u1ef1 bi\u1ebfn \u0111\u1ed5i c\u1ee7a c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean. C\u00e1c ph\u00e2n b\u1ed1 n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u0111\u1eb7c tr\u01b0ng b\u1edfi c\u00e1c tham s\u1ed1, nh\u1eefng gi\u00e1 tr\u1ecb quan tr\u1ecdng \u0111\u1ec3 m\u00f4 t\u1ea3 t\u00ednh ch\u1ea5t c\u1ee7a ph\u00e2n b\u1ed1.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du_ve_tham_so_va_cac_phan_bo_xac_suat\"><\/span>V\u00ed d\u1ee5 v\u1ec1 tham s\u1ed1 v\u00e0 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>V\u00ed d\u1ee5 v\u1ec1 m\u1ed9t ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t l\u00e0 ph\u00e2n b\u1ed1 chu\u1ea9n (normal distribution). Ph\u00e2n b\u1ed1 chu\u1ea9n \u0111\u01b0\u1ee3c \u0111\u1eb7c tr\u01b0ng b\u1edfi hai tham s\u1ed1 l\u00e0 gi\u00e1 tr\u1ecb k\u1ef3 v\u1ecdng (mean) v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n (standard deviation). Gi\u00e1 tr\u1ecb k\u1ef3 v\u1ecdng cho bi\u1ebft gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a ph\u00e2n b\u1ed1, trong khi \u0111\u1ed9 l\u1ec7ch chu\u1ea9n cho bi\u1ebft m\u1ee9c \u0111\u1ed9 bi\u1ebfn thi\u00ean c\u1ee7a d\u1eef li\u1ec7u.<\/p>\n<p>Th\u00f4ng qua vi\u1ec7c \u0111i\u1ec1u ch\u1ec9nh gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c tham s\u1ed1 n\u00e0y, ch\u00fang ta c\u00f3 th\u1ec3 t\u1ea1o ra nhi\u1ec1u lo\u1ea1i ph\u00e2n b\u1ed1 kh\u00e1c nhau. V\u00ed d\u1ee5, n\u1ebfu ta t\u0103ng gi\u00e1 tr\u1ecb k\u1ef3 v\u1ecdng, ta s\u1ebd d\u1ecbch chuy\u1ec3n ph\u00e2n b\u1ed1 chu\u1ea9n sang ph\u1ea3i, trong khi t\u0103ng \u0111\u1ed9 l\u1ec7ch chu\u1ea9n s\u1ebd l\u00e0m cho ph\u00e2n b\u1ed1 r\u1ed9ng h\u01a1n.<\/p>\n<p>C\u00e1c tham s\u1ed1 trong l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t gi\u00fap ch\u00fang ta hi\u1ec3u v\u00e0 m\u00f4 h\u00ecnh ho\u00e1 c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean, v\u00e0 cung c\u1ea5p nh\u1eefng c\u00f4ng c\u1ee5 quan tr\u1ecdng \u0111\u1ec3 nghi\u00ean c\u1ee9u v\u00e0 \u1ee9ng d\u1ee5ng trong c\u00e1c l\u0129nh v\u1ef1c kh\u00e1c nhau.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"5_Uoc_luong_cac_tham_so_dua_tren_du_lieu_quan_sat_duoc\"><\/span>5. \u01af\u1edbc l\u01b0\u1ee3ng c\u00e1c tham s\u1ed1 d\u1ef1a tr\u00ean d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"51_Phuong_phap_uoc_luong_hop_ly_toi_da_Maximum_Likelihood_Estimation_-_MLE\"><\/span>5.1 Ph\u01b0\u01a1ng ph\u00e1p \u01b0\u1edbc l\u01b0\u1ee3ng h\u1ee3p l\u00fd t\u1ed1i \u0111a (Maximum Likelihood Estimation &#8211; MLE)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Ph\u01b0\u01a1ng ph\u00e1p \u01b0\u1edbc l\u01b0\u1ee3ng h\u1ee3p l\u00fd t\u1ed1i \u0111a (MLE) l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u01b0\u1edbc l\u01b0\u1ee3ng c\u00e1c tham s\u1ed1 c\u1ee7a m\u1ed9t m\u00f4 h\u00ecnh d\u1ef1a tr\u00ean d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c. \u00dd t\u01b0\u1edfng ch\u00ednh c\u1ee7a MLE l\u00e0 t\u00ecm ra gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c tham s\u1ed1 sao cho x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n c\u1ee7a d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c, khi bi\u1ebft gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c tham s\u1ed1, l\u00e0 c\u1ef1c \u0111\u1ea1i.<\/p>\n<p>\u0110\u1ec3 \u00e1p d\u1ee5ng MLE, ta c\u1ea7n x\u00e1c \u0111\u1ecbnh h\u00e0m h\u1ee3p l\u00fd (likelihood function) v\u00e0 t\u00ecm gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m n\u00e0y. H\u00e0m h\u1ee3p l\u00fd l\u00e0 x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n c\u1ee7a d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c, khi bi\u1ebft gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c tham s\u1ed1. Vi\u1ec7c t\u00ecm gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n b\u1eb1ng c\u00e1ch t\u00ednh to\u00e1n \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m h\u1ee3p l\u00fd v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u00ecm ra \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Uu_diem\"><\/span>\u01afu \u0111i\u1ec3m:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Ph\u01b0\u01a1ng ph\u00e1p MLE c\u00f3 t\u00ednh to\u00e1n \u0111\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 hi\u1ec3u.<\/li>\n<li>N\u1ebfu c\u00e1c gi\u1ea3 \u0111\u1ecbnh c\u1ee7a m\u00f4 h\u00ecnh \u0111\u01b0\u1ee3c th\u1ecfa m\u00e3n, \u01b0\u1edbc l\u01b0\u1ee3ng c\u1ee7a MLE c\u00f3 t\u00ednh ch\u1ea5t t\u1ed1i \u01b0u v\u00e0 kh\u00f4ng b\u1ecb sai bi\u1ec7t (unbiased).<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Nhuoc_diem\"><\/span>Nh\u01b0\u1ee3c \u0111i\u1ec3m:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>MLE y\u00eau c\u1ea7u c\u00e1c gi\u1ea3 \u0111\u1ecbnh v\u1ec1 ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t c\u1ee7a d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c. N\u1ebfu gi\u1ea3 \u0111\u1ecbnh n\u00e0y kh\u00f4ng ch\u00ednh x\u00e1c, \u01b0\u1edbc l\u01b0\u1ee3ng c\u1ee7a MLE c\u00f3 th\u1ec3 kh\u00f4ng tin c\u1eady.<\/li>\n<li>MLE c\u00f3 th\u1ec3 b\u1ecb \u1ea3nh h\u01b0\u1edfng b\u1edfi c\u00e1c gi\u00e1 tr\u1ecb ngo\u1ea1i lai (outliers) trong d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"6_Thong_ke_phi_tham_so_va_thong_ke_co_tham_so\"><\/span>6. Th\u1ed1ng k\u00ea phi tham s\u1ed1 v\u00e0 th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"61_Thong_ke_phi_tham_so\"><\/span>6.1 Th\u1ed1ng k\u00ea phi tham s\u1ed1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Th\u1ed1ng k\u00ea phi tham s\u1ed1 l\u00e0 m\u1ed9t nh\u00e1nh c\u1ee7a khoa h\u1ecdc th\u1ed1ng k\u00ea nghi\u00ean c\u1ee9u v\u1ec1 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p v\u00e0 c\u00f4ng c\u1ee5 \u0111\u1ec3 ph\u00e2n t\u00edch d\u1eef li\u1ec7u khi kh\u00f4ng c\u00f3 gi\u1ea3 \u0111\u1ecbnh v\u1ec1 ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t c\u1ee7a d\u1eef li\u1ec7u. Trong th\u1ed1ng k\u00ea phi tham s\u1ed1, ta kh\u00f4ng c\u1ea7n bi\u1ebft hay \u01b0\u1edbc l\u01b0\u1ee3ng c\u00e1c th\u00f4ng s\u1ed1 (tham s\u1ed1) c\u1ee7a m\u1ed9t ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t nh\u01b0 trung b\u00ecnh, ph\u01b0\u01a1ng sai, hay h\u1ec7 s\u1ed1 t\u01b0\u01a1ng quan.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Phuong_phap_thong_ke_phi_tham_so\"><\/span>Ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea phi tham s\u1ed1:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Th\u1ed1ng k\u00ea m\u00f4 t\u1ea3: S\u1eed d\u1ee5ng c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng nh\u01b0 gi\u00e1 tr\u1ecb trung b\u00ecnh, ph\u01b0\u01a1ng sai, v\u00e0 t\u1ef7 l\u1ec7 \u0111\u1ec3 m\u00f4 t\u1ea3 d\u1eef li\u1ec7u.<\/li>\n<li>Ph\u00e2n t\u00edch h\u1ed3i quy phi tham s\u1ed1: S\u1eed d\u1ee5ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p nh\u01b0 h\u1ed3i quy kh\u00f4ng tham s\u1ed1 ho\u1eb7c h\u1ed3i quy lo\u1ea1i b\u1ecf bi\u1ebfn (stepwise regression) \u0111\u1ec3 x\u00e2y d\u1ef1ng m\u00f4 h\u00ecnh.<\/li>\n<li>Ph\u00e2n t\u00edch s\u1eafp x\u1ebfp (rank-based analysis): D\u1ef1a v\u00e0o v\u1ecb tr\u00ed c\u1ee7a c\u00e1c gi\u00e1 tr\u1ecb trong d\u1eef li\u1ec7u \u0111\u1ec3 r\u00fat ra k\u1ebft lu\u1eadn.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"62_Thong_ke_co_tham_so\"><\/span>6.2 Th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1 l\u00e0 m\u1ed9t nh\u00e1nh c\u1ee7a khoa h\u1ecdc th\u1ed1ng k\u00ea nghi\u00ean c\u1ee9u v\u1ec1 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p v\u00e0 c\u00f4ng c\u1ee5 \u0111\u1ec3 ph\u00e2n t\u00edch d\u1eef li\u1ec7u khi \u0111\u00e3 bi\u1ebft hay \u01b0\u1edbc l\u01b0\u1ee3ng c\u00e1c th\u00f4ng s\u1ed1 (tham s\u1ed1) c\u1ee7a m\u1ed9t ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t nh\u01b0 trung b\u00ecnh, ph\u01b0\u01a1ng sai, hay h\u1ec7 s\u1ed1 t\u01b0\u01a1ng quan. Trong th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1, ta s\u1eed d\u1ee5ng c\u00e1c gi\u1ea3 \u0111\u1ecbnh v\u1ec1 ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t c\u1ee7a d\u1eef li\u1ec7u \u0111\u1ec3 x\u00e2y d\u1ef1ng m\u00f4 h\u00ecnh v\u00e0 r\u00fat ra k\u1ebft lu\u1eadn.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Phuong_phap_thong_ke_co_tham_so\"><\/span>Ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea c\u00f3 tham s\u1ed1:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Ph\u00e2n ph\u1ed1i chu\u1ea9n: S\u1eed d\u1ee5ng gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng d\u1eef li\u1ec7u tu\u00e2n theo ph\u00e2n ph\u1ed1i chu\u1ea9n \u0111\u1ec3 x\u00e2y d\u1ef1ng m\u00f4 h\u00ecnh v\u00e0 ki\u1ec3m \u0111\u1ecbnh gi\u1ea3 thuy\u1ebft.<\/li>\n<li>Ph\u00e2n ph\u1ed1i t: S\u1eed d\u1ee5ng gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng d\u1eef li\u1ec7u tu\u00e2n theo ph\u00e2n ph\u1ed1i t \u0111\u1ec3 x\u00e2y d\u1ef1ng m\u00f4 h\u00ecnh v\u00e0 ki\u1ec3m \u0111\u1ecbnh gi\u1ea3 thuy\u1ebft khi s\u1ed1 l\u01b0\u1ee3ng quan s\u00e1t nh\u1ecf.<\/li>\n<li>H\u1ed3i quy tuy\u1ebfn t\u00ednh: S\u1eed d\u1ee5ng gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng m\u1ed1i quan h\u1ec7 gi\u1eefa bi\u1ebfn ph\u1ee5 thu\u1ed9c v\u00e0 c\u00e1c bi\u1ebfn \u0111\u1ed9c l\u1eadp l\u00e0 tuy\u1ebfn t\u00ednh \u0111\u1ec3 x\u00e2y d\u1ef1ng m\u00f4 h\u00ecnh v\u00e0 ki\u1ec3m \u0111\u1ecbnh gi\u1ea3 thuy\u1ebft.<\/li>\n<\/ul>\n<p>Tham s\u1ed1 l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong c\u00f4ng ngh\u1ec7 th\u00f4ng tin, to\u00e1n h\u1ecdc v\u00e0 c\u00e1c l\u0129nh v\u1ef1c kh\u00e1c \u0111\u1ec3 \u0111i\u1ec1u ch\u1ec9nh ho\u1ea1t \u0111\u1ed9ng c\u1ee7a m\u1ed9t h\u1ec7 th\u1ed1ng hay quy tr\u00ecnh. Ch\u00fang \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c t\u00f9y ch\u1ec9nh v\u00e0 ki\u1ec3m so\u00e1t k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng. Hi\u1ec3u r\u00f5 v\u1ec1 tham s\u1ed1 l\u00e0 c\u1ea7n thi\u1ebft \u0111\u1ec3 hi\u1ec7u ch\u1ec9nh v\u00e0 t\u1ed1i \u01b0u h\u00f3a c\u00e1c quy tr\u00ecnh v\u00e0 \u1ee9ng d\u1ee5ng.<br \/>\n<iframe loading=\"lazy\" title=\"Tham s\u1ed1 trong h\u00e0m\" width=\"790\" height=\"444\" src=\"https:\/\/www.youtube.com\/embed\/jE6UPl17Nvo?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;Tham s\u1ed1 l\u00e0 m\u1ed9t thu\u1eadt ng\u1eef quan tr\u1ecdng trong l\u0129nh v\u1ef1c khoa h\u1ecdc v\u00e0 c\u00f4ng ngh\u1ec7. \u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 bi\u1ec3u th\u1ecb c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o&#8230; <\/p>\n","protected":false},"author":1,"featured_media":29184,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-29185","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-khai-niem-1"],"_links":{"self":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/29185","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/comments?post=29185"}],"version-history":[{"count":0,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/29185\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media\/29184"}],"wp:attachment":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media?parent=29185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/categories?post=29185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/tags?post=29185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}